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Revised edition of a textbook last published in 1990, providing 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. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
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Read an Excerpt
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 singlevariable 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 realworld 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 selfcontained, 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 reallife 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 endoftext 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 handson 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 oddnumbered 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 mechanicaldrill type to more interesting thoughtprovoking problems. Many realworld type problems with real data are included. Considerable effort has been made to produce a proper balance between the drilltype 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 TI83 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 realworld 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 oddnumbered 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 oddnumbered 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. BulmanFleming (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 WisconsinMadison); 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 WisconsinMilwaukee); 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 WisconsinMilwaukee).
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 errorchecking 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
Part I. ALGEBRA
0. Review of Algebra
0.1 Sets of Real Numbers
0.2 Some Properties of Real Numbers
0.3 Exponents and Radicals
0.4 Operations with Algebraic Expressions
0.5 Factoring
0.6 Fractions
0.7 Equations, in Particular Linear, Equations
0.8 Quadratic Equations
1. Applications and More Algebra
1.1 Applications of Equations
1.2 Linear Inequalities
1.3 Applications of Inequalities
1.4 Absolute Value
1.5 Summation Notation
1.6 Sequences
2. Functions and Graphs
2.1 Functions
2.2 Special Functions
2.3 Combinations of Functions
2.4 Inverse Functions
2.5 Graphs in Rectangular Coordinates
2.6 Symmetry
2.7 Translations and Reflections
2.8 Functions of Several Variables
3. Lines, Parabolas, and Systems
3.1 Lines
3.2 Applications and Linear Functions
3.3 Quadratic Functions
3.4 Systems of Linear Equations
3.5 Nonlinear Systems
3.6 Applications of Systems of Equations
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
4.4 Logarithmic and Exponential Equations
Part II. FINITE MATHEMATICS
5. Mathematics of Finance
5.1 Compound Interest
5.2 Present Value
5.3 Interest Compounded Continuously
5.4 Annuities
5.5 Amortization of Loans
5.6 Perpetuities
6. Matrix Algebra
6.1 Matrices
6.2 Matrix Addition and Scalar Multiplication
6.3 Matrix Multiplication
6.4 Solving Systems by Reducing Matrices
6.5 Solving Systems by Reducing Matrices (continued)
6.6 Inverses
6.7 Leontief's InputOutput Analysis
7. Linear Programming
7.1 Linear Inequalities in Two Variables
7.2 Linear Programming
7.3 Multiple Optimum Solutions
7.4 The Simplex Method
7.5 Degeneracy, Unbounded Solutions, and Multiple Solutions
7.6 Artificial Variables
7.7 Minimization
7.8 The Dual
8. Introduction to Probability and Statistics
8.1 Basic Counting Principle and Permutations
8.2 Combinations and Other Counting Principles
8.3 Sample Spaces and Events
8.4 Probability
8.5 Conditional Probability and Stochastic Processes
8.6 Independent Events
8.7 Bayes's Formula
9. Additional Topics in Probability
9.1 Discrete Random Variables and Expected Value
9.2 The Binomial Distribution
9.3 Markov Chains
Part III. CALCULUS
10. Limits and Continuity
10.1 Limits
10.2 Limits (Continued)
10.3 Continuity
10.4 Continuity Applied to Inequalities
11. Differentiation
11.1 The Derivative
11.2 Rules for Differentiation
11.3 The Derivative as a Rate of Change
11.4 The Product Rule and the Quotient Rule
11.5 The Chain Rule
12. Additional Differentiation Topics
12.1 Derivatives of Logarithmic Functions
12.2 Derivatives of Exponential Functions
12.3 Elasticity of Demand
12.4 Implicit Differentiation
12.5 Logarithmic Differentiation
12.6 Newton's Method
12.7 HigherOrder Derivatives
13. Curve Sketching
13.1 Relative Extrema
13.2 Absolute Extrema on a Closed Interval
13.3 Concavity
13.4 The SecondDerivative Test
13.5 Asymptotes
13.6 Applied Maxima and Minima
14. Integration
14.1 Differentials
14.2 The Indefinite Integral
14.3 Integration with Initial Conditions
14.4 More Integration Formulas
14.5 Techniques of Integration
14.6 The Definite Integral
14.7 The Fundamental Theorem of Integral Calculus
14.8 Approximate Integration
14.9 Area between Curves
14.10 Consumers' and Producers' Surplus
15. Methods and Applications of Integration
15.1 Integration by Parts
15.2 Integration by Partial Fractions
15.3 Integration by Tables
15.4 Average Value of a Function
15.5 Differential Equations
15.6 More Applications of Differential Equations
15.7 Improper Integrals
16. Continuous Random Variables
16.1 Continuous Random Variables
16.2 The Normal Distribution
16.3 The Normal Approximation to the Binomial Distribution
17. Multivariable Calculus
17.1 Partial Derivatives
17.2 Applications of Partial Derivatives
17.3 Implicit Partial Differentiation
17.4 HigherOrder Partial Derivatives
17.5 Chain Rule
17.6 Maxima and Minima for Functions of Two Variables
17.7 Lagrange Multipliers
17.8 Lines of Regression
17.9 Multiple Integrals
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 singlevariable 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 realworld 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 selfcontained, 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 reallife 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 endoftext 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 handson 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 oddnumbered 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 mechanicaldrill type to more interesting thoughtprovoking problems. Many realworld type problems with real data are included. Considerable effort has been made to produce a proper balance between the drilltype 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 TI83 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 realworld 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 oddnumbered 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 oddnumbered 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. BulmanFleming (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 WisconsinMadison); 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 WisconsinMilwaukee); 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 WisconsinMilwaukee).
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 errorchecking 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