ISBN-10:
0134842138
ISBN-13:
9780134842134
Pub. Date:
02/28/1993
Publisher:
Prentice Hall Professional Technical Reference
Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences / Edition 7

Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences / Edition 7

by Ernest F. Haeussler Jr., Richard S. Paul

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Product Details

ISBN-13: 9780134842134
Publisher: Prentice Hall Professional Technical Reference
Publication date: 02/28/1993
Edition description: 7th ed
Pages: 1152
Product dimensions: 7.99(w) x 9.25(h) x (d)

Read an Excerpt

PREFACE:

PREFACE

This tenth edition of Introductory Mathematical Analysis continues to provide a mathematical foundation for students in business, economics, and the life and social sciences. It begins with noncalculus topics such as equations, functions, matrix algebra, linear programming, mathematics of finance, and probability. Then it progresses through both single-variable and multivariable calculus, including continuous random variables. Technical proofs, conditions, and the like are sufficiently described but are not overdone. At times, informal intuitive arguments are given to preserve clarity.

Applications

An abundance and variety of applications for the intended audience appear throughout the book; students continually see how the mathematics they are learning can be used. These applications cover such diverse areas as business, economics, biology, medicine, sociology, psychology, ecology, statistics, earth science, and archaeology. Many of these real-world situations are drawn from literature and are documented by references. In some, the background and context are given in order to stimulate interest. However, the text is virtually self-contained, in the sense that it assumes no prior exposure to the concepts on which the applications are based.

Changes to the Tenth Edition

Chapter Openers
New to the tenth edition, Chapter Openers appear at the beginning of every chapter, including the Concepts for Calculus appendix (see below). Each Chapter Opener presents a real-life application of the mathematics in the chapter. This new element gives students an intuitive introduction to the topics presented in thechapter.

Expanded Concepts for Calculus Appendix
Expanded for the tenth edition, this useful end-of-text appendix features calculus topics for student review. This appendix contains applications of calculus that can be understood before students have studied formal calculus.

Updated and Expanded Mathematical Snapshots
For the tenth edition, this popular feature has been expanded to appear at the end of Chapters 0 through 19. Each snapshot provides an interesting, and at times, novel application involving the mathematics of the chapter in which it occurs. Each of the snapshots includes exercises"reinforcing the texts strong emphasis on hands-on practice. The final exercise in each snapshot involves questions that are suitable for group discussion.

Suggested Chapter Review Tests
In the Review Problems of Chapters 1 through 19, selected problems are marked as suitable for the students to use as practice tests to gauge their mastery of the chapter material. All test items are odd-numbered problems, so that students can check their work against the answers at the back of the text.

Retained Features

Interspersed throughout the text are many warnings to the student that point out commonly made errors. These warnings are indicated under the heading Pitfall. Definitions are clearly stated and displayed. Key concepts, as well as important rules and formulas, are boxed to emphasize their importance. Throughout the text, notes to the student are placed in the margin. They reflect passing comments which supplement discussions.

More than 850 examples are worked out in detail. Some include a strategy that is specifically designed to guide the student through the logistics of the solution before the solution is obtained.

An abundant number of diagrams (almost 500) and exercises (more than 5000) are included. In each exercise set, grouped problems are given in increasing order of difficulty. In many exercise sets the problems progress from the basic mechanical-drill type to more interesting thought-provoking problems. Many real-world type problems with real data are included. Considerable effort has been made to produce a proper balance between the drill-type exercises and the problems requiring the integration of the concepts learned. Many of the exercises have been updated or revised.

In order that a student appreciates the value of current technology, optional graphics calculator material appears throughout the text both in the exposition and exercises. It appears for a variety of reasons: as a mathematical tool, to visualize a concept, as a computing aid, and to reinforce concepts. Although calculator displays for a TI-83 accompany the corresponding technology discussion, our approach is general enough so that it can be applied to other fine graphics calculators.

In the exercise sets, graphics calculator problems are indicated by an icon. To provide flexibility for an instructor in planning assignments, these problems are placed at the end of an exercise set.

The Principles in Practice element provides students with even more applications. Located in the margins of Chapters 1 through 19, these additional exercises give students real-world applications and more opportunities to see the chapter material put into practice. An icon indicates Principles in Practice applications that can be solved using a graphics calculator. Answers to Principles in Practice applications appear at the end of the text.

Each chapter (except Chapter 0) has a review section that contains a list of important terms and symbols, a chapter summary, and numerous review problems.

