Calculus and Its Applications, 10th Edition

Calculus and Its Applications, Tenth Edition, remains a best-selling text because of its accessible presentation that anticipates student needs. The writing style is ideal for today’s readers, providing intuitive explanations that work with the carefully crafted artwork to help them visualize new calculus concepts. Additionally, the text’s numerous and up-to-date applications from business, economics, life sciences, and social sciences help motivate readers. Algebra diagnostic and review material is available for those who need to strengthen basic skills. Every aspect of this revision is designed to motivate and help readers to more readily understand and apply the mathematics.

Preface

Diagnostic Test

R. Functions, Graphs, and Models

R.1 Graphs and Equations

R.2 Functions and Models

R.3 Finding Domain and Range

R.4 Slope and Linear Functions

R.5 Nonlinear Funtions and Models

R.6 Mathematical Modeling and Curve Fitting

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Average Price of a Movie Ticket

1. Differentiation

1.1 Limits: A Numerical and Graphical Approach

1.2 Algebraic Limits and Continuity

1.3 Average Rates of Change

1.4 Differentiation Using Limits of Difference Quotients

1.5 Differentiation Techniques: The Power and Sum-Difference Rules

1.6 Differentiation Techniques: The Product and Quotient Rules

1.7 The Chain Rule

1.8 Higher-Order Derivatives

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Path of a Baseball: The Tale of the Tape

2. Applications of Differentiation

2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs

2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs

2.3 Graph Sketching: Asymptotes and Rational Functions

2.4 Using Derivatives to Find Absolute Maximum and Minimum Values

2.5 Maximum-Minimum Problems; Business and Economics Applications

2.6 Marginals and Differentials

2.7 Implicit Differentiation and Related Rates

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Maximum Sustainable Harvest

3. Exponential and Logarithmic Functions

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Applications: Uninhibited and Limited Growth Models

3.4 Applications: Decay

3.5 The Derivatives of a^x and log_a^x

3.6 An Economics Application: Elasticity of Demand

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Business: Motion Picture and DVD Revenue

4. Integration

4.1 Antidifferentiation

4.2 Antiderivatives

4.3 Area and Definite Integrals

4.4 Properties of Definite Integrals

4.5 Integration Techniques: Substitution

4.6 Integration Techniques: Integration by Parts

4.7 Integration Techniques: Tables

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Business: Distribution of Wealth

5. Applications of Integration

5.1 An Economics Application: Consumer Surplus and Producer Surplus

5.2 Applications of the Integration of Growth and Decay Models

5.3 Improper Integrals

5.4 Probability

5.5 Probability: Expected Value; The Normal Distribution

5.6 Volume

5.7 Differential Equations

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda

6. Functions of Several Variables

6.1 Functions of Several Variables

6.2 Partial Derivatives

6.3 Maximum-Minimum Problems

6.4 An Application: The Least-Squares Technique

6.5 Constrained Optimization

6.6 Double Integrals

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Minimizing Employees' Travel Time in a Building

Cumulative Review

Appendix A: Review of Basic Algebra

Appendix B: Regression and Microsoft Excel

Appendix C: The TI MathPrint Operating System

Tables

Answers

Index of Applications

Index