Calculus Made Easy

Silvanus Phillips Thompson, 1914. Macmillan, 2nd ed., 1914

Provenance and licence

Text: Project Gutenberg eBook #33283, released October 9, 2012. The transcription's licence, as it states it:

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Chapters

Preface to the Second Edition 3 excerpts, 0 equations, 0 problems
Prologue 6 excerpts, 0 equations, 0 problems
To deliver you from the Preliminary Terrors 8 excerpts, 0 equations, 0 problems
On Different Degrees of Smallness 9 excerpts, 1 equations, 0 problems
On Relative Growings 10 excerpts, 8 equations, 0 problems
Simplest Cases 8 excerpts, 7 equations, 10 problems
Next Stage. What to do with Constants 9 excerpts, 13 equations, 20 problems
Sums, Differences, Products and Quotients 9 excerpts, 7 equations, 20 problems
Successive Differentiation 7 excerpts, 21 equations, 7 problems
When Time Varies 13 excerpts, 10 equations, 17 problems
Introducing a Useful Dodge 6 excerpts, 21 equations, 12 problems
Geometrical Meaning of Differentiation 10 excerpts, 8 equations, 15 problems
Maxima and Minima 12 excerpts, 39 equations, 20 problems
Curvature of Curves 9 excerpts, 8 equations, 22 problems
Other Useful Dodges 10 excerpts, 11 equations, 18 problems
On true Compound Interest and the Law of Organic Growth 10 excerpts, 32 equations, 39 problems
How to deal with Sines and Cosines 7 excerpts, 20 equations, 28 problems
Partial Differentiation 11 excerpts, 43 equations, 24 problems
Integration 11 excerpts, 11 equations, 6 problems
Integrating as the Reverse of Differentiating 13 excerpts, 28 equations, 18 problems
On Finding Areas by Integrating 13 excerpts, 28 equations, 27 problems
Dodges, Pitfalls, and Triumphs 9 excerpts, 7 equations, 14 problems
Finding some Solutions 13 excerpts, 40 equations, 0 problems
Epilogue and Apologue 8 excerpts, 0 equations, 0 problems
Table of Standard Forms 6 excerpts, 38 equations, 0 problems

Index of terms 210 terms, by chapter

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Errata (43)