Answers to odd-numbered problems appear at the end of the book. For many of the differentiation problems, the answers appear in both unsimplified and simplified forms. This allows students to readily check their work.

Course Planning

Because instructors plan a course outline to serve the individual needs of a particular class and curriculum, we shall not attempt to provide sample outlines. However, depending on the background of the students, some instructors will choose to omit Chapter 0, Algebra Refresher, or Chapter 1, Equations. Others may exclude the topics of matrix algebra and linear programming. Certainly there are other sections that may be omitted at the discretion of the instructor. As an aid to planning a course outline, perhaps a few comments may be helpful. Section 2.1 introduces some business terms, such as total revenue, fixed cost, variable cost and profit. Section 4.2 introduces the notion of supply and demand equations, and Section 4.6 discusses the equilibrium point. Optional sections, which will not cause problems if they are omitted, are: 7.3, 7.5, 15.4, 17.1, 17.2, 19.4, 19.6, 19.9 and 19.10. Section 17.8 may be omitted if Chapter 18 is not covered.

Supplements

For Instructors

Instructors Solution Manual. Worked out solutions to all exercises and Principles in Practice applications.

Test Item File. Provides over 1700 test questions, keyed to chapter and section.

Prentice Hall Custom Test. Allows the instructor to access from the computerized Test Item File and personally prepare and print out tests. Includes an editing feature which allows questions to be added or changed.

For Students

Student Solutions Manual with Visual Calculus and Explorations in Finite Mathematics Software. Worked out solutions for every odd-numbered exercise and all Principles in Practice applications. Software includes unique programs which enhance the fundamental concepts of calculus and finite mathematics visually, and include exercises taken directly from the text.

For Instructors and Students

PH Companion Website. Designed to complement and expand upon the text, the PH Companion Website offers a variety of interactive learning tools, including: links to related websites, practice work for students, and the ability for instructors to monitor and evaluate students work on the website. For more information, contact your local Prentice Hall representative.
www.prenhall.com/Haeussler

Acknowledgments

We express our appreciation to the following colleagues who contributed comments and suggestions that were valuable to us in the evolution of this text:

R.M. Alliston (Pennsylvania State University); R. A. Alo (University of Houston); K. T. Andrews (Oakland University); M. N. de Arce (University of Puerto Rico); G. R. Bates (Western Illinois University); D. E. Bennett (Murray State University); C. Bernett (Harper College); A. Bishop (Western Illinois University); S.A. Book (California State University); A. Brink (St. Cloud State University); R. Brown (York University); R.W. Brown (University of Alaska); S.D. Bulman-Fleming (Wilfrid Laurier University); D. Calvetti (National College); D. Cameron (University of Akron); K. S. Chung (Kapiolani Community College); D. N. Clark (University of Georgia); E. L. Cohen (University of Ottawa); J. Dawson (Pennsylvania State University); A. Dollins (Pennsylvania State University); G.A. Earles (St. Cloud State University); B. H. Edwards (University of Florida); J.R. Elliott (Wilfrid Laurier University); J. Fitzpatrick (University of Texas at El Paso); M. J. Flynn (Rhode Island Junior College); G. J. Fuentes (University of Maine); S.K. Goel (Valdosta State University); G. Goff (Oklahoma State University); J. Goldman (DePaul University); J.T. Gresser (Bowling Green State University); L. Griff (Pennsylvania State University); F.H. Hall (Pennsylvania State University); V.E. Hanks (Western Kentucky University); R.C. Heitmann (The University of Texas at Austin); J.N. Henry (California State University); W.U. Hodgson (West Chester State College); B.C. Horne, Jr. (Virginia Polytechnic Institute and State University); J. Hradnansky (Pennsylvania State University); C. Hurd (Pennsylvania State University); J.A. Jiminez (Pennsylvania State University); W.C. Jones (Western Kentucky University); R.M. King (Gettysburg College); M.M. Kostreva (University of Maine); G.A. Kraus (Gannon University); J. Kucera (Washington State University); M.R. Latina (Rhode Island Junior College); J.F. Longman (Villanova University); I. Marshak (Loyola University of Chicago); D. Mason (Elmhurst College); F.B. Mayer (Mt. San Antonio College); P. McDougle (University of Miami); F. Miles (California State University); E. Mohnike (Mt. San Antonio College); C. Monk (University of Richmond); R.A. Moreland (Texas Tech University); J.G. Morris (University of Wisconsin-Madison); J.C. Moss (Paducah Community College); D. Mullin (Pennsylvania State University); E. Nelson (Pennsylvania State University); S.A. Nett (Western Illinois University); R.H. Oehmke (University of Iowa); Y.Y. Oh (Pennsylvania State University); N.B. Patterson (Pennsylvania State University); V. Pedwaydon (Lawrence Technical University); E. Pemberton (Wilfrid Laurier University); M. Perkel (Wright State University); D.B. Priest (Harding College); J.R. Provencio (University of Texas); L.R. Pulsinelli (Western Kentucky University); M. Racine (University of Ottawa); N.M. Rice (Queens University); A. Santiago (University of Puerto Rico); J.R. Schaefer (University of Wisconsin-Milwaukee); S. Sehgal (The Ohio State University); W.H. Seybold, Jr. (West Chester State College); G. Shilling (The University of Texas at Arlington); S. Singh (Pennsylvania State University); L. Small (Los Angeles Pierce College); E. Smet (Huron College); M. Stoll (University of South Carolina); A. Tierman (Saginaw Valley State University); B. Toole (University of Maine); J.W. Toole (University of Maine); D.H. Trahan (Naval Postgraduate School); J.P. Tull (The Ohio State University); L.O. Vaughan, Jr. (University of Alabama in Birmingham); L.A. Vercoe (Pennsylvania State University); M. Vuilleumier (The Ohio State University); B.K. Waits (The Ohio State University); A. Walton (Virginia Polytechnic Institute and State University); H. Walum (The Ohio State University); E.T.H. Wang (Wilfrid Laurier University); A.J. Weidner (Pennsylvania State University); L. Weiss (Pennsylvania State University); N.A. Weigmann (California State University); G. Woods (The Ohio State University); C.R.B. Wright (University of Oregon); C. Wu (University of Wisconsin-Milwaukee).

