derivations (0.56.20180123.1)

  * Fixed a false PDF titlebar by frustrating Libpoppler's GooString
    destructor from btool/PDF/update_catalog.cc.  (This is a
    workaround.  It seems to address the problem but, should the
    problem continue to emerge sporadically, a better fix might be
    needed.  We shall see.)
  * Deleted spurious source files of the Quilt patch manager.
  * Changed nothing else.  Observed that this revision introduces no
    new version of the book, for, other than perhaps the legend in
    the PDF viewer's title bar, the book will appear the same to
    its readers.

 -- Thaddeus H. Black <thb@derivations.org>  Sat, 05 Jan 2019 00:00:00 +0000

derivations (0.56.20180123)

  * Ceased to state on the reverse of the title page that the book is
    a prepublished draft, for it no longer is.  Accordingly,
    incremented the revision number to 0.56.  (The book remains
    incomplete.  Maybe it always will, but it is now after 34 years
    complete enough to drop the prepublication notice.)
  * Added "Reliance" to pref.tex.  Revised "A curiosity."  Removed the
    prepublication notice from the preface's head.
  * In inttx.tex:
    + Changed a few = signs to \equiv.
    + Added the new section "Reversal of the independent variable."
    + Based the table of antiderivatives by prepending a zeroth-order
      antiderivative.
  * In fours.tex, generally though not greatly revised "Time, space and
    frequency."
  * Generally revised fouri.tex, especially in its
    subsections "Metaduality" and "Convolution and correlation."  Also
    in the chapter:
    + Corrected false Fourier transforms in "Convolution and
      correlation."
    + Corrected a false Laplace transform in the table "Laplace
      transform pairs."
  * In fouri.tex, noted that the interpretation of the case of the
    Fourier transform of a function whose argument is complex remained
    unclear to the writer.
  * Deleted the very incomplete specf.tex.
  * Generally revised and corrected prob.tex.
  * Updated and condensed stub.tex.  Changed its title (and might
    change it again).
  * Polished the final paragraph of conclu.tex.
  * Polished the introduction to hex.tex.
  * Resolved references in hist.tex.
  * Cleared most of the book's remaining comment-tagged action items.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Tue, 23 Jan 2018 00:00:00 +0000

derivations (0.55.20180117)

  * In pref.tex:
    + Polished "A curiosity" to frame it better in the reader's
      context.
    + Rewrote the disclaimer of shortcomings in "Acknowledgements."
  * In alggeo.tex, "The Pythagorean theorem," clarified Euclid's
    footnote.
  * In trig.tex, "Trigonometric functions of the hour angles," added
    the quarters of a right angle to the table.
  * Refined the prose of drvtv.tex, "Remarks on the Leibnitz notation."
  * Revised the prose of cexp.tex in several relatively minor ways,
    especially in "The actuality of complex quantities."
  * In noth.tex, "Averages," clarified the circumstances under which
    the masons' example might prefer the parallel to the serial
    average.
  * In integ.tex, revised several points of "The length of a parabola."
  * In taylor.tex, revised the prose of the last two paragraphs
    of "Extrema over a complex domain."
  * In inttx.tex, "Pythagorean radicals," fixed the S_4 calculation,
    whose result had been right but whose details as previously printed
    were nonsensical.
  * In mtxinv.tex:
    + In "The general solution," extended and substantially rewrote the
      footnote on mantissas.
    + Slightly improved the prose of "Complex vector inequalities" and
      its subsections.
  * In vector.tex, added a reference from "Multiplication" back
    to "Reorientation."
  * Removed from the start of conclu.tex the caution that the chapter
    had been an early draft.
  * In greek.tex, framed the presentation more explicitly as from
    an English-language perspective.
  * Cleared most of the book's remaining comment-tagged action items
    through the end of part II.  (The tag is d-i-a-g-n without the
    hyphens.)
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Wed, 17 Jan 2018 00:00:00 +0000

derivations (0.55.20170703)

  * In integ.tex, formally defined Heaviside's u(0) = 1.
  * In inttx.tex, specially displayed the n = 1 and n = 2 cases in the
    antiderivative table.  Improved the general case's notation.
  * In fours.tex:
    + Slightly improved the introduction's style (though that still
      probably needs some more work).
    + Added to "Parseval's principle" a forward reference
      to the next chapter's "Parseval's theorem."
    + Revised and extended "Time, space and frequency."
    + Edited the rest of the chapter in various small and medium ways,
      too many to list here.  Deleted unnecessary adjectives and adverbs
      throughout (adverbs are often necessary than adjectives in
      general, but the first half of this chapter seems to have had an
      unusual number of unnecessary adverbs for some reason).
    + Elevated and revised a footnote in "Derivation of the
      Fourier-coefficient formula," raising to make a new paragraph with
      which to end the subsection.  (The old footnote and new paragraph
      regard convergence.)
    + Renamed the section on pulses as "Several useful pulses."  Added
      to it the raised-cosine pulse and partly explained why the
      section's nonanalytic pulses are useful to discretize a signal.
  * Generally revised and extended the existing draft of fouri.tex.
    Recognized it now to be a complete chapter rather than merely an
    early draft.
  * Revised the draft-stub specf.tex a bit (but there still isn't
    much there).
  * In conclu.tex, added to "Foundations athwart intuition" a reference
    into prob.txt.
  * Edited the rest of the book in further, minor ways.
  * Observed that the author has now reviewed the whole manuscript.

 -- Thaddeus H. Black <thb@derivations.org>  Mon, 03 Jul 2017 00:00:00 +0000

derivations (0.55.20170620)

  * In mtxinv.tex:
    + Reorganized, renamed, rereasoned and rewrote the section on
      triangle inequalities.  In that section, treated the Schwarz
      inequality explicitly.
    + Split a paragraph of "Inverting the square matrix" in two.  In
      the same section, tentatively footnoted an outline of additional,
      professionalesque rigor.
    + Rewrote "The general solution."
    + Slightly clarified "The Gauss-Jordan kernel formula."
    + Corrected and retitled material regarding Gram-Schmidt and
      orthogonal complements.
  * In eigen.tex, "Diagonalization," promoted an explanatory footnote
    to a parenthesized explanation.  Numbered the explained equation.
  * In vector.tex:
    + Revised the chapter's introduction.
    + Exampled a somewhat nonobvious calculation in "The cross product."
  * In vcalc.tex:
    + In "The Laplacian and other second-order derivatives," extended
      the footnote on American versus British symbology for
      the Laplacian.
    + Added an alternate reading to one entry of
      the "Metric coefficients" table.
    + Reworded the next-to-last paragraph of "Nonrectangular notation."
  * Divided conclu.txt into sections.  Revised and extended
    the chapter.
  * Added a few decimal numerals and/or spelled-out names of numbers as
    alternatives to hexadecimal.
  * Edited the rest of the book in further, minor ways.
  * Observed that the author has now reviewed the manuscript through
    the end of the manuscript's part II.

 -- Thaddeus H. Black <thb@derivations.org>  Tue, 20 Jun 2017 00:00:00 +0000

derivations (0.55.20170612)

  * Throughout, in source expressions like "\appendix~\ref{APPENDIX}.",
    changed the "." to "\@."
  * In the matrix chapters, changed "correct order" of indices
    to "proper sequence" thereof.
  * Retitled the chapter drvtv.tex as "The derivative and
    its incidents."
  * In pref.tex, gave Alma Noe his own paragraph.
  * In intro.tex, extended "Rigor to forestall error."
  * In alggeo.tex:
    + Renamed "Sums of powers" as "sums of exponents."
    + Added to "Variations on the geometric series" a forward reference
      to taylor.tex, "The power-series expansion of 1/(1-z)^(n+1)."
  * In cexp.tex:
    + Rewrote the chapter's introduction.
    + Improved notation in "The real exponential."
    + Extended the explanation of the boundary between domains
      in "Euler's formula."
    + In "The hyperbolic functions," rewrote the prose on extension to
      complex phi.  Restored a missing asterisk for conjugation in a
      footnote.
    + In "Inverse complex trigonometrics," filled an omitted step of
      algebra.
    + Revised the first paragraph of "Derivatives of sine and cosine."
    + Deleted the sister's-handwriting analogy from "The actuality of
      complex quantities."
  * In noth.tex:
    + In "Rational and irrational numbers," restricted the ratios to
      have positive denominators.
    + In "The fundamental theorem of algebra," outlined a potential
      response to a hypothetical purist's objection; and explained why
      no alternate roots are possible.
    + To make the example of "Serial and parallel addition," et seq.,
      more realistic, halved the bricklayers' productivity.
    + Deleted the digression on business and the footnote
      on Congressional apportionment from "Averages."
  * In integ.tex:
    + Revised and substantially expanded "Areas and volumes."
    + Changed the shape of the cone's base in the figure "The volume of
      a cone".
    + Revised the final paragraph of "Checking an integration" to
      comport with the last two points.
    + Added some exercises.
  * In taylor.tex:
    + Slightly improved the wording of the chapter's introduction.
    + In "The power-series expansion of 1/(1-z)^(n+1)," improved
      notation, changed some indices and explained a few points better.
    + Supplied a missing sign in "Shifting a power series'
      expansion point" (and checked the corrected formula using a
      computer-calculated test case).
    + Revised and extended "Branch points."  Added two figures.
    + Revised and extended "Extrema over a complex domain."
    + Added a quasijustification of the stair-stepping approximation
      to "Integrating along the contour."
    + Added another example to "Calculation outside the fast convergence
      domain," this example in the narratives rather than the footnotes.
      In a footnote in the same subsection, corrected an instance of
      arctan(omega) to read arctan(zeta) as it ought.
  * In inttx.tex:
    + Added the new sections "Integration by the manipulation of a
      Pythagorean radical" and "Trial derivatives."
    + Split "An example" off as a separate subsection from "Repeated
      poles."  In those subsections, clarified the explanation of
      shadow poles.
    + Otherwise in "Integration by partial-fraction expansion,"
      clarified a few points and supplied a missing subscript.
    + Slightly modified the conditions of "Frullani's integral."
    + Corrected a significant error in the table "Antiderivatives of
      products of exponentials, powers and logarithms," and in its
      supporting derivation, now multiplying by k rather than dividing.
      Reformatted the table.
    + In "Integrating products of exponentials, powers and logarithms,"
      commented out a questionable L'Hospital-based explanation.
  * In cubic.tex, added an alternate explanation regarding an
    edge case.
  * In matrix.tex, "The truncation operator," corrected a misnotation of
    the general identity matrix, which runs from negative infinity
    rather than from 1.
  * In gjrank.tex:
    + In "The elementary similarity transformation," improved several
      instances of awkward and/or imprecise English.
    + In the table "Some elementary similarity transformations,"
      slightly extended the rule by which scaling similarity operations
      affect unit triangulars.
    + Explained more in "The Gauss-Jordan decomposition."
    + Revised the heretofore confusing subsection "Decomposing an
      extended operator."  Especially, clarified a paragraph regarding
      full-rank extended operators.
    + Slightly revised and clarified "A logical maneuver."
    + In "General matrix rank and its uniqueness," explictly observed
      that transposition/adjointing does not alter rank; and then
      referred to the fact in "Full column rank and...."  In the latter
      section, clarified that the last paragraph speaks specifically of
      square matrices.
  * Added an early draft of the new concluding Remarks, conclu.tex.
  * Edited the rest of the book in further, minor ways.
  * Observed that, after years of inactivity, the author has now
    reviewed the manuscript through the end of chapter 12,
    gjrank.tex, "Matrix rank and the Gauss-Jordan decomposition" (and
    has reviewed the four appendices, too).  These first 12 chapters
    form the applied mathematical foundation for the whole book.
    Significant improvements to the 12 chapters having been made, the
    chapters have now perhaps been put in as good an order as the author
    is likely to put them.  The chapters seem finally to make a mostly
    adequate foundation for the rest of the book.

