Theory_and_Problems_of_College_Mathematics-Ayres-Schmidt-3e.pdf

SCHAUM’S

OUTLINE OF

Theory and Problems of

COLLEGE

THIRD EDITION

Algebra

Discrete Mathematics

Precalculus

Introduction to Calculus

FRANK AYRES, Jr., Ph.D.

Formerly Professor and Head

Department of Mathematics, Dickinson College

PHILIP A. SCHMIDT, Ph.D.

Program Coordinator, Mathematics and Science Education

The Teachers College, Western Governors University

Salt Lake City, Utah

Schaum’s Outline Series

McGRAW-HILL

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MATHEMATICS

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DOI: 10.1036/0071425888

PREFACE

In the Third Edition of College Mathematics, I have maintained the point-of-view of

the ﬁrst two editions.Students who are engaged in learning mathematics in the

mathematical range from algebra to calculus will ﬁnd virtually all major topics from

those curricula in this text.However, a substantial number of important changes have

been made in this edition.First, there is more of an emphasis now on topics in discrete

mathematics.Second, the graphing calculator is introduced as an important problem-

solving tool.Third, material related to manual and tabular computations of logarithms

has been removed, and replaced with material that is calculator-based.Fourth, all

material related to the concepts of locus has been modernized.Fifth, tables and graphs

have been changed to reﬂect current curriculum and teaching methods.Sixth, all

material related to the conic sections has been substantially changed and modernized.

Additionally, much of the rest of the material in the third edition has been changed

to reﬂect current classroom methods and pedagogy, and mathematical modeling is

introduced as a problem-solving tool.Notation has been changed as well when

necessary.

My thanks must be expressed to Barbara Gilson and Andrew Littell of

McGraw-Hill.They have been supportive of this project from its earliest stages.I

also must thank Dr.Marti Garlett, Dean of the Teachers College at Western Governors

University, for her professional support as I struggled to meet deadlines while

beginning a new position at the University.I thank Maureen Walker for her handling

of the manuscript and proofs.And ﬁnally, I thank my wife, Dr.Jan Zlotnik Schmidt,

for putting up with my frequent need to work at home on this project.Without her

support, this edition would not have been easily completed.

P HILIP A.S CHMIDT

New Paltz, NY

iii

For more information about this title, click here.

CONTENTS

PART I

Review of Algebra

1. Elements of Algebra

2. Functions

3. Graphs of Functions

4. Linear Equations

5. Simultaneous Linear Equations

6. Quadratic Functions and Equations

7. Inequalities

8. The Locus of an Equation

9. The Straight Line

10. Families of Straight Lines

11. The Circle

PART II

Topics in Discrete Mathematics

12. Arithmetic and Geometric Progressions

13. Inﬁnite Geometric Series

14. Mathematical Induction

15. The Binomial Theorem

16. Permutations

17. Combinations

104

18. Probability

109

19. Determinants of Orders Two and Three

117

20. Determinants of Order n

122

21. Systems of Linear Equations

129

22. Introduction to Transformational Geometry

136

PART III

Topics in Precalculus

153

23. Angles and Arc Length

155

24. Trigonometric Functions of a General Angle

161

25. Trigonometric Functions of an Acute Angle

169

26. Reduction to Functions of Positive Acute Angles

178

27. Graphs of the Trigonometric Functions

183

28. Fundamental Relations and Identities

189

29. Trigonometric Functions of Two Angles

195

30. Sum, Difference, and Product Formulas

207

31. Oblique Triangles

211

32. Inverse Trigonometric Functions

222

33. Trigonometric Equations

232

34. Complex Numbers

242

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