Some exercises are taken from problem supplements used by students at Wilfrid Laurier University. We wish to extend special thanks to the Department of Mathematics of Wilfrid Laurier University for granting Prentice Hall permission to use and publish this material, and also to thank Prentice Hall, who in turn allowed us to make use of this material.

We also thank LaurelTech for their input to the Concepts for Calculus appendix, for error-checking the text, and for their efforts in the revision process.

Finally, we express our sincere gratitude to the faculty and course coordinators of The Ohio State University and Columbus State University who took a keen interest in the tenth edition, offering a number of invaluable suggestions.

Ernest F. Haeussler, Jr.
Richard S. Paul

Table of Contents

(NOTE: Each chapter ends with a Review.)
0. Algebra Refresher.

Purpose. Sets and Real Numbers. Some Properties of Real Numbers. Operations with Real Numbers. Exponents and Radicals. Operations with Algebraic Expressions. Factoring. Fractions.

1. Equations.
Linear Equations. Equations Leading to Linear Equations. Quadratic Equations. Supplement. Mathematical Snapshot: Real Growth of an Investment.

2. Applications of Equations and Inequalities.
Applications of Equations. Linear Inequalities. Applications of Inequalities. Absolute Value. Mathematical Snapshot: Quality VCR Recording.

3. Functions and Graphs.
Functions. Special Functions. Combinations of Functions. Graphs in Rectangular Coordinates. Symmetry. Translations and Reflections. Mathematical Snapshot: A Taxing Experience!

4. Lines, Parabolas, and Systems.
Lines. Applications and Linear Functions. Quadratic Functions. Systems of Linear Equations. Nonlinear Systems. Applications of Systems of Equations. Mathematical Snapshot: Anyone for Tennis?

5. Exponential and Logarithmic Functions.
Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Mathematical Snapshot: Drug Dosages.

6. Matrix Algebra.
Matrices. MatrixAddition and Scalar Multiplication. Matrix Multiplication. Method of Reduction. Method of Reduction (Continued). Inverses. Determinants. Cramer's Rule. Input-Output Analysis with a Graphics Calculator. Mathematical Snapshot: Insulin Requirements as a Linear Process.

7. Linear Programming.

Linear Inequalities in Two Variables. Linear Programming. Multiple Optimum Solutions. The Simplex Method. Degeneracy, Unbounded Solutions, Multiple Optimum Solutions. Artificial Variables. Minimization. The Dual. Mathematical Snapshot: Drug and Radiation Therapies.

8. Mathematics of Finance.
Compound Interest. Present Value. Annuities. Amortization of Loans. Mathematical Snapshot: The Rule of 78's.