 -- Thaddeus H. Black <thb@derivations.org>  Mon, 12 Jun 2017 00:00:00 +0000

derivations (0.55.20170530)

  * Again because of the interval between public releases, advanced the
    book's version number to 0.55.
  * Noted here that the overall theme of this revision is
    mathematics-philosophical.  A book like this, which respects but
    nevertheless deliberately eschews the professional mathematician's
    rigor, and which covers such a broad mathematical territory, is
    always in danger of incurring censure for sloppiness.  Much of the
    potential censure is perhaps more mathematics-cultural than
    actually helpful but it must nevertheless be taken seriously by the
    writer.  In this revision, the first four chapters, where much or
    most of the book's philosophy is, are overhauled -- especially in
    their more philosophical passages.
  * Slightly condensed the preface.  Admitted there that the book's
    shortcomings remain the author's own.
  * Converted to use AMSmath's macro to style the combinatorial
    notation.
  * Changed "Ch." and "Chs." to "chapter" and "chapters" throughout.
  * Shifted the positions of many adverbs to more standard spots in
    their sentences.
  * Because of TeX's miskerning of the italic "f", retypeset "d^kf"
    as "d^k\!f" throughout (where anything might take the place of
    the k but not of the f).
  * Moved the proof of the Pythagorean theorem up to lead off chapter 1,
    thus starting the book with something to grab the reader's attention
    before descending into the first chapter's philosophical slog.
  * In intro.tex:
    + In "Axiom and definition," bridged the first two paragraphs with
      an example.
    + Elevated "Mathematical extension" from a subsection to a section.
    + To "Mathematical Platonism," added a quip by Wittgenstein, a
      quote by Noe, and some new/revised text to link these into the
      narrative.  Also, appropriately to such a subsection, added a
      quote by Plato!
    + Split off the new "Methods, notations, propositions and premises"
      from the existing "Mathematical Platonism."
  * In alggeo.tex:
    + Improved several points of "Functions."
    + Deleted from "Power series and analytic functions (preview)" an
      inadvertently meaningless statement about sums of power series.
      Also deleted the accompanying footnote.
    + Combined all the triangle sections, reducing these sections to
      subsections.  Added a second proof of the Pythagorean theorem and
      a supporting proof of Euclid's.
  * In trig.tex:
    + In "Definitions," rewrote the paragraph about radians, splitting
      it into two paragraphs.  Added an arc length to and otherwise
      improved the figure.
    + In "Scalars, vectors, and vector notation," added a paragraph to
      explain how a nonphysical distance can still be a mathematical
      distance.
  * In drvtv.tex:
    + Extensively revised "Considerations of the Leibnitz notation."
      Also, split off the last part of that subsection to form the new
      subsection "Higher-order derivatives."
    + Added more rows to the display of Pascal's triangle.  Also, added
      a display in decimal notation.
    + In "Combinations and permutations," added a long footnote on
      mathematical philosophy.
    + To "Complex powers of numbers near unity," added a new paragraph
      to lend the reader more confidence in the subsection's chief
      assumption.
    + In "The Leibnitz notation," expanded the already long footnote on
      individual Leibnitz elements, adding quotes of Robinson and
      Derbyshire.  Made other changes, too.
    + Then, extracted the long footnote and some other material and used
      it to form the new subsection "Remarks on the Leibnitz notation."
    + In "The derivative of a function of a complex variable," deleted
      most of the footnote on the unbalanced definition.  Generally
      revised the subsection.
    + Added the new subsection, "An alternate definition of the
      derivative."
    + Improved notation in "The Newton-Raphson iteration."
  * In cexp.tex, slightly improved the introduction's wording.
  * Improved notation in mtxinv.tex, "The multivariate Newton-Raphson
    iteration."
  * Generally revised hex.tex.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Tue, 30 May 2017 00:00:00 +0000

derivations (0.54.20170508)

  * Integrated various old, half-remembered development branches to
    form this release.
  * Acknowledged that the changelog stanza you are reading is probably
    incomplete.
  * Found the new place at which TeXlive keeps LaTeX's book.cls.
  * Revised README and the man page, improving style and deleting
    obsolete text.

 -- Thaddeus H. Black <thb@derivations.org>  Mon, 08 May 2017 00:00:00 +0000

derivations (0.54.20120813)

  * Because of the interval, 2009 to 2012, between the last two public
    releases, advanced the book's version number to 0.54.
  * Rewrote and extended the preface and introduction.
  * Reviewed and slightly revised all the appendices.
  * Shifted the positions of several adverbs in their sentences,
    scattered across the book, usually to precede their verbs.
  * Changed several, though not all, instances of "although"
    to "though."
  * Added to the narrative the birth and death dates of some
    people quoted.
  * Reformed several, incorrect instances of "thus" and "hence" used as
    conjunctions (for, according to Webster, these words are adverbs
    only, despite that "whence" can be a conjunction).
  * In tex/alggeo.tex (Classical algebra and geometry):
    + Rewrote the chapter's introduction.  Significantly, among others,
      added the adverb "fast" to the sentence, "The book starts fast
      with these."
    + Filled an oversight re the ordering of 1/a and 1/b
      in "Inequality."
    + Added the new subsection "Power-related inequality."
    + Generally revised "Constants and variables."
    + In "Functions," split the one-line definition of the inverse
      function into two lines.  Otherwise refined the section's text.
    + In "Rectangular complex multiplication," commented on sqrt(i).
    + Make several, smaller changes.
  * In tex/drvtv.tex (The derivative),
    + Reluctantly granted at least the real form of the unbalanced
      definition of the derivative an equation number.
    + Generally revised the subsection "The Leibnitz notation,"
      splitting it into two, separate subsections, naming the second of
      the two "Considerations of the Leibnitz notation."
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Mon, 13 Aug 2012 00:00:00 +0000

derivations (0.53.20120811)

  * In tex/specf.tex (Introduction to special functions),
    corrected the title of the section "The Gaussian pulse and
    its moments," and rewrote the section, as far as it had gone.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@debian.org>  Sat, 11 Aug 2012 00:00:00 +0000

derivations (0.53.20120414)

  * Generally reorganized the book's development toward, presentation
    of, and plan for the mathematics of special functions, an effort
    which involved fairly extensive changes in, among others,
    + tex/integ.tex (The integral),
    + tex/fours.tex (The Fourier series),
    + tex/fouri.tex (The Fourier transform),
    + tex/prob.tex (Probability), and
    + tex/stub.tex;
    plus various minor changes in other parts of the book.  Because of
    this reorganization, advanced the book's version number to 0.53.
  * Renamed the book's third part as "Transforms and special functions."
  * Rewrote the book's preface.
  * In tex/alggeo.tex (Classical algebra and geometry), renamed
    "Triangle area" as "The area of a triangle."
  * As a temporary workaround to aid the book's packaging on Debian (and
    maybe on other platforms), borrowed the following files from
    ftp://ftp.ctan.org/tex-archive/macros/latex/contrib/xkeyval/run/:
    keyval.tex; pst-xkey.sty; pst-xkey.tex; xkeyval.sty; xkeyval.tex;
    xkvltxp.sty; xkvtxhdr.tex; xkvview.sty.

 -- Thaddeus H. Black <thb@derivations.org>  Sat, 14 Apr 2012 00:00:00 +0000

derivations (0.52.20100629)

