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Applied Calculus

Applied Calculus - 2nd edition

Applied Calculus - 2nd edition

ISBN13: 9780395978177

ISBN10: 0395978173

Applied Calculus by Geoffrey C. Berresford and Andrew M. Rockett - ISBN 9780395978177
Edition: 2ND 00
Copyright: 2000
Publisher: Houghton Mifflin Harcourt
International: No
Applied Calculus by Geoffrey C. Berresford and Andrew M. Rockett - ISBN 9780395978177

ISBN13: 9780395978177

ISBN10: 0395978173

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The hallmark of this popular text for the two-semester applied or business calculus course is its ability to engage students with a wealth of intriguing real-world applications.

Retaining the strengths of its first edition, Applied Calculus, 2/e, features updated optional graphing calculator coverage. In addition, project and essay questions previously found at the end of each chapter are now incorporated into the section exercise sets.

  • New! Updated calculator references, which remain optional, apply to the TI-83 calculator and, where appropriate, the TI-89. Berresford's thoughtful integration of technology includes boxed Graphing Calculator Explorations and Exercises that examine new topics, carry out complex calculations, or show the limitations and pitfalls of technology.
  • Application Previews introducing most sections offer in-depth, real-life applications that anticipate the section material.
  • Contemporary and interesting applications are selected from such wide-ranging fields as athletics, biomedical and environmental sciences, management and business, personal finance and management, social and behavioral sciences, and other topics of general interest.
  • Unique Section Summaries reinforce students' understanding by restating essential formulas and key concepts.
  • Chapter Summary with Hints and Suggestions provide review and specific reminders, with references to relevant practice exercises.
  • Practice Problems follow the more difficult worked-out examples, giving students an extra chance to assimilate the material.
  • Full solutions are included at the back of the book.
  • Applications and exercises are graded according to difficulty. Applied Exercises are clearly labeled to highlight content and relevance. Projects and Essays, promoting writing and collaborative work, have been moved to section exercise sets.
  • Review Exercises following each chapter are accompanied by suggestions for compiling student practice tests. Cumulative Review Exercises at the conclusion of chapter groups reinforce previously learned concepts.

Table of Contents

Table of Contents

Preliminary Contents
Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises.

1. Functions

1.1 Real Numbers, Inequalities, and Lines
1.2 Exponents
1.3 Functions
1.4 Functions, Continued

2. Derivatives and Their Uses

2.1 Limits and Continuity
2.2 Slopes, Rates of Change, and Derivatives
2.3 Some Differentiation Formulas
2.4 The Product and Quotient Rules
2.5 Higher-Order Derivatives
2.6 The Chain Rule and the Generalized Power Rule
2.7 Nondifferentiable Functions

3. Further Applications of The Derivative

3.1 Graphing Using the First Derivative
3.2 Graphing Using the First and Second Derivatives
3.3 Optimization
3.4 Further Applications of Optimization
3.5 Optimizing Lost Size and harvest Size
3.6 Implicit Differentiation and Related Rates
Cumulative Review for Chapters 1-3

4. Exponential and Logarithmic Functions

4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Differentiation of Logarithmic and Exponential Functions
4.4 Two Applications to Economics: Relative Rates and Elasticity of Demand

5. Integration and Its Applications

5.1 Antiderivatives
5.2 Integration Using Logarithmic and Exponential Functions
5.3 Definite Integrals and Areas
5.4 Further Applications of Definite Integrals: Average Value and Area Between Curves
5.5 Two Applications to Economics: Consumers' Surplus and Income Distribution
5.6 Integration by Substitution

6. Integration Techniques

6.1 Integration by Parts
6.2 Integration Using Tables
6.3 Improper Integrals
6.4 Numerical Integration

7. Calculus of Several Variables

7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Several Variables
7.4 Least Squares
7.5 Lagrange Multipliers and Constrained optimization
7.6 Total Differentials and Approximate Changes
7.7 Multiple Integrals
Cumulative Review for Chapters 1-7

8. Trigonometric Functions

8.1 Angles, Triangles, and Radian Measure
8.2 Sine and Cosine Functions
8.3 Derivatives of Sine and Cosine Functions
8.4 Integrals of Sine and Cosine Functions
8.5 Other Trigonometric Functions

9. Differential Equations

9.1 Separation of Variables
9.2 Further Applications of Differential Equations: Three Models of Growth
9.3 First-Order Differential Equations
9.4 Approximate Solutions of Differential Equations: Euler's Method

10. Sequences and Series

10.1 Geometric Series
10.2 Taylor Polynomials
10.3 Taylor Series
10.4 Newton's Method

11. Probability

11.1 Discrete Probability
11.2 Continuous Probability
11.3 Uniform and Exponential Random Variables
11.4 Normal Random Variables
Cumulative Review for Chapters 1-11

Appendix Normal Probabilities from Tables
Solutions to Practice Problems
Answers to Selected Exercises