Understanding Calculus
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簡介
Everything you need to know-basic essential concepts-about calculus
For anyone looking for a readable alternative to the usual unwieldy calculus text, here's a concise, no-nonsense approach to learning calculus. Following up on the highly popular first edition of Understanding Calculus, Professor H. S. Bear offers an expanded, improved edition that will serve the needs of every mathematics and engineering student, or provide an easy-to-use refresher text for engineers.
Understanding Calculus, Second Edition provides in a condensed format all the material covered in the standard two-year calculus course. In addition to the first edition's comprehensive treatment of one-variable calculus, it covers vectors, lines, and planes in space; partial derivatives; line integrals; Green's theorem; and much more. More importantly, it teaches the material in a unique, easy-to-read style that makes calculus fun to learn. By explaining calculus concepts through simple geometric and physical examples rather than formal proofs, Understanding Calculus, Second Edition, makes it easy for anyone to master the essentials of calculus.
If the dry "theorem-and-proof" approach just doesn't work, and the traditional twenty pound calculus textbook is just too much, this book is for you.
目錄
AUTHOR'S MESSAGE TO THE READER vii
ANNOTATED TABLE OF CONTENTS ix
ACKNOWLEDGMENTS xv
CHAPTER 1 Lines 1
CHAPTER 2 Parabolas, Ellipses, Hyperbolas 7
CHAPTER 3 Differentiation 13
CHAPTER 4 Differentiation Formulas 19
CHAPTER 5 The Chain Rule 25
CHAPTER 6 Trigonometric Functions 31
CHAPTER 7 Exponential Functions and Logarithms 39
CHAPTER 8 Inverse Functions 45
CHAPTER 9 Derivatives and Graphs 51
CHAPTER 10 Following the Tangent Line 57
CHAPTER 11 The Indefinite Integral 63
CHAPTER 12 The Definite Integral 69
CHAPTER 13 Work, Volume, and Force 75
CHAPTER 14 Parametric Equations 81
CHAPTER 15 Change of Variable 87
CHAPTER 16 Integrating Rational Functions 91
CHAPTER 17 Integration By Parts 97
CHAPTER 18 Trigonometric Integrals 101
CHAPTER 19 Trigonometric Substitution 107
CHAPTER 20 Numerical Integration 115
CHAPTER 21 Limits At oo; Sequences 119
CHAPTER 22 Improper Integrals 127
CHAPTER 23 Series 133
CHAPTER 24 Power Series 141
CHAPTER 25 Taylor Polynomials 149
CHAPTER 26 Taylor Series 155
CHAPTER 27 Separable Differential Equations 161
CHAPTER 28 First-Order Linear Equations 167
CHAPTER 29 Homogeneous Second-Order Linear Equations 173
CHAPTER 30 Nonhomogeneous Second-Order Equations 179
CHAPTER 31 Vectors 185
CHAPTER 32 The Dot Product 195
CHAPTER 33 Lines and Planes in Space 201
CHAPTER 34 Surfaces 211
CHAPTER 35 Partial Derivatives 217
CHAPTER 36 Tangent Plane and Differential Approximation
CHAPTER 37 Chain Rules 227
CHAPTER 38 Gradient and Directional Derivatives 233
CHAPTER 39 Maxima and Minima 239
CHAPTER 40 Double Integrals 245
CHAPTER 41 Line Integrals 255
CHAPTER 42 Green's Theorem 259
CHAPTER 43 Exact Differentials 267
ANSWERS 273
INDEX 299
ABOUT THE AUTHOR 303
