Calculus for Business, Economics, Life Sciences & Social Sciences

PART 1 A LIBRARY OF ELEMENTARY FUNCTIONS

1 Linear Equations and Graphs

1-1 Linear Equations and Inequalities

1-2 Graphs and Lines

1-3 Linear Regression

Chapter 1 Review

Review Exercise

2 Functions and Graphs

2-1 Functions

2-2 Elementary Functions: Graphs and Transformations

2-3 Quadratic Functions

2-4 Exponential Functions

2-5 Logarithmic Functions

Chapter 2 Review

Review Exercise

PART 2 CALCULUS

3 Limits and the Derivative

3-1 Introduction to Limits

3-2 Continuity

3-3 Infinite Limits and Limits at Infinity

3-4 The Derivative

3-5 Basic Differentiation Properties

3-6 Differentials

3-7 Marginal Analysis in Business and Economics

Chapter 3 Review

Review Exercise

4 Additional Derivative Topics

4-1 The Constant e and Continuous Compound Interest

4-2 Derivatives of Exponential and Logarithmic Functions

4-3 Derivatives of Products and Quotients

4-4 The Chain Rule

4-5 Implicit Differentiation

4-6 Related Rates

4-7 Elasticity of Demand

Chapter 4 Review

Review Exercise

5 Graphing and Optimization

5-1 First Derivative and Graphs

5-2 Second Derivative and Graphs

5-3 L’Hôpital’s Rule

5-4 Curve-Sketching Techniques

5-5 Absolute Maxima and Minima

5-6 Optimization

Chapter 5 Review

Review Exercise

6 Integration

6-1 Antiderivatives and Indefinite Integrals

6-2 Integration by Substitution

6-3 Differential Equations; Growth and Decay

6-4 The Definite Integral

6-5 The Fundamental Theorem of Calculus

Chapter 6 Review

Review Exercise

7 Additional Integration Topics

7-1 Area between Curves

7-2 Applications in Business and Economics

7-3 Integration by Parts

7-4 Integration Using Tables

Chapter 7 Review

Review Exercise

8 Multivariable Calculus

8-1 Functions of Several Variables

8-2 Partial Derivatives

8-3 Maxima and Minima

8-4 Maxima and Minima Using Lagrange Multipliers

8-5 Method of Least Squares

8-6 Double Integrals over Rectangular Regions

8-7 Double Integrals over More General Regions

Chapter 8 Review

Review Exercise

9 Trigonometric Functions

9-1 Trigonometric Functions Review

9-2 Derivatives of Trigonometric Functions

9-3 Integration of Trigonometric Functions

Chapter 9 Review

Review Exercise

A Basic Algebra Review

Self-Test on Basic Algebra

A-1 Algebra and Real Numbers

A-2 Operations on Polynomials

A-3 Factoring Polynomials

A-4 Operations on Rational Expressions

A-5 Integer Exponents and Scientific Notation

A-6 Rational Exponents and Radicals

A-7 Quadratic Equations

B Special Topics

B-1 Sequences, Series, and Summation Notation

B-2 Arithmetic and Geometric Sequences

B-3 Binomial Theorem

C Tables

Table I Basic Geometric Formulas

Table II Integration Formulas

Answers

Index

Applications Index

A Library of Elementary Functions