Kolman / Shapiro College Algebra and Trigonometry

2. Auflage 2014
ISBN: 978-1-4832-7713-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 672 Seiten, Web PDF

College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry. The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.

Autoren/Hrsg.

Kolman, Bernard

Shapiro, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;College Algebra and Trigonometry
;4
3;Copyright Page;5
4;Table of Contents;6
5;Dedication;5
6;PREFACE;10
7;ACKNOWLEDGMENTS;12
8;TO THE STUDENT;14
9;CHAPTER 1. THE FOUNDATIONS OF
ALGEBRA;18
9.1;1.1 THE REAL NUMBER
SYSTEM;18
9.2;1.2 THE REAL NUMBER LINE;27
9.3;1.3 ALGEBRAIC EXPRESSIONS;
POLYNOMIALS;32
9.4;1.4
FACTORING;40
9.5;1.5 RATIONAL EXPRESSIONS;48
9.6;1.6 INTEGER EXPONENTS;55
9.7;1.7 RATIONAL EXPONENTS
AND RADICALS;59
9.8;1.8 COMPLEX NUMBERS;69
10;CHAPTER 2. EQUATIONS AND
INEQUALITIES;78
10.1;2.1 LINEAR EQUATIONS
IN ONE UNKNOWN;78
10.2;2.2 APPLICATIONS;84
10.3;2.3 LINEAR INEQUALITIES;94
10.4;2.4 ABSOLUTE VALUE IN EQUATIONS AND
INEQUALITIES;100
10.5;2.5 THE QUADRATIC EQUATION;104
10.6;2.6 APPLICATIONS OF
QUADRATIC EQUATIONS;117
10.7;2.7 SECOND-DEGREE INEQUALITIES;121
11;CHAPTER 3. FUNCTIONS;130
11.1;3.1 THE RECTANGULAR COORDINATE
SYSTEM;131
11.2;3.2 FUNCTIONS AND FUNCTION NOTATION;141
11.3;3.3 GRAPHS OF FUNCTIONS;147
11.4;3.4 LINEAR FUNCTIONS;157
11.5;3.5 DIRECT AND INVERSE VARIATION
(Optional);168
11.6;3.6 COMBINING FUNCTIONS; INVERSE
FUNCTIONS;173
12;CHAPTER 4. EXPONENTIAL AND
LOGARITHMIC FUNCTIONS;188
12.1;4.1 EXPONENTIAL
FUNCTIONS;188
12.2;4.2 LOGARITHMIC FUNCTIONS;200
12.3;4.3 FUNDAMENTAL PROPERTIES OF LOGARITHMS;208
12.4;4.4 COMPUTING WITH LOGARITHMS (Optional);215
12.5;4.5 EXPONENTIAL AND LOGARITHMIC EQUATIONS;221
13;CHAPTER 5. THE TRIGONOMETRIC
FUNCTIONS;230
13.1;5.0 REVIEW OF
GEOMETRY;230
13.2;5.1 ANGLES AND THEIR MEASUREMENT;231
13.3;5.2 THE SINE,COSINE, AND TANGENT FUNCTIONS;242
13.4;5.3 VALUES OF SINE, COSINE, AND
TANGENT;250
13.5;5.4 GRAPHS OF SINE, COSINE, AND TANGENT;262
13.6;5.5 SECANT, COSECANT, AND
COTANGENT;273
13.7;5.6 THE INVERSE TRIGONOMETRIC FUNCTIONS;278
14;CHAPTER 6. TRIGONOMETRY: MEASURING
TRIANGLES;292
14.1;6.1 RIGHT TRIANGLE
TRIGONOMETRY;292
14.2;6.2 APPLICATIONS OF RIGHT TRIANGLE
TRIGONOMETRY;299
14.3;6.3 LAW OF COSINES;305
14.4;6.4 LAW OF SINES;309
15;CHAPTER 7. ANALYTIC TRIGONOMETRY;318
15.1;7.1 TRIGONOMETRIC IDENTITIES;318
15.2;7.2 THE ADDITION
FORMULAS;324
15.3;7.3 DOUBLE- AND HALF-ANGLE FORMULAS;332
15.4;7.4 THE PRODUCT-SUM
FORMULAS;339
15.5;7.5 TRIGONOMETRIC EQUATIONS;343
15.6;7.6 TRIGONOMETRY AND
COMPLEX NUMBERS;348
16;CHAPTER 8. ANALYTIC GEOMETRY: THE CONIC
SECTIONS;360
16.1;8.1 ANALYTIC GEOMETRY;360
16.2;8.2 THE CIRCLE;364
16.3;8.3 THE PARABOLA;369
16.4;8.4 THE ELLIPSE AND
HYPERBOLA;377
16.5;8.5 IDENTIFYING THE
CONIC SECTIONS;385
17;CHAPTER 9. SYSTEMS OF EQUATIONS
AND INEQUALITIES;392
17.1;9.1 SYSTEMS OF
EQUATIONS;392
17.2;9.2 SOLVING BY
ELIMINATION;397
17.3;9.3 APPLICATIONS;400
17.4;9.4 SYSTEMS OF LINEAR EQUATIONS IN THREE
UNKNOWNS;408
17.5;9.5 SYSTEMS OF LINEAR
INEQUALITIES;413
17.6;9.6 LINEAR PROGRAMMING (Optional);422
18;CHAPTER 10. MATRICES AND
DETERMINANTS;432
18.1;10.1 MATRICES AND LINEAR
SYSTEMS;432
18.2;10.2 MATRIX OPERATIONS AND APPLICATIONS
(Optional);441
18.3;10.3 INVERSES OF
MATRICES (Optional);450
18.4;10.4 DETERMINANTS AND
CRAMER'S RULE;460
19;CHAPTER 11. THEORY OF
POLYNOMIALS;476
19.1;11.1 POLYNOMIAL DIVISION AND SYNTHETIC
DIVISION;477
19.2;11.2 THE REMAINDER AND FACTOR
THEOREMS;481
19.3;11.3 FACTORS AND ZEROS;486
19.4;11.4 REAL AND RATIONAL
ZEROS;497
19.5;11.5 RATIONAL FUNCTIONS AND
THEIR GRAPHS;506
20;CHAPTER 12. TOPICS IN ALGEBRA;520
20.1;12.1 SEQUENCES AND
SIGMA NOTATION;521
20.2;12.2 ARITHMETIC
SEQUENCES;529
20.3;12.3 GEOMETRIC
SEQUENCES;535
20.4;12.4 MATHEMATICAL
INDUCTION;544
20.5;12.5 THE BINOMIAL
THEOREM;548
20.6;12.6 COUNTING: PERMUTATIONS AND
COMBINATIONS;554
20.7;12.7 PROBABILITY;563
21;TABLES APPENDIX;576
22;ANSWERS TO ODD-NUMBERED EXERCISES, AND TO REVIEW EXERCISES AND
PROGRESS TESTS;594
23;SOLUTIONS TO SELECTED REVIEW EXERCISES;644
24;Index;660