T001: , p. 25
Printed: .
Corrected:
In the source: em{(7)} $u = \sqrt[5]{\dfrac{1}{x^8}}$ \Item{(8)} $y = 2x^a$
spacing-or-punctuation
Marked by Project Gutenberg's proofreaders in the transcription.
T002: , p. 27
Printed: proceding
Corrected: proceeding
In the source: as a simple experiment this case: Let $y = 7x^2$. \\ Then on
content
Marked by Project Gutenberg's proofreaders in the transcription.
T003: , p. 44
Printed: 3
Corrected: t^3
In the source: \dfrac{4a}{\sqrt[3]{t}} - 9a \sqrt[2]{t}} {6(1 + a \sqrt[2]{
content
Marked by Project Gutenberg's proofreaders in the transcription.
T004: , p. 48
Printed:
Corrected: -
In the source: s. Find an expression for the variation of the electromotive
content
Marked by Project Gutenberg's proofreaders in the transcription.
T005: , p. 59
Printed:
Corrected: ,
In the source: in{center} \begin{tabular}{l@{\qquad\qquad}l} distance & $x$
spacing-or-punctuation
Marked by Project Gutenberg's proofreaders in the transcription.
T006: , p. 61
Printed: 4
Corrected: .4
In the source: gan moving, let $v = 0$; then $0.4t + 3 = 0$, $t= -\frac{3}{
spacing-or-punctuation
Marked by Project Gutenberg's proofreaders in the transcription.
T007: , p. 70
Printed: exercise
Corrected: example
In the source: ate as a product.) \DPPageSep{082.png}{70}% Proceeding as in
content
Marked by Project Gutenberg's proofreaders in the transcription.
T008: , p. 70
Printed: exercise
Corrected: example
In the source: her*} Differentiating $(1+x^2)^{-\efrac{1}{2}}$, as shown in
content
Marked by Project Gutenberg's proofreaders in the transcription.
T009: , p. 75
Printed: =
Corrected: -
In the source: c{1-\theta}{1+\theta}};\quad \text{and}\quad \phi = \sqrt{3}
content
Marked by Project Gutenberg's proofreaders in the transcription.
T010: , p. 86
Printed:
Corrected: ,
In the source: ray} \] Then plot them out in two curves, \Figs{23}{and}{24}
spacing-or-punctuation
Marked by Project Gutenberg's proofreaders in the transcription.
T011: , p. 107
Printed: (2x - 5)^2
Corrected: (2x - 4)^2
In the source: = 0 \] for maximum or minimum; or \[ \dfrac{2x^2 - 8x + 10}{
content
Marked by Project Gutenberg's proofreaders in the transcription.
T012: , p. 107
Printed: .55
Corrected: (.5)^5
In the source: \sqrt[2]{-(.5)^5}$, and if $x = +0.5$, $y = 0.25 ± \sqrt[2]{
content
Marked by Project Gutenberg's proofreaders in the transcription.
T013: , p. 115
Printed: \dfrac{dx}{dy}
Corrected: \dfrac{dy}{dx}
In the source: s~$+$; hence it is a minimum.} \\ % \text{(\textit{b})}\quad
content
Marked by Project Gutenberg's proofreaders in the transcription.
T014: , p. 136
Printed: 2.59375
Corrected: 2.59374
In the source: ctor ten times over) will multiply the original capital by~$
content
Marked by Project Gutenberg's proofreaders in the transcription.
T015: , p. 136
Printed: 2.654
Corrected: 2.653
In the source: extit{s}.~$7$\textit{d}.}; for \[ (1 + \tfrac{1}{20})^{20} =
content
Marked by Project Gutenberg's proofreaders in the transcription.
T016: , p. 139
Printed: 2.593
Corrected: 2.594
In the source: be \DPPageSep{151.png}{139}% $(1 + \tfrac{1}{10})^{10}$ or $
content
Marked by Project Gutenberg's proofreaders in the transcription.
T017: , p. 140
Printed: 2.489
Corrected: 2.488
In the source: )^2 &&= 2.25. \\ &(1 + \tfrac{1}{5})^5 &&=
content
Marked by Project Gutenberg's proofreaders in the transcription.
T018: , p. 140
Printed: 2.704
Corrected: 2.705
In the source: })^{20} &&= 2.653. \\ &(1 + \tfrac{1}{100})^{100} &&=
content
Marked by Project Gutenberg's proofreaders in the transcription.
T019: , p. 140
Printed: 2.7171
Corrected: 2.7169
In the source: \DPtypo{2.704}{2.705}. \\ &(1 + \tfrac{1}{1000})^{1000} &&=
content
Marked by Project Gutenberg's proofreaders in the transcription.
T020: , p. 140
Printed: 2.7182
Corrected: 2.7181
In the source: po{2.7171}{2.7169}. \\ &(1 + \tfrac{1}{10,000})^{10,000} &&=
content
Marked by Project Gutenberg's proofreaders in the transcription.
T021: , p. 146
Printed: 7.69
Corrected: 7.39
In the source: c]{1} & \Td[l]{1.65} & \Td[l]{2.71} & \Td[l]{4.50} & \Td[l]{
content
Marked by Project Gutenberg's proofreaders in the transcription.
T022: , p. 147
Printed: 7.6010
Corrected: 7.6009
In the source: \\ 3.0 & 1.0986 && 1,000 & 6.9078 \\ 3.5 & 1.2528 && 2,000 &
content
Marked by Project Gutenberg's proofreaders in the transcription.
T023: , p. 147
Printed: 9.2104
Corrected: 9.2103
In the source: \ 4.0 & 1.3863 && 5,000 & 8.5172 \\ 4.5 & 1.5041 && 10,000 &
content
Marked by Project Gutenberg's proofreaders in the transcription.
T024: , p. 151
Printed: (x^2+)a
Corrected: (x^2+a)
In the source: }}};\quad \frac{dv}{dx} = 2x;\quad \frac{du}{dx} = \frac{x}{
content
Marked by Project Gutenberg's proofreaders in the transcription.
T025: , p. 159
Printed: 5.754
Corrected: 5.755
In the source: 0.7135 \\ 1.50 & 4.4817 & 0.2231 & 0.7769 \\ 1.75 &
content
Marked by Project Gutenberg's proofreaders in the transcription.
