9780130873033

Brief Calculus and Its Applications

by ; ;
  • ISBN13:

    9780130873033

  • ISBN10:

    0130873039

  • Edition: 9th
  • Format: Paperback
  • Copyright: 7/1/2000
  • Publisher: PRENTICE HALL
  • View Upgraded Edition

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Summary

Improved from previous editions based on reader suggestions, but focused on the same goals: to begin the calculus as soon as possible, present it in an intuitive and intellectually satisfying way, and to illustrate the many application of calculus to social, biological, and management sciences. Previous edition: c1999. DLC: Calculus.

Table of Contents

Preface ix
Introduction 1(2)
Functions
3(67)
Functions and Their Graphs
3(15)
Some Important Functions
18(9)
The Algebra of Functions
27(7)
Zeros of Functions---The Quadratic Formula and Factoring
34(8)
Exponents and Power Functions
42(7)
Functions and Graphs in Applications
49(21)
Graphing Functions Using Technology
62(6)
Chapter Project
68(2)
The Derivative
70(74)
The Slope of a Straight Line
72(11)
The Slope of a Curve at a Point
83(6)
The Derivative
89(12)
Limits and the Derivative
101(10)
Differentiability and Continuity
111(5)
Some Rules for Differentiation
116(7)
More About Derivatives
123(5)
The Derivative as a Rate of Change
128(16)
Chapter Project
143(1)
Applications of the Derivative
144(70)
Describing Graphs of Functions
144(12)
The First and Second Derivative Rules
156(10)
Curve Sketching (Introduction)
166(7)
Curve Sketching (Conclusion)
173(7)
Optimization Problems
180(9)
Further Optimization Problems
189(9)
Applications of Derivatives to Business and Economics
198(16)
Chapter Project
213(1)
Techniques of Differentiation
214(29)
The Product and Quotient Rules
214(8)
The Chain Rule and the General Power Rule
222(6)
Implicit Differentiation and Related Rates
228(15)
Chapter Project
242(1)
The Exponential and Natural Logarithm Functions
243(31)
Exponential Functions
243(4)
The Exponential Function ex
247(5)
Differentiation of Exponential Functions
252(5)
The Natural Logarithm Function
257(5)
The Derivative of ln x
262(4)
Properties of the Natural Logarithm Function
266(8)
Chapter Project
272(2)
Applications of the Exponential and Natural Logarithm Functions
274(39)
Exponential Growth and Decay
274(10)
Compound Interest
284(8)
Applications of the Natural Logarithm Function to Economics
292(6)
Further Exponential Models
298(15)
Chapter Project
312(1)
The Definite Integral
313(76)
Antidifferentiation
314(9)
Areas and Riemann Sums
323(9)
Definite Integrals and the Fundamental Theorem
332(12)
Areas in the xy-Plane
344(10)
Applications of the Definite Integral
354(9)
Techniques of Integration
363(9)
Improper Integrals
372(7)
Applications of Calculus to Probability
379(10)
Chapter Project
388(1)
Functions of Several Variables
389(63)
Examples of Functions of Several Variables
389(7)
Partial Derivatives
396(9)
Maxima and Minima of Functions of Several Variables
405(8)
Lagrange Multipliers and Constrained Optimization
413(11)
The Method of Least Squares
424(7)
Nonlinear Regression
431(12)
Double Integrals
443(9)
Chapter Project
451(1)
The Trigonometric Functions
452(1)
Radian Measure of Angles
452(4)
The Sine and the Cosine
456(8)
Differentiation and Integration of sin t and cos t
464(10)
The Tangent and Other Trigonometric Functions
474(7)
Chapter Project
481
Appendix A: Calculus and the TI-82 Calculator A1
Appendix B: Calculus and the TI-83/TI-83 Plus Calculators A5
Appendix C: Calculus and the TI-85 Calculator A9
Appendix D: Calculus and the TI-86 Calculator A13
Answers to Exercises A19
Index I1

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