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Understanding Calculus, 2nd Edition

H. S. Bear

ISBN: 978-0-471-43307-1 March 2003 Wiley-IEEE Press 320 Pages


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.

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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




"...expands coverage to vectors and calculus of several variables...plenty of worked out problems..." (American Mathematical Monthly, August/September 2003)

"...material included is well formulated and approachable...recommended." (Choice, Vol. 41, No. 1, September 2003)