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

Chapter 1: Functions, Graphs, and Limits

1.1 Functions

1.2 The Graph of a Function

1.3 Lines and Linear Functions

1.4 Functional Models

1.5 Limits

1.6 One-Sided Limits and Continuity

Chapter 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 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; Elasticity of Demand

3.5 Additional Applied Optimization

Chapter 4: Exponential and Logarithmic Functions

4.1 Exponential Functions; Continuous Compounding

4.2 Logarithmic Functions

4.3 Differentiation of Exponential and Logarithmic Functions

4.4 Additional Applications; Exponential Models

Chapter 5: Integration

5.1 Indefinite Integration and Differential Equations

5.2 Integration by Substitution

5.3 The Definite Integral and the Fundamental Theorem of Calculus

5.4 Applying Definite Integration: Distribution of Wealth and Average Value

5.5 Additional Applications to Business and Economics

5.6 Additional Applications to the Life and Social Sciences

Chapter 6: Additional Topics in Integration

6.1 Integration by Parts; Integral Tables

6.2 Numerical Integration

6.3 Improper Integrals

Chapter 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 8: Trigonometric Functions

8.1 Angle Measurement; Trigonometric Functions

8.2 Trigonometric Applications Involving Differentiation

8.3 Trigonometric Applications Involving Integration

Chapter 9: Differential Equations

9.1 Modeling with Differential Equations

9.2 First-Order Linear Differential Equations

9.3 Additional Applications of Differential Equations

9.4 Approximate Solutions of Differential Equations

9.5 Difference Equations; The Cobweb Model

Chapter 10: Infinite Series and Taylor Series Approximations

10.1 Infinite Series; Geometric Series

10.2 Tests for Convergence

10.3 Functions as Power Series; Taylor Series

Chapter 11: Probability and Calculus

11.1 Introduction to Probability; Discrete Random Variables

11.2 Continuous Probability Distributions

11.3 Expected Value and Variance of Continuous Random Variables

10.4 Normal and Poisson Probability Distributions

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’Hopital’s Rule

A.4 The Summation Notation

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