  * Did not release this version, which represented a internal stage for
    convenience of development.
  * Added to the preface a paragraph suggesting the book's standing
    with respect to a collegiate curriculum.
  * Extended the very end of tex/intro.tex (Introduction), adding two
    paragraphs to warn the reader fairly that the book can sometimes
    make dry reading.
  * In tex/alggeo.tex (Classical algebra and geometry), "Functions,"
    added a paragraph introducing function inverses and their notation.
  * In tex/cexp.tex (The complex exponential):
    + Shortened the beginning of the chapter's opening paragraph.
    + Divided "Complex trigonometrics" into subsections, adding the new
      subsection "Inverse complex trigonometrics."  Included the new
      subsection's results in the existing table "Complex exponential
      properties," reformatting the table to accommodate.
    + Propagated Edward Feser's geographical orthography,
      correcting "Occam" to "Ockham," and (to the extent to which the
      author grasps it) propagated Feser's contra-Ockham credit to
      Aristotle.
  * In tex/integ.tex (The integral), explained better in "Multiple
    integrals" why formal tests for convergence are sometimes not
    recommended in applications.
  * In tex/taylor.tex (The Taylor series):
    + In "Expanding functions in Taylor series," substantially rewrote
      the long footnote on the Taylor series' sufficiency.  (Ordinarily
      this changelog tends not mention changes to mere footnotes, but
      the peculiar footnote in question had been excluded from the main
      narrative for an unusual reason.  In any event, the change seemed
      worth mentioning here.)
    + Added a non-Taylor-based division to "Odd and even functions."
  * Ended tex/inttx.tex (Integration techniques) with a forward
    reference to the new tex/fouri.tex (The Fourier transform), drawing
    the reader's attention to the cylindrical technique introduced in
    the latter chapter to integrate the Gaussian pulse.
  * In tex/gjrank.tex (Rank and the Gauss-Jordan), extended and
    generally clarified the subsection "The impossibility of
    identity-matrix promotion."
  * In tex/eigen.tex (The eigenvalue), "The eigenvalue itself,"
    explained why a characteristic polynomial cannot lack full order.
  * In tex/fours.tex (The Fourier series):
    + Slightly improved the style of the chapter's introduction.
    + Substantially rewrote "Derivation of the Fourier-coefficient
      formula."
  * Continued, generally revised and completed the draft of the new
    chapter tex/fouri.tex (The Fourier transform).
  * Opened the new chapter tex/prob.tex (Probability).  Completed
    a very rough draft of the chapter.
  * Extended tex/purec.tex (A sketch of pure complex theory) to explain
    why a Taylor series remains everywhere valid out the the distance of
    the nearest nonanalytic point.  Also, removed from this appendix an
    unnecessary protest against unnecessity.
  * Consistently hyphenated well-adjectival and ill-adjectival
    constructs throughout the book, and consistently unhyphenated them
    where the constructs were well adjectival and ill adjectival, the
    stylistic difference (as the writer has belatedly come clearly to
    understand; doesn't the publisher have a competent editor on staff
    discreetly to teach the writer these things?!) being that the
    hyphenated compounds immediately modify their nouns without the
    mediation of a copular verb like "to be."
  * In tex/thb.sty, regulated the internal spacing in the four-dot
    ellipsis \mdots.
  * In tex/Makefile, caused the already implemented modification
    of LaTeX's 'book' class to columnize the lists of tables and
    figures like the contents.
  * In btool/fill-toc-ends and tex/main.tex:
    + Changed the "List of Tables" to the "List of tables," and likewise
      for the "List of Figures."
    + Caused the PDF table of contents (that is, the special table of
      contents which is not on any page of the book but which a PDF
      reader can display in a separate panel) to list the book's lists
      of tables and figures.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Tue, 29 Jun 2010 00:00:00 +0000

derivations (0.52.20100310)

  * Recognizing that recent versions of some of the software the
    computer uses to build the book's PostScript and PDF files have
    changed in operation, updated the code in btool/ as follows.
    + Since a recent version of Ghostscript seems to refuse to propagate
      the document's embedded title to the PDF, added to complete-pdf(1)
      a fourth command-line argument to specify a title to post-embed.
      Changed several *.h and *.cc files in the btool/ hierarchy to this
      end.
    + Observing that Libpoppler's Dict::add() does not copy the
      key-strings one feeds it (and seeming to recall that an earlier
      Libpoppler did copy them), rewrote the btool/ code to preserve the
      relevant key-strings until the Dict objects that use them go out
      of scope.
    + Moved the definition of the PDF::Iref struct from btool/PDF/PDF.h
      to its own, new header at btool/PDF/Iref.h.
    + Fixed complete-pdf(1)'s long-form options and help list.
  * Let tex/Makefile use the new complete-pdf(1).
  * Again refined the preface.
  * In tex/alggeo.tex (Classical algebra and geometry), "Multiplication
    and division of complex numbers in rectangular form," appended a
    sentence on real and imaginary parts by superposition.
  * In tex/fours.tex (The Fourier series), "The square and triangular
    pulses," mentioned the Gaussian pulse.
  * Began the new chapter tex/fouri.tex (The Fourier transform).
  * Deleted much of tex/greek.tex (The Greek alphabet), which was too
    prolix.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Wed, 10 Mar 2010 00:00:00 +0000

derivations (0.52.20090107)

  * Added hyphens throughout in "singular-value decomposition."
  * In a continuing gradual refinement, further tweaked the book's
    preface.  (The preface is important because readers first opening
    the book will judge the book's style by it.  This is why the preface
    continues to get attention, a little here and a little there.)
  * To comply with van der Vorst, reversed the definition of the
    residual throughout the book but particularly in tex/taylor.tex (The
    Taylor series) and tex/mtxinv.tex (Inversion and
    orthonormalization).
  * In tex/mtxinv.tex (Inversion and orthonormalization), "The
    Moore-Penrose pseudoinverse," corrected the inadvertently
    nonsensical symbolization of the squared residual norm.
  * Added the brief new appendix tex/purec.tex (A sketch of pure complex
    theory) (four pages only! it is an exceptionally brief sketch).  Let
    other parts of the book refer to it where appropriate.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Wed, 07 Jan 2009 00:00:00 +0000

derivations (0.52.20081219)

  * Had tex/thb.sty use the package amssymb, which provides useful
    mathematical symbols including some, like \triangleq, \lesssim and
    \gtrsim, the book had previously tried to compose of existing
    elements.  Substituted the newly available symbols generally into
    the book.
  * Added to tex/thb.sty the mathematical functions Sa(z), Si(z), Ci(z)
    and Ei(z), respectively by the new \sinarg, \sinint, \cosint
    and \expint macros.
  * In many formulas, improved the spacing about equal signs and other
    elements.  Mostly, by substituting the {split} rather than the
    {eqnarray} environment, narrowed the space about equal signs where
    it seemed appropriate to do so.  (When the author first started
    typesetting the book, he did not know about the {split} environment.
    Later he adopted it only fitfully.  This change was not to
    eliminate {eqnarray}, which has its uses, but rather to go back and
    use {split} where it ought to have been used all along.)
  * Corrected several (but purposely not all) grammatically incorrect
    uses of the noun "example" to the adjectival "exemplary" and the
    genitival "example's."
  * Changed the types of several pairs of parentheses
    between (), [] and {}.
  * Renamed the book's Part III from "Advanced calculus"
    to "Transforms, special functions and other topics."
  * Feeling that the book's preface, tex/pref.tex, had much good
    material not woven tightly enough, reorganized the preface,
    separating (a) comments on the book's features (footnotes, etc.)
    and (b) acknowledgements into a distinct, unnumbered subsection.
    Acknowledged the author's parents there, boldly suggested that other
    authors cite the book, and otherwise modified the preface in a few
    minor respects.
  * In tex/alggeo.tex (Classical algebra and geometry), renamed the
    section "Notation for series sums and products" as "Integer and
    series notation."  In the section, defined the $\in \mathbb Z$
    notation.
  * In several spots throughout the book, explicitly stated by
    the $\in \mathbb Z$ notation that certain quantities were integers.
  * In tex/trig.tex (Trigonometry) and tex/inttx.tex (Integration
    techniques), extended the complex triangle sum inequality to the
    continuous case.
  * In tex/drvtv.tex (The derivative), revised the section "The binomial
    theorem" in several respects.
  * In tex/taylor.tex (The Taylor series):
    + In "Expanding functions in Taylor series," inserted into an
      existing footnote a new paragraph formalizing the footnote's
      justification of the Taylor series' sufficiency.
    + In "Taylor series for specific functions," appended a brief
      paragraph giving first-order approximate forms for the exponential
      and sine functions.
    + In "Geometric majorization," subscripted \rho_n, formerly styled
      merely as \rho.  Further refined the subsection generally.
    + In "Calculation outside the fast convergence domain," observed
      explicitly that one had to have a fast means of calculating the
      function in question within at least one domain to apply the
      subsection's technique.
  * In tex/inttx.tex (Integration techniques):
    + In "Integration by closed contour," extended the complex triangle
      inequality to the continuous case.
    + In "The derivatives of a rational function," changed the index
      letters.
  * In several instances in the matrix chapters, wrote together on a
    single line a group of short equations each of which had previously
    had its own line.
  * In tex/vector.tex (Vector analysis):
    + Rewrote the latter part of the section "Orthogonal bases."
    + In "The parabola," changed $\alpha x^2$ to $\mu x^2$, since the
      chapter uses \alpha for an unrelated purpose.
    + Generally improved the style of some prose scattered across the
      section "Parabolic coordinates."
  * In tex/vcalc.tex (Vector calculus), renamed the subsection "The
    vector field as a sum of scalar fields" as "The vector field and its
    scalar components."
  * Completed tex/vcalc.tex (Vector calculus).
  * Added tex/fours.tex (The Fourier series) and drafted the whole
    chapter.
  * Opened a file for (and wrote a few words in) tex/fouri.tex (The
    Fourier and Laplace transforms).
  * Made the use of quotation marks more consistent in the bibliography.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Fri, 19 Dec 2008 00:00:00 +0000

derivations (0.52.20081003)

  * Divided the book into three parts, using the \part{} command
    in main.tex.  Because of this division, advanced the version number
    to 0.52.
  * Also in tex/main.tex, anticipating the first edition's future
    release, added a (presently) commented-out "first printing" line for
    the bottom of the title page's reverse side.
  * Reconfigured the several Makefiles in the btool/ directory not to
    die on C++ compiler warnings when the BUILD_FOR_PACKAGING
    environment variable is set.
  * In btool/TOC/Table.cc, told the PDF table-of-contents code to ignore
    the book's new \part{} parts.  (At present, the code mishandles the
    parts.  Maybe this can be fixed at a future date but, in any case,
    to ignore the parts may be the right thing to do in any case.)
  * Added to tex/thb.sty the abbreviating macro \pl for \partial.
  * In tex/pref.tex (Preface):
    + Added some comments to show changes the author should make to the
      file before the book's actual, first-editional release.
    + Removed an unnecessary sentence from the end of the paragraph on
      the book's plan.
    + Extended and polished the remarks regarding the book's index.
  * In tex/trig.tex (Trigonometry):
    + In "Rotation," substituted \phi for \psi as the rotation angle, so
      as not to conflict with the Tait-Bryan \psi newly treated in
      tex/vector.tex (Vector analysis).  Added a reference to the latter
      chapter.
    + In "Cylindrical and spherical coordinates," added several
      identities.
    + Rendered "The complex triangle inequalities" more precise.
  * In tex/drvtv.tex (The derivative), added the new
    subsection "A derivative product pattern."
  * In tex/integ.tex (The integral), changed several incorrect instances
    of various forms of the verb "to transit" to "to commute," including
    in one section title.
  * In tex/taylor.tex (The Taylor series), "Error bounds," and elsewhere
    in the book, let the symbols S_n and R_n consistently stand for the
    partial sum and remainder of a series truncated before rather than
    after the nth-order term.
  + In tex/mtxinv.tex (Inversion and orthonormalization), added the new
    section "The complex vector triangle inequalities."
  + Divided the chapter tex/vector.tex (Vector analysis) into a
    relatively short chapter with the same name and filename and the
    longer, new chapter tex/vcalc.tex (Vector calculus).  Revised and
    completed tex/vector.tex.  Revised and continued tex/vcalc.tex
    through the end of the subsection "Derivatives in spherical
    coordinates."
  + Altered the short form of the title of the appendix tex/hex.tex
    to read "Hexadecimal notation, et al."
  + Reworked a tract of tex/hist.tex (Manuscript history) to remove,
    shorten or de-emphasize comparisons against some other authors like
    Weisstein.  Rewove some of the surrounding text in the process.
  * Changed some instances of the words "to the extent that"
    to "to the extent to which."
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Fri, 03 Oct 2008 00:00:00 +0000

derivations (0.51.20080419)