T026: , p. 159
Printed: 12.183
Corrected: 12.182
In the source: 0.8262 \\ 2.00 & 7.389 & 0.1353 & 0.8647 \\ 2.50 &
content
Marked by Project Gutenberg's proofreaders in the transcription.
T027: , p. 159
Printed: 20.085
Corrected: 20.086
In the source: & \DPtypo{12.183}{12.182} & 0.0821 & 0.9179 \\ 3.00 &
content
Marked by Project Gutenberg's proofreaders in the transcription.
T028: , p. 159
Printed: 0.00053
Corrected: 0.00055
In the source: \\ 6.00 & 403.43 & 0.00248 & 0.99752 \\ 7.50 & 1808.04 &
content
Marked by Project Gutenberg's proofreaders in the transcription.
T029: , p. 162
Printed: 34.5
Corrected: 34.7
In the source: frac{\DPchg{\overset{-}{1}.6990}{-0.3010}}{-0.02 × 0.4343} =
content
Marked by Project Gutenberg's proofreaders in the transcription.
T030: , p. 170
Printed: \cos \theta
Corrected: \sin \theta
In the source: ta$ it becomes $-\sin \theta$; or, in symbols, \[ \frac{d^2(
content
Marked by Project Gutenberg's proofreaders in the transcription.
T031: , p. 171
Printed:
Corrected: .
In the source: {1}{\sqrt{1-x^2}}, \end{DPalign*} a rather unexpected result
spacing-or-punctuation
Marked by Project Gutenberg's proofreaders in the transcription.
T032: , p. 173
Printed:
Corrected: (
In the source: ec^2 \theta; \\ % \lintertext{hence} \frac{dv}{d\theta} &= 6
content
Marked by Project Gutenberg's proofreaders in the transcription.
T033: , p. 202
Printed: 2\cos 2\theta - 1
Corrected: 2\cos^2 \theta - 1
In the source: {DPgather*} \cos 2\theta = \cos^2\theta - \sin^2\theta =
content
Marked by Project Gutenberg's proofreaders in the transcription.
T034: , p. 202
Printed: \cos^2 \theta + 1
Corrected: \cos 2\theta + 1
In the source: eta - 1}; \\ \lintertext{hence} \cos^2\theta = \tfrac{1}{2}(
content
Marked by Project Gutenberg's proofreaders in the transcription.
T035: , p. 254
Printed: -\efrac{8}{5}
Corrected: -\efrac{8}{3}
In the source: efrac{2}{3}}$. \Item{(6)} $\dfrac{dy}{dx} = -\dfrac{5}{3}x^{
content
Marked by Project Gutenberg's proofreaders in the transcription.
T036: , p. 255
Printed: 0.000828
Corrected: 0.001024
In the source: \dfrac{R^2 (a + 2bt)}{R_0}$. \Item{(13)} $1.4340(0.000014t -
content
Marked by Project Gutenberg's proofreaders in the transcription.
T037: , p. 256
Printed:
Corrected: .
In the source: c{18b \sqrt[3]{a}}{x^4} - \dfrac{3a \sqrt{b}}{4 \sqrt{x^3}}$
spacing-or-punctuation
Marked by Project Gutenberg's proofreaders in the transcription.
T038: , p. 264
Printed: e
Corrected: \epsilon
In the source: _\epsilon x - \dfrac{1}{a + 1}\right) + C$. \Item{(4)} $\sin
content
Marked by Project Gutenberg's proofreaders in the transcription.
T039: , p. 264
Printed: e
Corrected: \epsilon
In the source: Cols{2} \Item{(5)} $\sin(\log_\epsilon x) + C$. \Item{(6)} $
content
Marked by Project Gutenberg's proofreaders in the transcription.
F001: Answers to Exercises III, item (12), third formula: the alternative form, p. 255
Printed: \dfrac{R^2 (a + 2bt)}{R_0}
Corrected: -\dfrac{R^2 (a + 2bt)}{R_0}
content (sign)
Confirmed: found by computation and read against the printed page.
Under the book's own relation R = R_0/(1 + at + bt^2), the printed alternative equals +R_0(a + 2bt)/(1 + at + bt^2)^2, the main answer with its sign lost. Numeric check at seeded rational points, 50 digits (our answer checker, verdict PASS-ALT-ERRATUM on record III.12 part 3); confirmed by hand algebra (a reviewer).
C001: Answers to Exercises XII, item (14): the minimum
Printed: x = 0.694
Corrected: x = 0.693
content (last digit)
Candidate: reported, not yet confirmed.
Status: to be checked by the judge at set XII. 3^(-1/3) = 0.693361..., 0.693 at the printed digits; the STU-32 core and mpmath agree (the lesson checker's acceptance run). y = 0.7 is right.
C002: Answers to Exercises VII, item (1)
Printed: \dfrac{dw}{dx} = \dfrac{3x^2 (3 + 3x^3)}{27 (\frac{1}{2} x^3 + \frac{1}{4} x^6)^3}
Corrected: \dfrac{dw}{dx} = -\dfrac{3x^2 (3 + 3x^3)}{27 (\frac{1}{2} x^3 + \frac{1}{4} x^6)^3}
content (sign)
Candidate: reported, not yet confirmed.
Status: found by the pilot's judge; awaiting review. w = 1/v^2 with v = 3(u + u^2), u = x^3/2, so dw/dx = -2 v^-3 dv/dx: negative where the printed answer is positive. The judge's values at a seeded point are exactly opposite (-1023.988... against +1023.988...). The extractor flagged it in its notes before the judge ran.
C003: Exercises XII, item (5), and its answer
Printed: problem: w = p n^v, find dw/dv; answer: n p v^{n-1}
Corrected: either the answer p n^v log_e n, or the problem w = p v^n
content (problem and answer do not match)
Candidate: reported, not yet confirmed.
Status: found by the pilot's judge; awaiting review. n p v^(n-1) is the derivative of p v^n, not of p n^v (whose derivative is p n^v ln n). The judge's values disagree at seeded points (3.8659... against 6.9563...). Which of the two lines is misprinted cannot be told from the text alone.