Applied Calculus For Business, Economics, and the Social and Life Sciences

Tittle
Contents
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 Exercises
Explore! Update
Think About It
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 Exercises
Explore! Update
Think About It
iii
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 Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 3
Review Exercises
Explore! Update
Think About It
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 Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 4
Review Exercises
Explore! Update
Think About It
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 Exercises
Explore! Update
Think About It
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 Exercises
Explore! Update
Think About It
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 Exercises
Explore! Update
Think About It
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 Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 8
Review Exercises
Explore! Update
Think About It
9 Calculus of Several Variables
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 Exercises
Explore! Update
Think About It
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 Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 10
Review Exercises
Explore! Update
Think About It
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 Exercises
Explore! Update
Think About It
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'Hôpital's Rule
TA B L E S I Powers of e
II The Natural Logarithm (Base e)
III Trigometric Functions
A.4 The Summation Notation
Appendix Summary
Important Terms, Symbols, and Formulas
Review Exercises
Think About It
Tables
Answers to Odd-Numbered Excercises, Chapter Checkup Exercises, and Odd-Numbered Chapter Review Exercises
Index