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CALCULUS MADE EASY BEING A VERY-SIMPLEST INTRODUCTION TO THOSE BEAUTIFUL METHODS OF RECKONING WHICH ARE GENERALLY CALLED BY THE TERRIFYING NAMES OF THE DIFFERENTIAL CALCULUS AND THE INTEGRAL CALCULUS. Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics and they are mostly clever fools seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can. Contents: 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. Other Useful Dodges XIV. 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 some Solutions Table of Standard Forms Answers to Exercises
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CALCULUS MADE EASY BEING A VERY-SIMPLEST INTRODUCTION TO THOSE BEAUTIFUL METHODS OF RECKONING WHICH ARE GENERALLY CALLED BY THE TERRIFYING NAMES OF THE DIFFERENTIAL CALCULUS AND THE INTEGRAL CALCULUS. Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics and they are mostly clever fools seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can. Contents: 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. Other Useful Dodges XIV. 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 some Solutions Table of Standard Forms Answers to Exercises
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