Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition

by HOFFMANN

• ISBN13: 9780073229799
• ISBN10: 0073229792
• Edition: 9th
• Format: Hardcover
• Copyright: 2005-12-16
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition introduces calculus in real-world contexts and provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, the life sciences, and the social sciences. This EXPANDED EDITION includes four additional chapters on Differential Equations, Infinite Series and Taylor Approximations, Probability, and Trigonometric Functions. The new Ninth Edition builds on the straightforward writing style, practical applications from a variety of disciplines, clear step-by-step problem solving techniques, and comprehensive exercise sets that have been hallmarks of Hoffmann/Bradley's success through the years.

Table of Contents

Preface

Calculator Introduction

1 Functions, Graphs, and Limits

1.1 Functions

1.2 The Graph of a Function

1.3 Linear Functions

1.4 Functional Models

1.5 Limits

1.6 One-Sided Limits and Continuity

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 1

Review Problems

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2 Differentiation: Basic Concepts

2.1 The Derivative

2.2 Techniques of Differentiation

2.3 Product and Quotient Rules; Higher Order Derivatives

2.4 The Chain Rule

2.5 Marginal Analysis and Approximations Using Increments

2.6 Implicit Differentiation and Related Rates

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 2

Review Problems

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3 Additional Applications of the Derivative

3.1 Increasing and Decreasing Functions; Relative Extrema

3.2 Concavity and Points of Inflection

3.3 Curve Sketching

3.4 Optimization

3.5 Additional Applied Optimization

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 3

Review Problems

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4 Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Differentiation of Logarithmic and Exponential Functions

4.4 Additional Exponential Models

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 4

Review Problems

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5 Integration

5.1 Antidifferentiation: The Indefinite Integral

5.2 Integration by Substitution

5.3 The Definite Integral and the Fundamental Theorem of Calculus

5.4 Applying Definite Integration: Area Between Curves and Average Value

5.5 Additional Applications to Business and Economics

5.6 Additional Applications to the Life and Social Sciences

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 5

Review Problems

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6 Additional Topics in Integration

6.1 Integration by Parts; Integral Tables

6.2 Improper Integrals

6.3 Numerical Integration

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 6

Review Problems

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7 Calculus of Several Variables

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Two Variables

7.4 The Method of Least-Squares

7.5 Constrained Optimization: The Method of Lagrange Multipliers

7.6 Double Integrals

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 7

Review Problems

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8 Differential Equations

8.1 Introduction to Differential Equations

8.2 First-Order Linear Differential Equations

8.3 Additional Applications of Differential Equations

8.4 Approximate Solutions of Differential Equations

8.5 Difference Equations

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 8

Review Problems

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9 Infinite Series and Taylor Series Approximations

9.1 Infinite Series; Geometric Series

9.2 Tests for Convergence

9.3 Functions as Power Series; Taylor Series

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 9

Review Problems

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10 Probability and Calculus

10.1 Discrete Random Variables

10.2 Continuous Random Variables

10.3 Expected Value and Variance of Continuous Random Variables

10.4 Normal and Poisson Probability Distributions

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 10

Review Problems

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11 Trigonometric Functions

11.1 The Trigonometric Functions

11.2 Differentiation and Integration of Trigonometric Functions

11.3 Additional Applications Involving Trigonometric Functions

Chapter Summary

Important Terms, Symbols, and Formulas

Checkup for Chapter 11

Review Problems

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Appendix A: Algebra Review

A.1 A Brief Review of Algebra

A.2 Factoring Polynomials and Solving Systems of Equations

A.3 Evaluating Limits with L'Hpital's Rule

Appendix Summary

Important Terms, Symbols, and Formulas

Review Problems

Think About It

Tables

I Powers of e

II The Natural Logarithm (Base e)

III Trigonometric Functions

Text Solutions

Answers to Odd-Numbered Problems, Chapter Checkup Problems, and Chapter Review Problems

Index