Summary

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Author Biography

Raymond A. Barnett, a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish.

Michael R. Ziegler (late) received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing post doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he held the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler published over a dozen research articles in complex analysis and co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen.

Karl E. Byleen received his B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.

Christopher Stocker received his B.S. in mathematics and computer science from St. John’s University in Minnesota and his M.A. and Ph.D. degrees in mathematics from the University of Illinois in Urbana-Champaign. He is currently an Adjunct Assistant Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University. He has published eight research articles in the areas of graph theory and combinatorics.

Preface

Diagnostic Prerequisite Test

1. Functions and Graphs

1.1 Functions

1.2 Elementary Functions: Graphs and Transformations

1.3 Linear and Quadratic Functions

1.4 Polynomial and Rational Functions

1.5 Exponential Functions

1.6 Logarithmic Functions

Chapter 1 Summary and Review

Review Exercises

2. Limits and the Derivative

2.1 Introduction to Limits

2.2 Infinite Limits and Limits at Infinity

2.3 Continuity

2.4 The Derivative

2.5 Basic Differentiation Properties

2.6 Differentials

2.7 Marginal Analysis in Business and Economics

Chapter 2 Summary and Review

Review Exercises

3. Additional Derivative Topics

3.1 The Constant e and Continuous Compound Interest

3.2 Derivatives of Exponential and Logarithmic Functions

3.3 Derivatives of Products and Quotients

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Related Rates

3.7 Elasticity of Demand

Chapter 3 Summary and Review

Review Exercises

4. Graphing and Optimization

4.1 First Derivative and Graphs

4.2 Second Derivative and Graphs

4.3 L’Hôpital’s Rule

4.4 Curve-Sketching Techniques

4.5 Absolute Maxima and Minima

4.6 Optimization

Chapter 4 Summary and Review

Review Exercises

5. Integration

5.1 Antiderivatives and Indefinite Integrals

5.2 Integration by Substitution

5.3 Differential Equations; Growth and Decay

5.4 The Definite Integral

5.5 The Fundamental Theorem of Calculus

Chapter 5 Summary and Review

Review Exercises

6. Additional Integration Topics

6.1 Area Between Curves

6.2 Applications in Business and Economics

6.3 Integration by Parts

6.4 Other Integration Methods

Chapter 6 Summary and Review

Review Exercises

7. Multivariable Calculus

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Maxima and Minima

7.4 Maxima and Minima Using Lagrange Multipliers

7.5 Method of Least Squares

7.6 Double Integrals over Rectangular Regions

7.7 Double Integrals over More General Regions

Chapter 7 Summary and Review

Review Exercises

8. Trigonometric Functions

8.1 Right Triangle Trigonometry

8.2 Trigonometric Functions

8.3 Derivatives of Trigonometric Functions

8.4 Integration of Trigonometric Functions

Chapter 8 Summary and Review

Review Exercises

9. Differential Equations

9.1 Basic Concepts

9.2 Separation of Variables

9.3 First-Order Linear Differential Equations

Chapter 9 Summary and Review

Review Exercises

10. Taylor Polynomials and Infinite Series

10.1 Taylor Polynomials

10.2 Taylor Series

10.3 Operations on Taylor Series

10.4 Approximations Using Taylor Series

Chapter 10 Summary and Review

Review Exercises

11. Probability and Calculus

11.1 Improper Integrals

11.2 Continuous Random Variables

11.3 Expected Value, Standard Deviation, and Median

11.4 Special Probability Distributions

Chapter 11 Summary and Review

Review Exercises

Appendix A: Basic Algebra Review

A.1 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

Appendix B: Special Topics (online at goo.gl/mjbXrG)

B.1 Sequences, Series, and Summation Notation

B.2 Arithmetic and Geometric Sequences

B.3 Binomial Theorem

B.4 Interpolating Polynomials and Divided Differences

Appendix C: Integration Using Tables

Answers

Index

Index of Applications

Supplemental Materials

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