  * In btool/Makefile and btool/Makefile-subdir, reversed $(filter)
    to $(filter-out) to enable "make clean [program]" as a single
    command to work as expected.  Also told the `cleanless:' target to
    remake any %.d files it removes when (and only when) the makefile
    itself has $(include)d them, so that "make clean [program]" not
    mysteriously seem to have used invisible %.d files.
  * Revised and continued tex/vector.tex (Vector analysis).  Added the new
    section "Integral forms."
  * In tex/stub.tex (Plan), reported the recent download rate of 4000
    copies of the book per year.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Sat, 19 Apr 2008 00:00:00 +0000

derivations (0.51.20080324)

  * (Debian) Removed an unnecessary, malformed groff comment from the
    man page doc/derivations.7.
  * Added a specific `derivations.ps:' target to tex/Makefile, including
    there a sed(1) command to change the internally embedded PostScript
    document title, hence also indirectly the internally embedded PDF
    document title, to the author's name, rather than the cryptic
    default "derivations.dvi" it had been.
  * Replaced tex/use.tex and tex/def.tex with the new tex/thb.sty, a
    proper LaTeX style file.  Told tex/main.tex to use it and
    tex/Makefile to rely on it.
  * In tex/trig.tex (Trigonometry) and tex/vector.tex (Vector analysis),
    disambiguated the amplitude of a vector (generally a complex scalar)
    from the magnitude of a vector (a positive, real scalar).
  * In tex/drvtv.tex (The derivative), "The Leibnitz notation," defined
    the partial derivative, thus correcting an oversight.
  * Revised and continued tex/vector.tex (Vector analysis).
  * In tex/stub.tex (Plan), appended to the plan the proposition of a
    chapter "Information theory."  Changed the name of the proposed
    chapter "Kepler's laws" to "Differential geometry and Kepler's
    laws."
  * Deleted altogether from the source several disused passages already
    commented out.
  * Edited the rest of the book in further, minor ways.
  * Noted for historical interest that the book had 488 pages, with
    fourteen chapters and a fifteenth partly typeset, plus appendices, a
    preface and other such auxiliary parts.

 -- Thaddeus H. Black <thb@derivations.org>  Mon, 24 Mar 2008 00:00:00 +0000

derivations (0.51.20080307)

  * Because the book had begun to progress beyond the matrix chapters,
    advanced the version number to 0.51.  (To a Debian developer,
    version 0.9 of something is followed by version 0.10, but such
    numbering naturally can confuse people who unlike the author happen
    not to be Debian developers.  And even in the Debian world,
    version 0.9 implies "almost complete," which this book is not.
    Since even to a Debian developer 51 is unambiguously greater than 5,
    there seems little reason not to conserve the number line between
    0.50 and 0.90 by adding the extra digit.  The only version number
    that has a real, semantical meaning, anyway, is 1.0; as for the
    rest, so long as each number is greater than the last, the exact
    choice of numbers does not matter much.)
  * In tex/Makefile, revised the $(gs) macro to create the empty file
    tex/cidfmap when needed, and revised the `cleanless' rule to remove
    the same file.  Consequently, removed the empty file tex/cidfmap
    from the distributed source.
  * In tex/README, noted that index entries can run 9.0 points too wide
    without unduly ill effect.
  * Began to typeset the new chapter tex/vector.tex (Vector analysis),
    up through its section "Notation."
  * In tex/cexp.tex (The complex exponential,) "Complex trigonometrics,"
    explained why the Pythagorean theorem for trigonometrics does not
    involve a complex conjugate as the Pythagorean theorem for vectors
    does.
  * In tex/taylor.tex (The Taylor series), slightly revised "Calculation
    outside the fast convergence domain."
  * In tex/matrix.tex (The matrix), "The Kronecker delta," added a
    reference to the new section "The Kronecker delta and the
    Levi-Civita epsilon" of tex/vector.tex (Vector analysis).
  * Reformed stub.tex (now titled ``Plan'') into a proper plan for the
    rest of the book.
  * Revised and extended tex/greek.tex (The Greek alphabet) generally.
  * In the appendix tex/hist.tex (Manuscript history), extended the
    remarks concerning Wikipedia.
  * Throughout the book, in the notation for the alternate, x-
    and y-oriented cylindrical and spherical bases, lifted the
    subscripted "x" and "y" up to the superscript position.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Fri, 07 Mar 2008 00:00:00 +0000

derivations (0.5.20071222)

  * Integrating patches from Debian downstream, edited the btool/ code
    in several spots, altering no semantics but eliminating warnings by
    newer G++ compilers, mostly regarding a C string literal's type.
    (Maybe the warnings show deficiencies in the libpoppler headers
    rather than in the btool/ code, but, anyway, the change eliminates
    the warnings.)
  * In btool/Page_no/PS_page_numbering.cc, added a missing initializer
    to int n_page_whole.
  * Generally reviewed, slightly revised and where necessary corrected
    tex/mtxinv.tex (Inversion and orthonormalization).  Notably, in "The
    Gram-Schmidt kernel formula," corrected the algorithm's handling of
    indices.
  * Generally reviewed, slightly revised and where necessary corrected
    tex/eigen.tex (The eigenvalue).
  * In tex.eigen.tex (The eigenvalue), rewrote "The singular value
    decomposition."
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Sat, 22 Dec 2007 00:00:00 +0000

derivations (0.5.20071110)

  * In tex/eigen.tex (The eigenvalue):
    + In "The nondiagonalizable matrix," explained in a footnote why the
      Schur U_S has the same multiplicities of eigenvalues as does the A
      it comes from.  (Maybe this belongs in the body of the text, but
      it does not flow well there as the body currently is written.)
    + In "The singular value decomposition," explained the step
      to $I_n\Sigma^{*}\Sigma I_n$ more thoroughly.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Sat, 10 Nov 2007 00:00:00 +0000

derivations (0.5.20071108)

  * In btool/fill-toc-ends, tex/main.tex and tex/Makefile, corrected
    the PDF table-of-contents regimen to create and use a new
    page-number file tex/main.pgn at build time, rather than trying to
    glean the needed page numbers unreliably from the *.log file.
  * Corrected "this is because" to "this is so because" throughout the
    manuscript.
  * Gave Richard Courant and David Hilbert their full names in the
    narrative and bibliography.
  * In tex/drvtv.tex (The derivative), "The Newton-Raphson iteration,"
    slightly improved the form of the iteration formula, letting the
    specification apply to the formula's entire right side; and referred
    to the new Newton-Raphson section in tex/mtxinv.tex (Inversion and
    orthonormalization).
  * In tex/taylor.tex (The Taylor series):
    + Corrected the title of "The power series expansion
      of 1/(1-z)^{n+1}" to "The power-series expansion...."
    + Added the new "Extrema over a complex domain."
    + Generalized and rewrote "Calculation outside the fast convergence
      domain."
  * Throughout the matrix chapters, where displayed matrices were
    stacked, either split the stack with appropriate verbiage or
    combined the stack into a single LaTeX equation environment of the
    appropriate kind, to prevent LaTeX from splitting the stack at a
    page boundary.  (This is not a wholly satisfactory solution.  The
    stacks are tall.  They leave some pages pretty empty.  Keeping the
    stack together however seems preferable to beginning a page with a
    displayed equation.)
  * In tex/matrix.tex (The matrix):
    + In "The general scaling operator," introduced the "diag" notation.
    + In "The unit triangular matrix," explained and symbolized the
      Schur-form triangular matrices better.
    + Added "The Jacobian derivative."
  * In tex/gjrank.tex (Rank and the Gauss-Jordan), at the close of the
    section "The Gauss-Jordan" decomposition, warned the reader to
    expect also the Gram-Schmidt and Schur decompositions in the
    following chapters.
  * Extended, generally reorganized and significantly rewrote the two
    chapters tex/mtxinv.tex (Inversion and orthonormalization) and
    tex/eigen.tex (The eigenvalue).  Even moved some material from one
    chapter to the other.  Retitled the former chapter, whose old name
    was "Matrix inversion."
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Thu, 08 Nov 2007 00:00:00 +0000

derivations (0.5.20071015)

  * Prepared this revision as an editing checkpoint for internal use
    only, not for release.  Did not release it.  (The reason to do such
    a thing is that the author habitually uses diff(1) to check the
    changes each new revision brings against the revision before it.
    This is hard to do when the chapter/file structure of the source
    changes from one revision to the next.  This revision more or less
    isolates changes that disrupt the author's use of diff(1).)
  * Cancelled the planned chapter tex/mtxalg.tex (Matrix algebra),
    moving its section "The pseudoinverse" to the end of the newly
    constituted tex/mtxinv.tex (Matrix inversion).
  * Split the existing chapter tex/eigen.tex (Inversion and eigenvalue)
    in two: tex/mtxinv.tex (Matrix inversion); tex/eigen.tex (The
    eigenvalue).  Planned to add to these chapters some of the material
    earlier planned for the now canceled "Matrix algebra" chapter.
  * Conventionalized the book's terminology to read "unit triangular
    matrix" where it had read "triangular matrix."  Added the standard
    definition of the "triangular matrix," and added definitions of the
    "strictly triangular matrix" and the "diagonal matrix" for good
    measure.
  * Conventionalized the book's terminology to read "Gauss-Jordan (LU)
    decomposition," "orthonormalizing (QR) decomposition," etc., rather
    than "factorization" in each case.
  * Abandoned the archaic notation |A| for the determinant, converting
    generally to "det A".
  * Noted here for general interest is that the fact that a particular
    revision of the book is not released does not make the changelog for
    that revision irrelevant to readers who follow the changelog file.
    On the contrary, the changes in an unreleased revision normally
    carry through to future released revisions.  Their changelogs are
    relevant for this reason.

