Quick Calculus: A Self–Teaching Guide, Third Editi on: Wiley Self-Teaching Guides

Daniel KLEPPNER is the Lester Wolfe Professor of Physics at MIT. He was awarded the National Medal of Science and the Oersted Medal of the American Association of Physics Teachers. peter DOURMASHKIN is Senior Lecturer at MIT. The late Norman RAMSEY was the Higgins Professor of Physics at Harvard University and the recipient of the 1989 Nobel Prize in Physics.

Preface iii Chapter One Starting Out 1 1.1 A Few Preliminaries 1 1.2 Functions 2 1.3 Graphs 5 1.4 Linear and Quadratic Functions 11 1.5 Angles and Their Measurements 19 1.6 Trigonometry 28 1.7 Exponentials and Logarithms 42 Summary of Chapter 1 51 Chapter Two Differential Calculus 57 2.1 The Limit of a Function 57 2.2 Velocity 71 2.3 Derivatives 83 2.4 Graphs of Functions and Their Derivatives 87 2.5 Differentiation 97 2.6 Some Rules for Differentiation 103 2.7 Differentiating Trigonometric Functions 114 2.8 Differentiating Logarithms and Exponentials 121 2.9 Higher-Order Derivatives 130 2.10 Maxima and Minima 134 2.11 Differentials 143 2.12 A Short Review and Some Problems 147 Conclusion to Chapter 2 164 Summary of Chapter 2 165 Chapter Three Integral Calculus 169 3.1 Antiderivative, Integration, and the Indefinite Integral 170 3.2 Some Techniques of Integration 174 3.3 Area Under a Curve and the Definite Integral 182 3.4 Some Applications of Integration 201 3.5 Multiple Integrals 211 Conclusion to Chapter 3 219 Summary of Chapter 3 219 Chapter Four Advanced Topics: Taylor Series, Numerical Integration, and Differential Equations 223 4.1 Taylor Series 223 4.2 Numerical Integration 232 4.3 Differential Equations 235 4.4 Additional Problems for Chapter 4 244 Summary of Chapter 4 248 Conclusion (frame 449) 250 Appendix A Derivations 251 A.1 Trigonometric Functions of Sums of Angles 251 A.2 Some Theorems on Limits 252 A.3 Exponential Function 254 A.4 Proof That dy/dx = 1/dx/dy 255 A.5 Differentiating X¯n 256 A.6 Differentiating Trigonometric Functions 258 A.7 Differentiating the Product of Two Functions 258 A.8 Chain Rule for Differentiating 259 A.9 Differentiating Ln X 259 A.10 Differentials When Both Variables Depend on a Third Variable 260 A.11 Proof That if Two Functions Have the Same Derivative They Differ Only by a Constant 261 A.12 Limits Involving Trigonometric Functions 261 Appendix B Additional Topics in Differential Calculus 263 B.1 Implicit Differentiation 263 B.2 Differentiating the Inverse Trigonometric Functions 264 B.3 Partial Derivatives 267 B.4 Radial Acceleration in Circular Motion 269 B.5 Resources for Further Study 270 Frame Problems Answers 273 Answers to Selected Problems from the Text 273 Review Problems 277 Chapter 1 277 Chapter 2 278 Chapter 3 282 Tables 287 Table 1: Derivatives 287 Table 2: Integrals 288 Indexes 291 Index 291 Index of Symbols 295