9. Introduction to Probability and Statistics.
Basic Counting Principles and Permutations. Combinations and Other Counting Principles. Sample Spaces and Events. Probability. Conditional Probability and Stochastic Processes. Independent Events. Bayes' Formula.

10. Additional Topics in Probability.
Discrete Random Variables and Expected Value. The Binomial Distribution. Markov Chains. Mathematical Snapshot: Is the Price Right?

11. Limits and Continuity.
Limits. Limits (Continued). Interest Compounded Continuously. Continuity. Continuity Applied to Inequalities. Mathematical Snapshot: National Debt.

12. Differentiation.
The Derivative. Rules for Differentiation. The Derivative as a Rate of Change. Differentiability and Continuity. Product and Quotient Rules. The Chain Rule and Power Rule.

13. Additional Differentiation Topics.
Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Logarithmic Differentiation. Higher-Order Derivatives.

14. Curve Sketching.
Relative Extrema. Absolute Extrema on a Closed Interval. Concavity. The Second-Derivative Test. Asymptotes.

15. Applications of Differentiation.
Applied Maxima and Minima. Differentials. Elasticity of Demand. Newtons Method.

16. Integration.
The Indefinite Integral. Integration with Initial Conditions. More Integration Formulas. Techniques of Integration. Summation. The Definite Integral. The Fundamental Theorem of Integral Calculus. Area. Area between Curves. Consumers' and Producers' Surplus. Mathematical Snapshot: Delivered Price.

17. Methods and Applications of Integration.
Integration by Parts. Integration by Partial Fractions. Integration by Tables. Average Value of a Function. Approximate Integration. Differential Equations. More Applications of Differential Equations. Improper Integrals. Mathematical Snapshot: Dieting.

18. Continuous Random Variables.
Continuous Random Variables. The Normal Distribution. The Normal Approximation to the Binomial Distribution.

19. Multivariable Calculus.
Functions of Several Variables. Partial Derivatives. Applications of Partial Derivatives. Implicit Partial Differentiation. Higher-Order Partial Derivatives. Chain Rule. Maxima and Minima for Functions of Two Variables. Lagrange Multipliers. Lines of Regression. A Comment on Homogeneous Functions. Multiple Integrals. Mathematical Snapshot: Data Analysis to Model Cooling.

Appendix A: Concepts for Calculus.
Appendix B: Compound Interest Tables.
Appendix C: Table of Selected Integrals.
Appendix D: Areas Under the Standard Normal Curve.
Answers to Odd-Numbered Problems.
Index.

Preface

PREFACE:

PREFACE

This tenth edition of Introductory Mathematical Analysis continues to provide a mathematical foundation for students in business, economics, and the life and social sciences. It begins with noncalculus topics such as equations, functions, matrix algebra, linear programming, mathematics of finance, and probability. Then it progresses through both single-variable and multivariable calculus, including continuous random variables. Technical proofs, conditions, and the like are sufficiently described but are not overdone. At times, informal intuitive arguments are given to preserve clarity.

Applications

An abundance and variety of applications for the intended audience appear throughout the book; students continually see how the mathematics they are learning can be used. These applications cover such diverse areas as business, economics, biology, medicine, sociology, psychology, ecology, statistics, earth science, and archaeology. Many of these real-world situations are drawn from literature and are documented by references. In some, the background and context are given in order to stimulate interest. However, the text is virtually self-contained, in the sense that it assumes no prior exposure to the concepts on which the applications are based.

Changes to the Tenth Edition

Chapter Openers
New to the tenth edition, Chapter Openers appear at the beginning of every chapter, including the Concepts for Calculus appendix (see below). Each Chapter Opener presents a real-life application of the mathematics in the chapter. This new element gives students an intuitive introduction to the topics presented inthechapter.

Expanded Concepts for Calculus Appendix
Expanded for the tenth edition, this useful end-of-text appendix features calculus topics for student review. This appendix contains applications of calculus that can be understood before students have studied formal calculus.

Updated and Expanded Mathematical Snapshots
For the tenth edition, this popular feature has been expanded to appear at the end of Chapters 0 through 19. Each snapshot provides an interesting, and at times, novel application involving the mathematics of the chapter in which it occurs. Each of the snapshots includes exercises"reinforcing the texts strong emphasis on hands-on practice. The final exercise in each snapshot involves questions that are suitable for group discussion.

