Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition - 8th edition

1 Functions, Graphs, and Limits

1. Functions
2. The Graph of a Function
3. Linear Functions
4. Functional Models
5. Limits
6. One-Sided Limits and Continuity

2 Differentiation: Basic Concepts

1. The Derivative
2. Techniques of Differentiation
3. Product and Quotient Rules; Higher Order Derivatives
4. The Chain Rule
5. Marginal Analysis and Approximations Using Increments
6. Implicit Differentiation and Related Rates

3 Additional Applications of the Derivative

1. Increasing and Decreasing Functions; Relative Extrema
2. Concavity and Points of Inflection
3. Curve Sketching
4. Optimization
5. Additional Applied Optimization

4 Exponential and Logarithmic Functions

1. Exponential Functions
2. Logarithmic Functions
3. Differentiation of Logarithmic and Exponential Functions
4. Additional Exponential Models

5 Integration

1. Antidifferentiation: The Indefinite Integral
2. Integration by Substitution
3. The Definite Integral and the Fundamental Theorem of Calculus
4. Applying Definite Integration: Area Between Curves and Average Value
5. Additional Applications to Business and Economics
6. Additional Applications to the Life and Social Sciences

6 Additional Topics in Integration

1. Integration by Parts; Integral Tables
2. Improper Integrals
3. Numerical Integration

7 Calculus of Several Variables

1. Functions of Several Variables
2. Partial Derivatives
3. Optimizing Functions of Two Variables
4. The Method of Least-Squares
5. Constrained Optimization: The Method of Lagrange Multipliers
6. Double Integrals

8 Differential Equations

1. Introduction to Differential Equations
2. First-Order Linear Differential Equations
3. Additional Applications of Differential Equations
4. Approximate Solutions of Differential Equations
5. Difference Equations

9 Infinite Series and Taylor Series Approximations

1. Infinite Series
2. Tests for Convergence
3. Functions as Power Series; Taylor Series

10 Probability and Calculus

1. Discrete Random Variables
2. Continuous Random Variables
3. Expected Value and Variance of Continuous Random Variables
4. Normal and Poisson Probability Distributions

11 Trigonometric Functions

1. The Trigonometric Functions
2. Differentiation and Integration of Trigonometric Functions
3. Additional Applications Involving Trigonometric Functions
Appendix A Algebra Review
1. A Brief Review of Algebra
2. Factoring Polynomials and Solving Systems of Equations
Tables
I Powers of e
II The Natural Logarithm (Base e)
III Trigonometric Functions