 -- Thaddeus H. Black <thb@derivations.org>  Mon, 15 Oct 2007 00:00:00 +0000

derivations (0.5.20071011)

  * After changing the several items listed below, found the overall
    result unsatisfactory.  Closed the revision as it stood but did not
    release it.  Thought for the next revision to cancel the old plan
    for the fourth chapter of the matrix sequence, to have been titled
    "Matrix algebra"; and instead to split the third chapter of the
    sequence, tex/eigen.tex (Inversion and eigenvalue), in two,
    distributing some of the formerly planned "Matrix algebra" material
    between the two.
  * In tex/Makefile:
    + Added a long comment to guide a hypothetical future maintainer of
      the book.
    + As an alternative to shipping a modified book.cls with the source,
      caused the book's build procedure to copy and modify LaTeX's
      standard book.cls locally.  (The resulting modified class file is
      named derivations-book.cls, but this class file is generated only
      at build time.  It cannot be found among the source files, because
      almost all its content is already present in the LaTeX
      installation required to build the book, anyway.  It can however
      be generated from the top source directory by "make
      tex/derivations-book.cls" whenever it is wanted.)
  * In tex/main.tex, changed(!) to \documentclass{derivations-book}.
  * In tex/matrix.tex (The matrix):
    + Gave C^{-1} = 2I - C identities to some of the addition operators
      for which they hold.
    + Introduced the new table "Properties of the parallel triangular
      matrix."
    + Added shift-and-truncate identities to "The shift operator."
  * In tex/gjrank.tex (Rank and the Gauss-Jordan):
    + Added "Properties of the factors."
    + Added "Factoring an extended operator."
    + Added "Under- and overdetermined systems (introduction)."
  * Revised tex/eigen.tex (Inversion and eigenvalue) generally.
  * Started the first few words of a new chapter tex/mtxalg.tex (Matrix
    algebra), but see the first changelog item in this entry above.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Thu, 11 Oct 2007 00:00:00 +0000

derivations (0.5.20070926)

  * Moved the list of figures to after the list of tables.
  * Reread the rest of the manuscript, improving, correcting and
    supplying as in the last changelog.
  * Introduced the shorthand matrix notations A^{-T} and A^{-*}.
  * In tex/pref.tex (Preface), acknowledged G.S. Brown and noted that
    the book does not number theorems.
  * In tex/matrix.tex (The matrix):
    + In the introduction to the section "Dimensionality and matrix
      forms," acknowledged that the section's formalisms are nonstandard.
    + In "The rank-r identity matrix," promoted a footnote on I_3's
      infinite dimensionality to an in-line parenthetical note.
    + In "The scaling quasielementary or general scaling operator,"
      gave a summational decomposition of D.
  * In tex/gjrank.tex (Rank and the Gauss-Jordan):
    + Eliminated several confusing, unnecessary transpositions.
    + Gave definitions of full row and column rank in "The full-rank
      matrix."
    + Added the new subsection "Full column rank and the Gauss-Jordan
      factors K and S."
  * In tex/eigen.tex (Inversion and eigenvalue):
    + Repaired and rewrote "Inverting the square matrix."
    + Integrated some motivational narrative into "The exactly
      determined linear system."
    + In "The eigenvector," defined the term "eigensolution."
    + Appended the new "Matrix condition."
  * Generally in the matrix chapters, changed C_> and C_< to G_>
    and G_<; and changed the generic notation for the full-rank
    factorization from XY to BC.
  * In tex/def.tex, added the new macro \mdots.
  * Scanned the LaTeX source for obsolete commented-out markup.
    Deleted such.

 -- Thaddeus H. Black <thb@derivations.org>  Wed, 26 Sep 2007 00:00:00 +0000

derivations (0.5.20070921)

  * Added an explicit "all:" target to the root Makefile.
  * Reread the manuscript through the end of tex/cubic.tex (Cubics and
    quartics) and reread the appendices, improving the manuscript's
    style in numerous small instances, correcting a few minor errors,
    and supplying some relatively insubstantial omissions along the way.
  * Unsure of the number, stopped trying to count "the [four] most
    famous results in all of mathematics."
  * In tex/alggeo.tex (Classical algebra and geometry):
    + In "Properties of the logarithm," added two properties to the
      table explicitly expressing the inverse relationship between
      exponentiation and the logarithmic operation.  Explained the
      derivations of two of the properties already in the table more
      thoroughly.
    + In "Multiplication and division of complex numbers in rectangular
      form," added an equation about (z^*)(z).
    + In "Complex conjugation," linked the reverse induction logic more
      explicitly, and put the observation that the product of conjugates
      is the conjugate of the product in symbolic form.
  * In tex/trig.tex (Trigonometry), partly rewrote the start of the
    "Definitions" section.
  * In tex/drvtv.tex (The derivative), "L'Hospital's rule," pointed out
    that one can apply the rule recursively, and otherwise generally
    explained things better.
  * In tex/cexp.tex (The complex exponential):
    + Removed the unnecessary "+" signs from the several "lim_{z->0^+}".
    + In "The natural logarithm," wrote briefly about converting from
      other bases.
    + In "The actuality of complex quantities," extended the remarks on
      Occam's razor."
  * In tex/noth.tex (Primes, roots and averages), "Compositional
    uniqueness," covered prime C/r.
  * In tex/taylor.tex (The Taylor series):
    + In "Shifting a power series' expansion point" and "Analytic
      continuation," treated more carefully the fact that the new
      expansion point of a directly shifted series must lie within the
      original series' convergence domain.
    + In "Error bounds, examples," subscripted R.
  * In tex/inttx.tex (Integration techniques):
    + Rewrote the latter half of the chapter's introduction.
    + Renamed "Integrating rational functions" to "Integrating a
      rational function."
    + Rewrote the subsection "Multiple poles (the conventional
      technique)," splitting it in three: "The derivatives of a rational
      function"; "Repeated poles (the conventional technique)"; and "The
      existence and uniqueness of solutions."  Gave a different
      derivation, since the old one was wrong.
    + Generally renamed the "multiple pole" to the "repeated pole,"
      including in (sub)section titles.
  * Having partly neglected to do so for the last release, properly
    spell-checked this release.

 -- Thaddeus H. Black <thb@derivations.org>  Fri, 21 Sep 2007 00:00:00 +0000

derivations (0.5.20070912)

  * Added the new build tool btool/complete-pdf, along with its C++
    source, which tool gives proper page numbering and a PDF table of
    contents to the book's PDF.  Updated the Makefile accordingly.
  * Corrected some entries in the bibliography.
  * In tex/main.tex, issued \cleardoublepage commands before and
    after \makeindex, to cause the index to begin on an odd page and
    end on an even, as do all the book's other chapter-level elements.

 -- Thaddeus H. Black <thb@derivations.org>  Wed, 12 Sep 2007 00:00:00 +0000

derivations (0.5.20070703)

  * After considerable study and experimentation, found the proposed
    transition to PGF and PDFLaTeX too hard for now.  (PGF/TikZ seems to
    break at least LaTeX's $\:$ operator, but the real reason not to
    change over is that the manuscript is now too long; the changeover
    would take too much effort.  It seems preferable eventually to hack
    correct PDF page numbers and a PDF table of contents within the
    framework of the existing document source.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <thb@derivations.org>  Tue, 03 Jul 2007 00:00:00 +0000

derivations (0.5.20070524)

  * Did not actually release this version, meant only to mark internal
    development.  However, recorded changes here anyway because the
    changes must accumulate toward the next version actually released.
  * Updated the author's e-mail address.
  * In tex/def.tex, defaulted to the newer, correct \scalebox usage
    rather than to the older, incorrect usage.  (Left the older usage in
    the file, only commented out, for those who still need it.)
  * Edited the rest of the book in further, minor ways.
  * Wanted to migrate toward building the book by PDFLaTeX, but observed
    that this was easier said than done.  Noted that the book's many
    PSTricks diagrams regrettably seem not to carry gracefully over to
    PDFLaTeX, leaving the author with a dilemma: to migrate the diagrams
    to a compatible format like PGF, or to forego PDFLaTeX?  Thought
    that going to PDFLaTeX was probably a necessary step.  Reached no
    decision, but leaned toward the PGF solution.  Feared that
    translating the diagram sources by hand would take many hours,
    though.  (Noted that there exists a PDFTricks package, but that the
    package seems inadequate to the purpose.)

 -- Thaddeus H. Black <thb@derivations.org>  Thu, 24 May 2007 00:00:00 +0000

derivations (0.5.20070327)

  * In tex/alggeo.tex (Classical algebra and geometry):
    - Added the new subsection "Dividing power series by matching
      coefficients."
    - In the subsection "Properties of the logarithm" and also in its
      table, added the property that w^p == a^(p*log_a(w)).
  * In tex/drvtv.tex (The derivative), in the "l'Hospital's rule"
    section, corrected several instances of "singularity" to "pole."
    Slightly revised the surrounding text accordingly.
  * In tex/cexp.tex (The complex exponential), added more information on
    the hyperbolic functions.
  * In tex/taylor.tex (The Taylor series):
    - Added Taylor series for sinh and cosh to the Taylor-series table.
    - Added the new section "Trigonometric poles."
  * In tex/inttx.tex (Integration techniques), added the new
    section "Integrating products of exponentials, powers and
    logarithms," including a short table of relevant antiderivatives.
  * Realizing that the book's existing citation style burdened the text,
    lightened the style by shifting most of the citations to footnotes.
  * In the book's index, added the birth and death dates of most of the
    mathematicians named there, mostly per Wikipedia.
  * Improved the typesetting of the magnitude sign |z|.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 27 Mar 2007 00:00:00 +0000

derivations (0.5.20070322)

  * Linked the first three of the four matrix chapters officially into
    the book for the first time:
    - tex/matrix.tex (The matrix);
    - tex/gjrank.tex (Rank and the Gauss-Jordan);
    - tex/eigen.tex (Inversion and eigenvalue).
    Observed that these chapters did not just suddenly appear, but had
    been in various drafts for years.  Did not yet link the fourth
    matrix chapter tex/mtxalg.tex (Matrix algebra).
  * In tex/drvtv.tex (The derivative), expanded a footnote in
    the "Summational and integrodifferential transitivity" subsection
    into a more carefully turned warning against conditional
    convergence, in the main narrative.
  * In tex/def.tex, added the new typesetting macro \mfd to render a
    matrix's determinant.
  * Replaced several instances of the word "while" by the less ambiguous
    word "whereas."
  * Edited the rest of the book in further, minor ways.
  * Noted for historical interest that the book had 372 pages, with
    thirteen chapters plus appendices, a preface and other such
    auxiliary parts.