Suggested Chapter Review Tests
In the Review Problems of Chapters 1 through 19, selected problems are marked as suitable for the students to use as practice tests to gauge their mastery of the chapter material. All test items are odd-numbered problems, so that students can check their work against the answers at the back of the text.

Retained Features

Interspersed throughout the text are many warnings to the student that point out commonly made errors. These warnings are indicated under the heading Pitfall. Definitions are clearly stated and displayed. Key concepts, as well as important rules and formulas, are boxed to emphasize their importance. Throughout the text, notes to the student are placed in the margin. They reflect passing comments which supplement discussions.

More than 850 examples are worked out in detail. Some include a strategy that is specifically designed to guide the student through the logistics of the solution before the solution is obtained.

An abundant number of diagrams (almost 500) and exercises (more than 5000) are included. In each exercise set, grouped problems are given in increasing order of difficulty. In many exercise sets the problems progress from the basic mechanical-drill type to more interesting thought-provoking problems. Many real-world type problems with real data are included. Considerable effort has been made to produce a proper balance between the drill-type exercises and the problems requiring the integration of the concepts learned. Many of the exercises have been updated or revised.

In order that a student appreciates the value of current technology, optional graphics calculator material appears throughout the text both in the exposition and exercises. It appears for a variety of reasons: as a mathematical tool, to visualize a concept, as a computing aid, and to reinforce concepts. Although calculator displays for a TI-83 accompany the corresponding technology discussion, our approach is general enough so that it can be applied to other fine graphics calculators.

In the exercise sets, graphics calculator problems are indicated by an icon. To provide flexibility for an instructor in planning assignments, these problems are placed at the end of an exercise set.

The Principles in Practice element provides students with even more applications. Located in the margins of Chapters 1 through 19, these additional exercises give students real-world applications and more opportunities to see the chapter material put into practice. An icon indicates Principles in Practice applications that can be solved using a graphics calculator. Answers to Principles in Practice applications appear at the end of the text.

Each chapter (except Chapter 0) has a review section that contains a list of important terms and symbols, a chapter summary, and numerous review problems.

Answers to odd-numbered problems appear at the end of the book. For many of the differentiation problems, the answers appear in both unsimplified and simplified forms. This allows students to readily check their work.

Course Planning

Because instructors plan a course outline to serve the individual needs of a particular class and curriculum, we shall not attempt to provide sample outlines. However, depending on the background of the students, some instructors will choose to omit Chapter 0, Algebra Refresher, or Chapter 1, Equations. Others may exclude the topics of matrix algebra and linear programming. Certainly there are other sections that may be omitted at the discretion of the instructor. As an aid to planning a course outline, perhaps a few comments may be helpful. Section 2.1 introduces some business terms, such as total revenue, fixed cost, variable cost and profit. Section 4.2 introduces the notion of supply and demand equations, and Section 4.6 discusses the equilibrium point. Optional sections, which will not cause problems if they are omitted, are: 7.3, 7.5, 15.4, 17.1, 17.2, 19.4, 19.6, 19.9 and 19.10. Section 17.8 may be omitted if Chapter 18 is not covered.

Supplements

For Instructors

Instructors Solution Manual. Worked out solutions to all exercises and Principles in Practice applications.

Test Item File. Provides over 1700 test questions, keyed to chapter and section.

Prentice Hall Custom Test. Allows the instructor to access from the computerized Test Item File and personally prepare and print out tests. Includes an editing feature which allows questions to be added or changed.

For Students

Student Solutions Manual with Visual Calculus and Explorations in Finite Mathematics Software. Worked out solutions for every odd-numbered exercise and all Principles in Practice applications. Software includes unique programs which enhance the fundamental concepts of calculus and finite mathematics visually, and include exercises taken directly from the text.

For Instructors and Students

PH Companion Website. Designed to complement and expand upon the text, the PH Companion Website offers a variety of interactive learning tools, including: links to related websites, practice work for students, and the ability for instructors to monitor and evaluate students work on the website. For more information, contact your local Prentice Hall representative.
www.prenhall.com/Haeussler

Acknowledgments

We express our appreciation to the following colleagues who contributed comments and suggestions that were valuable to us in the evolution of this text:

