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

Chapter 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 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 Applications; Exponential Models

Chapter 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 6: Additional Topics in Integration

6.1 Integration by Parts; Integral Tables

6.2 Improper Integrals

6.3 Numerical Integration

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: 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; The Cobweb Model

Chapter 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 10: Probability and Calculus

10.1 Introduction to Probability; 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 11: Trigonometric Functions

11.1 The Trigonometric Functions

11.2 Differentiation and Integration of Trigonometric Functions

11.3 Additional Applications Involving Trigonometric Function

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