 -- Thaddeus H. Black <derivations@b-tk.org>  Thu, 22 Mar 2007 00:00:00 +0000

derivations (0.5.20070307)

  * Did not actually release this version, meant only to mark internal
    development.  However, recorded changes here anyway because the
    changes must accumulate toward the next version actually released.
  * In tex/intro.tex (Introduction), generally revised the "Complex
    numbers and complex variables" section.
  * In tex/alggeo.tex (Classical algebra and geometry),
    extended a footnote to treat the various connotations
    of the terms "polynomial," "power series" and "Laurent series"
    in professional and applied usage.
  * In tex/drvtv.tex (The derivative), in the section "The derivative
    product rule," added the two-element quotient form of the rule.
  * In tex/taylor.tex (The Taylor series):
    - In the "Expanding functions in Taylor series" section, defined the
      term "Maclaurin series."
    - Rewrote and extended the latter part of the "Analytic
      continuation" section.
    - Added the new "Entire and meromorphic functions" section.
    - Corrected a gruesome error in the subsection "Enclosing a multiple
      pole," where the book had previously, quite falsely, found every
      complex contour integral about a multiple pole to come to zero.
    - Added the new "Taylor series in 1/z" section.
  * In tex/inttx.tex (Integration techniques):
    - In the "Partial-fraction expansion" subsection, corrected the
      limits of summation on the numerator polynomial in the unexpanded
      form.
    - Added the new "Multiple poles (the conventional technique)"
      subsection.
  * In tex/bib.bib (bibliography), corrected the date of Dr. Kohler's
    lecture.
  * Observing that the English verb "to prove" declines in a strange
    way, changed several (but not all) instances of "proven" to the
    semantically equivalent alternative participle "proved," depending
    on the rhythm of the sentence in which the word appears.
  * Edited the rest of the book in further, minor ways.
  * Further worked on the four matrix chapters, but did not yet
    permanently link them into the book.  Brought tex/gjrank.tex (Rank
    and the Gauss-Jordan) to a first fully coherent draft.

 -- Thaddeus H. Black <derivations@b-tk.org>  Wed, 07 Mar 2007 00:00:00 +0000

derivations (0.5.20070219)

  * Added the author's year of birth and his estimate of the book's
    U.S. Library of Congress class to the back of the title page.
  * In tex/cubic.tex (Cubics and quartics), in the narrative of
    the "Guessing the roots" section, corrected a_0q to a_0q^n.
  * Edited the rest of the book in further, minor ways.
  * Finally worked tex/matrix.tex (The Matrix) into a usable form.
    Edited it down to 38 pages, which are still a lot but are a marked
    improvement against earlier drafts.  Cautiously refrained
    nevertheless, for the moment, from linking the chapter into the book
    proper, on the ground that the chapter alone is of limited interest
    without the (presently) three additional matrix chapters which
    follow.  Hoped that, with this foundational matrix chapter finally
    in good order, the other three matrix chapters (already partly
    written) would prove easier to complete than this one has done.
    (Will they?  We shall see.  On the other hand, the author has had
    limited time available to work on the book in recent months in any
    case, which is the main reason the Matrix chapter has taken so long
    to write.)

 -- Thaddeus H. Black <derivations@b-tk.org>  Mon, 19 Feb 2007 00:00:00 +0000

derivations (0.5.20070217)

  * Rendered the citation style more consistent throughout the book.
    (Remained somewhat dissatisfied with the style, however.  It's too
    bulky.)
  * Generally changed the default product dummy variable from k to j.
    Retained k for summations.  Also in the (not yet included) matrix
    chapters, retained k even for products, inasmuch as j serves a
    conflicting role there.
  * Promoted Cauchy's integral formula to the rank of one of the, now
    four, most famous results in all of mathematics.
  * In tex/alggeo.tex (Classical algebra and geometry), in the
    table "Power properties and definitions,"  corrected the
    condition z >= 0 to n >= 0.
  * In tex/drvtv.tex (The derivative), in the "Derivative product rule"
    subsection, extended the specialized form to handle logarithms.
  * In tex/inttx.tex (Integration techniques), in the "Integration by
    closed contour" section, added a second example which, unlike the
    first, does not extend the contour.
  * Edited the rest of the book in further, minor ways.
  * Further worked on the four matrix chapters, but did not yet link
    them into the book.

 -- Thaddeus H. Black <derivations@b-tk.org>  Sat, 17 Feb 2007 00:00:00 +0000

derivations (0.5.20070213)

  * In tex/taylor.tex (The Taylor series), numbered the formerly
    unnumbered first equation of the section "The Laurent series."
  * Did not otherwise edit the book, but noted here that the last
    changelog forgot to mention that additional, minor edits were made.

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 13 Feb 2007 00:00:00 +0000

derivations (0.5.20070212)

  * (Susan M. Doyle) Corrected several instances of incorrect
    punctuation throughout the book, particularly with respect to the
    use of ellipses.
  * Further refined the book's preface.
  * (Susan M. Doyle) In tex/intro.tex (Introduction), edited the header
    of the section "Rigor" to make the language there less strained.
  * In tex/cexp.tex (The complex exponential), extended the
    section "Fast and slow functions" to lend the reader a better
    subjective sense of the manner in which logarithms and exponentials
    diverge, and to observe the fundamental zeroth-order resemblance
    between logarithms and constants.
  * In tex/integ.tex (The integral), renamed the section "Checking
    integrations" to "Checking an integration."
  * In tex/taylor.tex (The Taylor series):
    - In the subsection "Convergence," extended a footnote to excuse the
      book from the (for it) unnecessary rigor of the Weierstrass M
      test.
    - Added the new section "The Laurent series."
  * In tex/inttx.tex (Integration techniques), added the new
    section "Frullani's integral."
  * In tex/cubic.tex (Cubics and quartics), corrected the quartic table
    to handle the degenerate case K = 0.

 -- Thaddeus H. Black <derivations@b-tk.org>  Mon, 12 Feb 2007 00:00:00 +0000

derivations (0.5.20070206)

  * Moved two philosophical paragraphs on convention from
    tex/pref.tex (Preface) to tex/hist.tex (Manuscript History).
    Generally revised the preface again.
  * In tex/taylor.tex (The Taylor series):
    - Revised the chapter generally, rendering it significantly easier
      for the reader to follow.
    - Corrected the Taylor series of the natural logarithm.
    - Added the new subsection "Enclosing a multiple pole".
    - Renamed the "Bounds" section to "Error bounds," and rewrote it.
    - Added the new section "Odd and even functions."
  * Further worked on the four matrix chapters, but did not yet link
    them into the book.
  * Slightly revised the outline of future work in tex/stub.tex (To be
    written).
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 06 Feb 2007 00:00:00 +0000

derivations (0.5.20061214)

  * Introduced the new file tex/use.tex, to include \usepackage{}
    commands formerly in tex/main.tex.
  * Expanded the club of "the most famous results in all of mathematics"
    from two to three, adding the fundamental theorem of calculus to the
    Pythagorean theorem and Euler's formula.  Revised the text
    accordingly.
  * Renamed the "principal angles" to the "hour angles."
  * Rewrote much of the book's preface, in tex/pref.tex.
  * In tex/drvtv.tex (The derivative), improved and expanded the section
    on the Newton-Raphson iteration.
  * Added the short but complete new chapter tex/cubic.tex (Cubics and
    quartics), between tex/inttx.tex (Integration techniques) and
    tex/matrix.tex (The matrix).
  * In tex/alggeo.tex (Classical algebra and geometry):
    - Ended the "Quadratics" section with a reference to the new chapter
      tex/cubic.tex (Cubics and quartics).
    - In "Dividing power series," changed a few of the symbols slightly
      and added an early note excusing some readers from reading the
      rest of the subsection.
    - In "Indeterminate constants, independent variables and dependent
      variables," added a parenthesized note on dummy variables.
    - Generally revised, clarified and improved the "Complex
      conjugation" subsection.
  * In tex/trig.tex (Trigonometry), rewrote "Scalars, vectors
    and vector notation."
  * In tex/drvtv.tex (The derivative), in the "Powers of numbers near
    unity" subsection, disambiguated two separate symbols formerly both
    represented as \epsilon.
  * In tex/cexp.tex (The Complex Exponential):
    - Footnoted an alternate derivation of Euler's formula.
    - In the "Euler's formula" section, restored a missing `i' to
      several exponents.
  * In tex/taylor.tex (The Taylor Series):
    - In "Integrating along the contour," corrected several typos in the
      various coefficients and integration limits, and added a footnote
      clarifying a point of rigor involving convergence domains.
    - In "Taylor series for specific functions," extended the
      convergence domains for exp, sin and cos.
    - Added the new section "Bounds."
  * Split the three draft matrix chapters again, now into four chapters:
    - tex/matrix.tex (The matrix);
    - tex/gjrank.tex (Rank and the Gauss-Jordan);
    - tex/eigen.tex  (Inversion and eigenvalue);
    - tex/mtxalg.tex (Matrix algebra).
    Observed that these chapters were certainly not yet ready for
    release, and in fact that they seemed likely to need to be
    reorganized and/or renamed again before release.
  * Excluded the four matrix chapters from the book (though included the
    four source files with the book's source).  In their place, added a
    stub chapter tex/stub.tex.
  * In tex/hist.tex (Manuscript history), expanded and partly rewrote
    the paragraph about encyclopedic works.
  * Edited the rest of the book in further, minor ways.