R.M. Alliston (Pennsylvania State University); R. A. Alo (University of Houston); K. T. Andrews (Oakland University); M. N. de Arce (University of Puerto Rico); G. R. Bates (Western Illinois University); D. E. Bennett (Murray State University); C. Bernett (Harper College); A. Bishop (Western Illinois University); S.A. Book (California State University); A. Brink (St. Cloud State University); R. Brown (York University); R.W. Brown (University of Alaska); S.D. Bulman-Fleming (Wilfrid Laurier University); D. Calvetti (National College); D. Cameron (University of Akron); K. S. Chung (Kapiolani Community College); D. N. Clark (University of Georgia); E. L. Cohen (University of Ottawa); J. Dawson (Pennsylvania State University); A. Dollins (Pennsylvania State University); G.A. Earles (St. Cloud State University); B. H. Edwards (University of Florida); J.R. Elliott (Wilfrid Laurier University); J. Fitzpatrick (University of Texas at El Paso); M. J. Flynn (Rhode Island Junior College); G. J. Fuentes (University of Maine); S.K. Goel (Valdosta State University); G. Goff (Oklahoma State University); J. Goldman (DePaul University); J.T. Gresser (Bowling Green State University); L. Griff (Pennsylvania State University); F.H. Hall (Pennsylvania State University); V.E. Hanks (Western Kentucky University); R.C. Heitmann (The University of Texas at Austin); J.N. Henry (California State University); W.U. Hodgson (West Chester State College); B.C. Horne, Jr. (Virginia Polytechnic Institute and State University); J. Hradnansky (Pennsylvania State University); C. Hurd (Pennsylvania State University); J.A. Jiminez (Pennsylvania State University); W.C. Jones (Western Kentucky University); R.M. King (Gettysburg College); M.M. Kostreva (University of Maine); G.A. Kraus (Gannon University); J. Kucera (Washington State University); M.R. Latina (Rhode Island Junior College); J.F. Longman (Villanova University); I. Marshak (Loyola University of Chicago); D. Mason (Elmhurst College); F.B. Mayer (Mt. San Antonio College); P. McDougle (University of Miami); F. Miles (California State University); E. Mohnike (Mt. San Antonio College); C. Monk (University of Richmond); R.A. Moreland (Texas Tech University); J.G. Morris (University of Wisconsin-Madison); J.C. Moss (Paducah Community College); D. Mullin (Pennsylvania State University); E. Nelson (Pennsylvania State University); S.A. Nett (Western Illinois University); R.H. Oehmke (University of Iowa); Y.Y. Oh (Pennsylvania State University); N.B. Patterson (Pennsylvania State University); V. Pedwaydon (Lawrence Technical University); E. Pemberton (Wilfrid Laurier University); M. Perkel (Wright State University); D.B. Priest (Harding College); J.R. Provencio (University of Texas); L.R. Pulsinelli (Western Kentucky University); M. Racine (University of Ottawa); N.M. Rice (Queens University); A. Santiago (University of Puerto Rico); J.R. Schaefer (University of Wisconsin-Milwaukee); S. Sehgal (The Ohio State University); W.H. Seybold, Jr. (West Chester State College); G. Shilling (The University of Texas at Arlington); S. Singh (Pennsylvania State University); L. Small (Los Angeles Pierce College); E. Smet (Huron College); M. Stoll (University of South Carolina); A. Tierman (Saginaw Valley State University); B. Toole (University of Maine); J.W. Toole (University of Maine); D.H. Trahan (Naval Postgraduate School); J.P. Tull (The Ohio State University); L.O. Vaughan, Jr. (University of Alabama in Birmingham); L.A. Vercoe (Pennsylvania State University); M. Vuilleumier (The Ohio State University); B.K. Waits (The Ohio State University); A. Walton (Virginia Polytechnic Institute and State University); H. Walum (The Ohio State University); E.T.H. Wang (Wilfrid Laurier University); A.J. Weidner (Pennsylvania State University); L. Weiss (Pennsylvania State University); N.A. Weigmann (California State University); G. Woods (The Ohio State University); C.R.B. Wright (University of Oregon); C. Wu (University of Wisconsin-Milwaukee).

Some exercises are taken from problem supplements used by students at Wilfrid Laurier University. We wish to extend special thanks to the Department of Mathematics of Wilfrid Laurier University for granting Prentice Hall permission to use and publish this material, and also to thank Prentice Hall, who in turn allowed us to make use of this material.

We also thank LaurelTech for their input to the Concepts for Calculus appendix, for error-checking the text, and for their efforts in the revision process.

Finally, we express our sincere gratitude to the faculty and course coordinators of The Ohio State University and Columbus State University who took a keen interest in the tenth edition, offering a number of invaluable suggestions.

Ernest F. Haeussler, Jr.
Richard S. Paul

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