Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences / Edition 6

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Overview

Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for readers to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercises–including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding.

ALGEBRA; Review of Algebra; Applications and More Algebra; Functions and Graphs; Lines, Parabolas, and Systems; Exponential and Logarithmic Functions; FINITE MATHEMATICS; Mathematics of Finance; Matrix Algebra; Linear Programming; Introduction to Probability and Statistics; Additional Topics in Probability; CALCULUS; Limits and Continuity; Differentiation; Additional Differentiation Topics; Curve Sketching; Integration; Methods and Applications of Integration; Continuous Random Variables; Multivariable Calculus

For all readers interested in introductory mathematical analysis.

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Editorial Reviews

Booknews
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)
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Product Details

  • ISBN-13: 9780134713922
  • Publisher: Prentice Hall Professional Technical Reference
  • Publication date: 1/1/1990
  • Edition number: 6
  • Pages: 872

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

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Table of Contents

Preface
0 Algebra Refresher 1
1 Equations 34
2 Applications of Equations and Inequalities 58
3 Functions and Graphs 87
4 Lines, Parabolas and Systems 130
5 Exponential and Logarithmic Functions 188
6 Matrix Algebra 232
7 Linear Programming 318
8 Mathematics of Finance 392
9 Introduction to Probability and Statistics 428
10 Additional Topics in Probability 520
11 Limits and Continuity 554
12 Differentiation 604
13 Additional Differentiation Topics 664
14 Curve Sketching 696
15 Applications of Differentiation 745
16 Integration 783
17 Methods and Applications of Integration 866
18 Continuous Random Variables 926
19 Multivariable Calculus 951
Appendix A. Table of Powers, Roots, Reciprocals 1027
Appendix B. Table of e[superscript x] and e[superscript -x] 1030
Appendix C. Table of Natural Logarithms 1033
Appendix D. Compound Interest Tables 1036
Appendix E. Table of Selected Integrals 1051
Appendix F. Areas Under the Standard Normal Curve 1055
Answers to Odd-Numbered Problems 1057
Index 1121
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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

Read More Show Less

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