 -- Thaddeus H. Black <derivations@b-tk.org>  Thu, 14 Dec 2006 00:00:00 +0000

derivations (0.5.20061014)

  * Did not actually release this version.  (The author's spare time to
    write the book, always limited, has been scanter than usual lately;
    but still the work creeps forward some evenings, half an hour here,
    an hour there.  The author did feel pretty good about the last
    version released, as far as the book had then gone, so is not now
    anxious to imbalance the work by rushing additional chapters to it.
    Under such conditions---when the author's writing time is
    fragmented---unreleased working versions, documented here, help keep
    the author's thoughts in order.)
  * Further generally revised the as yet immature tex/matrix.tex (The
    matrix).
  * Added a paragraph on footnotes to and otherwise slightly revised
    tex/pref.tex (Preface).  Also added, but for the time being
    commented out, a future draft alternative to the preface's "work in
    progress" paragraph.
  * Separated the last part of the section "L'Hopital's rule" of
    tex/drvtv.tex (The derivative).  Moved it to tex/cexp.tex (The
    complex exponential) as the new section "Fast and slow functions."
  * In the "Serial and parallel addition" subsection of
    tex/noth.tex (Primes, roots and averages), defined the
    word "iff."  (If memory serves, the word had once been defined
    earlier in the book, but redaction since then evidently has moved
    or removed the earlier definition.)
  * Noted the irony: sometimes, at least in some ways, the smaller the
    change a version represents, the longer the changelog.  For sweeping
    changes, one tends merely to log, "sweeping changes."  Odd, yes, but
    sometimes true nonetheless.
  * Renamed tex/invdet.tex (Matrix inversion and the determinant) to
    tex/eigen.tex (Inversion and eigenvalue).  Began typesetting the
    chapter, taking it up through the first page or two of the
    eigenvalue treatment, but then lost compositional coherence---lost
    the thread of the narrative, as it were.  Observed that the
    eigenvalue treatment did not flow sufficiently cleanly from what had
    gone before, indicating a need for some changes in what had gone
    before.  Halted for a time to mull the matter, logging this internal
    version to document the stopping point.

 -- Thaddeus H. Black <derivations@b-tk.org>  Sat, 14 Oct 2006 00:00:00 +0000

derivations (0.5.20060926)

  * Did not actually release this version.
  * Linked into the book the three new chapters
    - tex/matrix.tex (The matrix),
    - tex/invdet.tex (Matrix inversion and the determinant), and
    - tex/mtxalg.tex (Matrix algebra).
    Of the three, tentatively finished the first, but did not truly
    start the other two.
  * Because the book had begun to progress beyond its basic first nine
    chapters, advanced the version number to 0.5 (arguably the number
    could have been 1.1 rather than 0.5, but as decided in the
    derivations 0.4.20060804 changelog below, let us not rush that).

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 26 Sep 2006 00:00:00 +0000

derivations (0.4.20060920)

  * (Andreas Jochens and Julian Gilbey) Replaced all instances of the
    LaTeX \scalebox macro with the new \localscalebox, defined in
    tex/def.tex, thus allowing the user building from source to select
    teTeX-2 or teTeX-3 \scalebox syntax as appropriate.  Thanked Andreas
    Jochens for identifying the bug and Julian Gilbey for fixing it.
  * Identified and removed from the book source many commented-out
    passages of text never likely to be used again.
  * In tex/alggeo.tex (Classical algebra and geometry):
    - Explicitly pointed out that 0! == 1.
    - Better motivated the long division procedure.  Appended thereto an
      explanation of why remainders have order one less than divisors.
    - Extended the title of the subsection "Common power-series
      quotients" with "... and the geometric series."
    - Added the new subsection "Variations on the geometric series."
    - Appended to the discussion of roots and poles a brief
      parenthetical note on branch points.
    - Slightly expanded the narrative in the section "Complex
      numbers (introduction)."
  * In tex/trig.tex (Trigonometry), changed the angle symbol beta to psi
    in the "Rotation" section, to avoid confusion with the beta of the
    following section.
  * In tex/cexp.tex (The complex exponential):
    - Rewrote the discussion of the bound on the constant e.  Added
      plots of the natural exponential and the natural logarithm.
    - Replaced the analogy of the mirrored portrait with an analogy of
      reflected handwriting.
    - Corrected the several "d/dz" to "d/dw" in the table "Derivatives
      of the inverse trigonometrics."
  * In tex/noth.tex (Primes, roots and averages):
    - Replaced the entire convoluted contents of the "Polynomial roots"
      subsection with a simpler, much briefer argument to the same
      effect.
    - Slightly shortened and clarified the paragraph on finding roots
      and the Newton-Raphson.
  * In tex/integ.tex (The integral),
    - Reorganized and partly rewrote the chapter's introduction and
      first section.  Added a figure on the trapezoid rule.
    - Added the new section "Checking integrations."
    - Slightly revised the section "Remarks (and exercises)."
  * In tex/taylor.tex (The Taylor series):
    - Slightly reworded some parts of the section "Shifting a power
      series' expansion point."
    - In the section "The multidimensional Taylor series," explicitly
      displayed a few more instances of the k-vector.
  * In tex/inttx.tex (Integration techniques):
    - Clarified the integration checks.
    - Expanded the "Integration by parts" section.
    - Added a little more explanation to the end of the "Method of unknown
      coefficients" section.
    - In the section "Integration by closed contour," explained
      why I_1 + I_3 != 0.  Expanded and clarified the section.
    - In the section "Integration by partial-fraction expansion,"
      replaced a confusing limit with a more precise ratio of equations.
  * Reduced the type size in the book's index.
  * Edited the rest of the book in further, minor ways.
  * Split the two unlinked rough-draft chapters reluctantly into three,
    with the new, middle one being tex/invdet.tex, tentatively
    entitled "Matrix inversion and the determinant."  (The chapter
    tex/matrix.tex, "The matrix," had grown too long comfortably to
    accommodate further material.)
  * Below in this changelog, corrected the incorrect former version
    number (0.1.19891206) to the correct number (0.1.19890714).

 -- Thaddeus H. Black <derivations@b-tk.org>  Wed, 20 Sep 2006 00:00:00 +0000

derivations (0.4.20060804)

  * Advanced the version number to 0.4, observing that the typeset
    manuscript had grown into a concise but entire book.  (The previous
    revision might have been 0.4, too; but the author did not want to
    rush the revolution.  However, the time has come.  Many more
    chapters remain to be added to the book, but the book's basic
    content is all there now.  Arguably, this revision could even be
    numbered 1.0, but, well, let us not rush that.  The number 1.0 can
    afford to wait many years if we want.  The 0.4 will do for the time
    being.)
  * Started a new practice, appropriate now to the manuscript's rising
    overall maturity level, of not linking new, immature material into
    the actual book.  Noted therefore that the tex/ directory can now
    contain source files which the actual book does not yet include.
    Advised developers and others reading the source to review
    tex/main.tex to see which material the book does officially include.
  * Began the new chapters tex/matrix.tex and tex/mtxalg.tex---"The
    Matrix" and "Matrix Algebra," respectively---but in LaTeX source
    form only.  Did not yet link them into the actual book.
  * Throughout the LaTeX source, to improve the quality of the
    typesetting, added TeX tilde ~ ties as practical and appropriate to
    attach in-line variable names and short factors to the preceding
    words, thus preventing most lines of narrative text from beginning
    with a variable name.
  * Rationalized and explained the <- change-of-variable / assignment
    notation.  Corrected several instances where the notation had
    improperly been applied in reverse.
  * In tex/pref.tex (Preface), further slightly refined the rhetoric.
  * In tex/intro.tex (Introduction):
    - Added a pertinent 1924 quote of R. Courant and D. Hilbert.
    - Deleted unnecessary verbiage from the "Complex numbers and complex
      variables" section.
  * In tex/alggeo.tex (Classical algebra and geometry):
    - Added the new subsection "Negative numbers."
    - Added the new subsection "The change of variable."
    - Added the new section "The arithmetic series."
  * Edited most of the chapters and other parts of the book in further,
    minor ways.
  * Warmly welcomed Karl Sarnow and Xplora Knoppix
    [http://www.xplora.org/downloads/Knoppix] aboard as a distributor of
    the book.

 -- Thaddeus H. Black <derivations@b-tk.org>  Fri, 04 Aug 2006 00:00:00 +0000

derivations (0.3.20060607)

  * Reviewed the book line by line, finding and correcting many
    deficiencies.
  * Added the new file tex/sphere.tex, providing not a chapter but
    rather a detailed figure of the sphere and its parts, to be included
    in the book where needed.
  * In tex/pref.tex (Preface), reworded one sentence slightly.
  * In tex/intro.tex (Introduction), added the new section "Complex
    numbers and complex variables."
  * In tex/alggeo.tex (Classical algebra and geometry):
    - Added the new subsection "Negative numbers."
    - Improved the explanation of long division.
    - Distinguished poles from other singularities.
  * In tex/trig.tex (Trigonometry):
    - Added a plot of the sine function.
    - Condensed and clarified the formerly ponderous calculation of the
      trigonometrics of the principal angles.
    - Added the new section "Cylindrical and spherical coordinates."
  * In tex/drvtv.tex (The derivative):
    - Improved the introduction to combinatorics.
    - Added the new subsection "Complex powers of numbers near unity."
    - Contrasted the unbalanced against the balanced definition of the
      derivative.
    - Added the new subsection "The derivative of a function of a
      complex variable."
    - Expanded and slightly renamed the subsection "The derivative
      of z^a."
    - Added the new subsection "The logarithmic derivative."
  * In tex/cexp.tex (The complex exponential):
    - Sharpened the development of Euler's formula.
    - Refined the discussion of Occam's razor and the modeling of wave
      phenomena by complex functions.
  * In tex/noth.tex (Primes, roots and averages), oriented the reader
    subjectively to parallel addition.
  * In tex/integ.tex (The integral):
    - Rendered more precise the presentation of the basic integral
      concept.
    - Correcting an oversight, added a balanced definition of the
      integral to match the balanced definition of the derivative of
      tex/drvtv.tex.
    - Clarified the antiderivative.  Presented the fundamental theorem
      of calculus more explicitly.
    - Added the new section "Areas and volumes."
    - Correcting an oversight, properly introduced the contour
      integration symbol.
    - Added the new section "Discontinuities," presenting the Heaviside
      unit step and the Dirac delta.
  * Substantially rewrote tex/taylor.tex (The Taylor series).
  * In tex/inttx.tex (Integration techniques):
    - Rewrote the chapter's introduction.
    - Highlighted the usefulness of (d/dz) ln(z) as an antiderivative,
      even where z is not a real, positive number.
    - Motivated better the method of unknown coefficients.  Added a
      second example of the method, this time applied to a differential
      equation.
    - Cautioned the reader against enclosing branch points in Cauchy
      contours.
    - Fixed false counter indexing in the method of unknown
      coefficients.
    - Restored a missing coefficient in the pole-separation formula.
    - Added the new section "Integration by Taylor series."
  * In tex/hex.tex (Appendix: Hex and other notational matters), fixed
    some typos and slightly improved the prose in a few spots.
  * In tex/greek.tex (Appendix: The Greek alphabet), identified
    loop-counting variables more precisely.
  * In tex/main.tex, in the copyright and licensing statement,
    changed the word "may" to the more standard "can."
  * Edited the book in many lesser ways not itemized here.
  * Observed here that the book's first nine chapters, through
    tex/inttx.tex (Integration techniques), were now substantially
    complete; and that---although many, many interesting mathematical
    topics remained for the book to treat in coming years---the
    manuscript as it stood finally formed a concise but entire book.
    Noted for historical interest that the book had 212 pages, with nine
    chapters plus appendices, a preface and other such auxiliary parts.

