Calculus Made Easy - Silvanus P. Thompson, F.R.S.
Preface to the 1998 edition
Introductory courses in calculus are now routinely taught to high school students and college freshmen. For students who hope to become mathematicians or to enter professions that require a knowledge of calculus, such courses are the highest hurdle they have to jump.
Studies show that almost half of college freshmen who take a course in calculus fail to pass. Those who fail almost always abandon plans to major in mathematics, physics, or engi- neering-three fields where advanced calculus is essential.
They may even decide against entering such professions as architecture, the behavioral sciences, or the social sciences (especially econom-ics) where calculus can be useful. They exit what they fear will be too difficult a road to consider careers where entrance roads are easier.
One reason for such a high dropout rate is that introductory calculus is so poorly taught. Classes tend to be so boring that stu- dents sometimes fall asleep. Calculus textbooks get fatter and fat-ter every year, with more multi color overlays, computer graphics, and photographs of eminent mathematicians (starting with New- ton and Leibniz), yet they never seem easier to comprehend.
You look through them in vain for simple, clear exposition and for problems that will hook a student's interest. Their exercises have, as one mathematician recently put it, "the dignity of solving crossword puzzles." Modern calculus textbooks often contain more than a thousand pages-heavy enough to make excellent doorstops-and more than a thousand frightening exercises! Their prices are rapidly approaching $100.
Content:
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- Preface to the 1998 Edition 1
- Preliminary Chapters by Martin Gardner
- What Is a Function? 10
- What Is a Limit? 18
- What Is a Derivative? 30
- Calculus Made Easy by Silvanus P. Thompson Publisher's Note on the Third Edition Prologue
- I. To Deliver You from the Preliminary Terrors
- II. On Different Degrees of Smallness
- III. On Relative Growings
- IV. Simplest Cases
- V. Next Stage. What to Do with Constants
- VI. Sums, Differences, Products, and Quotients
- VII. Successive Differentiation
- VIII. When Time Varies
- IX. Introducing a Useful Dodge
- X. Geometrical Meaning of Differentiation
- XI. Maxima and Minima
- XII. Curvature of Curves
- XIII. Partial Fractions and Inverse Functions
- XlV. On True Compound Interest and the Law of Organic Growth
- Xv. How to Deal with Sines and Cosines
- XVI. Partial Differentiation
- XVII. Integration
- XVIII. Integrating as the Reverse of Differentiating
- XIX. On Finding Areas by Integrating
- XX. Dodges, Pitfalls, and Triumphs
- XXI. Finding Solutions
- XXII. A Little More about Curvature of Curves
- XXIII. How to Find the Length of an Arc on a Curve
- Table of Standard Forms
- Epilogue and Apologue
- Answers to Exercises
- Appendix:
- Some Recreational Problems Relating to
- Calculus, by Martin Gardner
- Index
- About the Authors
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