Brief Calculus : The Study of Rates of Change

by Armstrong, Bill; Davis, Donald E.

• ISBN13: 9780137549047
• ISBN10: 0137549040
• Format: Hardcover
• Copyright: 1999-12-01
• Publisher: Pearson College Div

Summary

This is the first post-reform calculus book that emphasizes applications and innovative approaches while preserving the underlying mathematics. Rich and varied, the abundant applications that use real data motivate the mathematics and underscore the importance of mathematical underpinnings. The graphing calculator and applications that use data on the World Wide Web are integrated as optional resources to support mathematical ideas, techniques, and applications. The informal tone and abundance and variety of elementary and moderately difficult problems make this book the ideal choice for math anxious people. Chapter 1 reviews functions and provides a solid foundation for the idea that the average rate of change over an interval is equivalent to the slope of the secant line. Introduction of limits at infinity and infinite limits. Strong introduction of the differential. This book devotes two sections to the difficult concept of optimization. For those working in a non-math field, who need/want to learn calculus.

Table of Contents

Preface	p. viii
Functions, Models, and Average Rate of Change	p. 1
The Coordinate System and Functions	p. 2
Linear Functions and Average Rate of Change	p. 13
Quadratic Functions and Average Rate of Change on an Interval	p. 31
Operations on Functions	p. 41
Rational, Radical, and Power Functions	p. 55
Exponential Functions	p. 69
Logarithmic Functions	p. 82
Regression and Mathematical Models	p. 92
Chapter Review Exercises	p. 104
Limits, Instantaneous Rate of Change, and the Derivative	p. 111
Limits	p. 112
Limits and Asymptotes	p. 124
Instantaneous Rate of Change and the Derivative	p. 136
Derivatives of Constants, Powers, and Sums	p. 151
Derivatives of Products and Quotients	p. 164
Continuity and Nondifferentiability	p. 173
Chapter Review Exercises	p. 183
Applications of the Derivative	p. 189
The Differential and Linear Approximations	p. 190
Marginal Analysis	p. 198
Measuring Rates and Errors	p. 208
Chapter Review Exercises	p. 217
Additional Differentiation Techniques	p. 223
The Chain Rule	p. 224
Derivatives of Logarithmic Functions	p. 233
Derivatives of Exponential Functions	p. 240
Implicit Differentiation and Related Rates	p. 249
Elasticity of Demand	p. 261
Chapter Review Exercises	p. 271
Further Applications of the Derivative	p. 275
First Derivatives and Graphs	p. 276
Second Derivatives and Graphs	p. 291
Graphical Analysis and Curve Sketching	p. 305
Optimizing Functions on a Closed Interval	p. 317
The Second Derivative Test and Optimization	p. 331
Chapter Review Exercises	p. 344
Integral Calculus	p. 351
The Indefinite Integral	p. 352
Area and the Definite Integral	p. 364
Fundamental Theorem of Calculus	p. 376
Integration by u-Substitution	p. 386
Integrals That Yield Logarithmic and Exponential Functions	p. 396
Differential Equations: Separation of Variables	p. 407
Differential Equations: Growth and Decay	p. 417
Chapter Review Exercises	p. 431
Applications of Integral Calculus	p. 437
Average Value of a Function and the Definite Integral in Finance	p. 438
Area between Curves and Applications	p. 451
Economic Applications of Area between Curves	p. 464
Integration by Parts	p. 479
Numerical Integration	p. 491
Improper Integrals	p. 503
Chapter Review Exercises	p. 515
Calculus of Several Variables	p. 521
Functions of Several Independent Variables	p. 522
Level Curves, Contour Maps, and Cross-sectional Analysis	p. 534
Partial Derivatives and Second-order Partial Derivatives	p. 547
Maxima and Minima	p. 560
Lagrange Multipliers	p. 571
Double Integrals	p. 584
Chapter Review Exercises	p. 597
Appendices	p. 603
Essentials of Algebra	p. 604
Calculator Programs	p. 609
Selected Proofs	p. 614
Photo and Illustration Credits	p. 622
Answers	p. 1
Index	p. 1
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