 -- Thaddeus H. Black <derivations@b-tk.org>  Wed, 07 Jun 2006 00:00:00 +0000

derivations (0.3.20060508)

  * In tex/alggeo.tex (Classical algebra and geometry):
    - (Juan Pedro Vallejo) Swapped p and q in the "Power properties and
      definitions" table.
    - Added a table summarizing general properties of the logarithm.
  * In tex/drvtv.tex (The derivative):
    - Slightly clarified the proof of l'Hopital's rule for infinite z_o.
  * In tex/trig.tex (Trigonometry):
    - Slightly refined the "Simple properties of the trigonometric
      functions" table.  Added a new table "Further properties of the
      trigonometric functions."
  * In tex/cexp.tex (The complex exponential):
    - Rewrote the introduction.
    - Somewhat clarified the subjective motivation for Euler's formula.
    - Converted generally to the symbol 'w' as complement of 'z'.
    - Added a formula for the natural logarithm of a complex number.
    - Gave the hyperbolic form of the Pythagorean theorem for
      trigonometrics.
    - Added a table summarizing properties of the complex exponential.
    - Wrote a new section on the derivatives of the various
      trigonometric and inverse trigonometric functions.
  * In tex/noth.tex (Primes, roots and averages):
    - Changed the chapter's title again, this time from "Primes and
      roots".
    - Added a subsection on rational and irrational numbers.
    - Revised the discussion of the fundamental theorem of algebra.
    - Added a new section on parallel addition and averages.
  * In tex/integ.tex (The integral), corrected the notation in the
    antiderivative definition.
  * In tex/taylor.tex (The Taylor series):
    - Added a stub for a future new section, "Taylor series for specific
      functions."
    - Integrated the concept of the nonanalytic point generally into the
      chapter's latter parts.
    - Extended the section "Cauchy's integral formula," and split it
      into subsections.
  * In tex/inttx.tex (Integration techniques):
    - Added an explicit section on integration by antiderivative.
      Generally corrected notation and explanations involving
      antiderivatives.
    - Removed a fallacious example from the "Integration by
      substitution" section.
    - Added new sections on integration by closed contour and by
      partial-fraction expansion.
  * In tex/hist.tex (appendix: Manuscript history):
    - Changed the appendix's title from "Document history".
    - Refined and improved the text generally.
    - Added a footnote on linearity.

 -- Thaddeus H. Black <derivations@b-tk.org>  Mon, 08 May 2006 00:00:00 +0000

derivations (0.3.20060502)

  * Removed a spurious non-source file from the source.
  * Added a period to a figure caption in tex/drvtv.tex (The
    derivative).

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 02 May 2006 00:00:00 +0000

derivations (0.3.20060501)

  * In tex/Makefile, replaced the old LaTeX build commands with a call
    to the Rubber LaTeX build system.
  * Added the new 'check' target to tex/Makefile.
  * Further polished the book's preface in tex/pref.tex.  Added
    observations on the book's relationship to open source culture.
  * In tex/intro.tex (Introduction), moved distracting remarks on
    hexadecimal from the beginning to the end of the chapter.
  * In tex/alggeo.tex (Classical algebra and geometry):
    - Extended the discussion of multiplicative associativity.
    - Renamed the section "One-dimensional quadratics" to the less
      pretentious "Quadratics."
    - Added a footnote explaining the term "order", the
      adjective "quadratic", and related words.
    - Corrected and rewrote the faulty treatment of the division of
      power series.  Added a pair of tables summarizing the long
      division procedure.
  * In tex/drvtv.tex (The derivative):
    - Corrected the misnaming of G.W. Leibnitz.
    - Further clarified the difficult discussion of the Leibnitz
      notation.
    - Added application examples to the treatment of l'Hopital's rule.
  * Inserted the new chapter tex/noth.tex (Primes and roots).
  * In tex/taylor.tex (The Taylor series):
    - In the integrand of the "Cauchy's integral formula" section,
      put "n-1" in place of "n".
    - Generalized the Cauchy integration where relevant to nonintegral
      exponents.
  * Partially filled the stub tex/inttx.tex (Integration techniques)
    with an actual chapter.
  * Edited most of the chapters in other, minor ways.
  * Added to the bibliography, and corrected a few typos therein.
  * Added an index to the book.
  * Closed some dangling references, replacing "[section not yet
    written]" with the appropriate section number.
  * Noted that future routine changes of the kinds of the last three
    bullets (bibliography updates, index updates and reference closures)
    will not normally be chronicled here.

 -- Thaddeus H. Black <derivations@b-tk.org>  Mon, 01 May 2006 00:00:00 +0000

derivations (0.3.20060425)

  * Removed the 'helper' directory and its contents.  (Shifted them to
    the Debian package only, as they are not relevant to non-Debian
    users.)
  * In tex/main.tex:
    - Added the new \verdate macro.
    - Because TeX apparently does not respect local scoping of lengths,
      reserved four TeX length variables \tla, \tlb, \tlc and \tld for
      general use and reuse throughout the book.
    - Rescripted the copyright page correctly to use
      \vspace{\stretch{1}} to force the text to the bottom of the page.
  * Further polished the book's preface in tex/pref.tex.  Added to it
    a brief observation about the book's bibliography.
  * In tex/alggeo.tex (Classical algebra and geometry):
    - Added distributivity to the basic arithmetic properties table.
    - Added a section on multiplying and dividing power series.
    - Removed one footnote on rigor.
  * In tex/trig.tex (Trigonometry), added a new section on the complex
    triangle inequalities.
  * In tex/drvtv.tex (The derivative):
    - Added to the list of combinatorics properties several properties
      relating Pascal's-triangle neighbors of various sorts.
    - Added a new section on extrema and higher derivatives.
  * In tex/cexp.tex, renamed the chapter from "Complex exponentials"
    to "The complex exponential".
  * In tex/integ.tex (The integral), extended the brief stub text to a
    full new chapter.
  * Added the new chapter tex/taylor.tex (The Taylor series).
  * Opened the stub tex/inttx.tex (Integration techniques) for a future
    chapter.
  * In several chapters, changed incorrect references to "Laurent
    series" to correct references to "power series".
  * Edited most of the chapters in other, minor ways.
  * Corrected and extended some old bibliography entries; and added new
    entries.
  * In tex/def.tex, added some new hyphenations.
  * Corrected a misspelling in tex/README.
  * In tex/Makefile, freed the main document build from dependency on
    local template files.

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 25 Apr 2006 00:00:00 +0000

derivations (0.3.20060410)

  * Repackaged the software in non-Debian native form, incrementing the
    minor version number for this reason.
  * Retained all the old changelog entries here.
  * Noted here for clarity that several of the items in
    the (0.2.20051112) changelog entry below do refer to Debian-only
    packaging matters.  Undertook to keep such Debian-only packaging
    matters from this changelog in the future.
  * As far as the book had yet gone (this is, through cexp.tex plus some
    appendices), generally refined and clarified the material already in
    the book.  Especially, clarified the book's development of complex
    numbers and the complex exponential by moving the introduction of
    de Moivre's theorem up to a new section at the end of trig.tex, thus
    logically decoupling de Moivre's theorem from Euler's formula as
    such.
  * Added sections on l'Hopital's rule and the Newton-Raphson iteration
    to drvtv.tex.
  * Began the new integ.tex, a chapter treating the integral.
  * Added \usepackage{amsmath} to main.tex.
  * Changed \usepackage{pstricks} to \usepackage{pst-plot}.
  * Noted here for future historical interest that the book is 90 pages
    long, not counting prefatory matter.  (Not much, but it's a start.)

 -- Thaddeus H. Black <derivations@b-tk.org>  Mon, 10 Apr 2006 00:00:00 +0000

derivations (0.2.20051112)

  * Adhered to Policy 3.6.2.1.
  * Updated the FSF's address in debian/copyright.
  * Corrected the book's text in minor ways.
  * Fixed tex/Makefile to use make(1)'s $(filter-out ()) function
    correctly.
  * Modified, debugged and extended the helper scripts significantly.
  * Added helper/RelSteps.
  * Uploaded the package to Debian's experimental archive for the first
    time (closes: #338520).

 -- Thaddeus H. Black <derivations@b-tk.org>  Sat, 12 Nov 2005 00:00:00 +0000

derivations (0.2.20051110)

  * Typeset part of the book in LaTeX and packaged it for Debian.
  * Noted that much of the version 0.1 hand-printed manuscript remains
    yet to be edited and typeset for this version 0.2.

 -- Thaddeus H. Black <derivations@b-tk.org>  Thu, 10 Nov 2005 00:00:00 +0000

derivations (0.1.20020419)

  * Observed that this changelog entry and the entries below for earlier
    dates were made 4 Nov 2005, not so much as an accurate record of
    changes, but rather as an extremely abbreviated approximate sketch
    of the package's long history.  (The precise dates given are chosen
    more or less randomly, but are probably correct to within two or
    three months.)
  * Added derivations including that of the method for calculating
    electrical resistance to earth ground.

 -- Thaddeus H. Black <derivations@b-tk.org>  Fri, 19 Apr 2002 00:00:00 +0000

derivations (0.1.19960131)

  * Added Fourier transforms and their properties.

 -- Thaddeus H. Black <derivations@b-tk.org>  Wed, 31 Jan 1996 00:00:00 +0000

derivations (0.1.19890714)

  * Misplaced and lost some of the original manuscript (but the ideas
    remain more or less intact in the author's thought, so the loss is
    tolerable).

 -- Thaddeus H. Black <derivations@b-tk.org>  Fri, 14 Jul 1989 00:00:00 +0000

derivations (0.1.19881206)

  * Added the Gaussian distribution and many others.

 -- Thaddeus H. Black <derivations@b-tk.org>  Tue, 06 Dec 1988 00:00:00 +0000

derivations (0.1.19831014)

  * Began the hand-printed manuscript with its first derivations,
    including the Pythagorean theorem.

 -- Thaddeus H. Black <derivations@b-tk.org>  Fri, 14 Oct 1983 00:00:00 +0000

