Kolman / Shapiro Introduction to Algebra and Trigonometry

1. Auflage 2014
ISBN: 978-1-4832-6391-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 620 Seiten, Web PDF

Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry. This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are likewise treated. Other topics include analytic geometry, conic sections, and use of a coordinate system to prove theorems from plane, and matrix operations and inverses. This publication is valuable to students aiming to gain more knowledge of the fundamentals of mathematics.

Autoren/Hrsg.

Kolman, Bernard

Shapiro, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;Introduction to Algebra and Trigonometry;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;12
7;ACKNOWLEDGMENTS;14
8;TO THE STUDENT;16
9;CHAPTER 1. THE FOUNDATIONS OF ALGEBRA;20
9.1;1.1 THE REAL NUMBER SYSTEM;20
9.2;1.2 THE REAL NUMBER LINE;28
9.3;1.3 ALGEBRAIC EXPRESSIONS; POLYNOMIALS;34
9.4;1.4 FACTORING;43
9.5;1.5 RATIONAL EXPRESSIONS;47
9.6;1.6 INTEGER EXPONENTS;55
9.7;1.7 RATIONAL EXPONENTS AND RADICALS;59
9.8;1.8 COMPLEX NUMBERS;67
9.9;KEY IDEAS FOR REVIEW;71
10;CHAPTER 2. EQUATIONS AND INEQUALITIES;77
10.1;2.1 LINEAR EQUATIONS IN ONE UNKNOWN;77
10.2;2.2 APPLICATIONS;83
10.3;2.3 UNEAR INEQUALITIES;92
10.4;2.4 ABSOLUTE VALUE IN EQUATIONS AND INEQUALITIES;98
10.5;2.5 THE QUADRATIC EQUATION;101
10.6;2.6 APPLICATIONS—QUADRATIC EQUATIONS;113
10.7;2.7 SECOND-DEGREE INEQUALITIES;116
10.8;KEY IDEAS FOR REVIEW;120
11;CHAPTER 3. FUNCTION;124
11.1;3.1 RECTANGULAR COORDINATE SYSTEMS;124
11.2;3.2 FUNCTIONS AND FUNCTION NOTATION;134
11.3;3.3 GRAPHS OF FUNCTIONS;141
11.4;3.4 LINEAR FUNCTIONS;148
11.5;3.5 DIRECT AND INVERSE VARIATION;159
11.6;3.6 COMBINING FUNCTIONS; INVERSE FUNCTIONS;163
11.7;KEY IDEAS FOR REVIEW;173
12;CHAPTER 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS;179
12.1;4.1 EXPONENTIAL FUNCTIONS;180
12.2;4.2 LOGARITHMIC FUNCTIONS;189
12.3;4.3 PROPERTIES OF LOGARITHMS;196
12.4;4.4 COMPUTING WITH LOGARITHM;200
12.5;4.5 EXPONENTIAL AND LOGARITHMIC EQUATIONS;206
12.6;KEY IDEAS FOR REVIEW;210
13;CHAPTER 5. TRIGONOMETRY: THE CIRCULAR FUNCTIONS;214
13.1;5.1 THE WRAPPING FUNCTION;216
13.2;5.2 THE SINE, COSINE, AND TANGENT FUNCTIONS;227
13.3;5.3 GRAPHS OF SINE, COSINE, AND TANGENT;233
13.4;5.4 VARIATION OF SINE, COSINE, AND TANGENT;239
13.5;5.5 GRAPHS: AMPLITUDE, PERIOD, AND PHASE SHIFT;242
13.6;5.6 SECANT, COSECANT, AND COTANGENT;247
13.7;5.7 THE INVERSE TRIGONOMETRIC FUNCTIONS;251
13.8;KEY IDEAS FOR REVIEW;257
14;CHAPTER 6. ANGLES AND TRIANGLES;263
14.1;6.1 ANGLES AND THEIR MEASUREMENT;263
14.2;6.2 TRIGONOMETRIC FUNCTIONS OF ANGLES;270
14.3;6.3 RIGHT TRIANGLE TRIGONOMETRY;273
14.4;6.4 LAW OF COSINES;285
14.5;6.5 LAW OF SINES;289
14.6;TERMS AND SYMBOLS;294
15;CHAPTER 7. ANALYTIC TRIGONOMETRY;298
15.1;7.1 TRIGONOMETRIC IDENTITIES;298
15.2;7.2 THE ADDITION FORMULAS;304
15.3;7.3 DOUBLE AND HALF-ANGLE FORMULAS;310
15.4;7.4 THE PRODUCT-SUM FORMULAS;316
15.5;7.5 TRIGONOMETRIC EQUATIONS;319
15.6;7.6 TRIGONOMETRY AND COMPLEX NUMBERS;323
15.7;KEY IDEAS FOR REVIEW;331
16;CHAPTER 8. ANALYTIC GEOMETRY: THE CONIC SECTIONS;336
16.1;8.1 ANALYTIC GEOMETRY;336
16.2;8.2 THE CIRCLE;340
16.3;8.3 THE PARABOLA;343
16.4;8.4 THE ELLIPSE AND HYPERBOLA;348
16.5;8.5 IDENTIFYING THE CONIC SECTIONS;354
16.6;KEY IDEAS FOR REVIEW;357
17;CHAPTER 9. SYSTEMS OF EQUATIONS AND INEQUALITIES;360
17.1;9.1 SYSTEMS OF LINEAR EQUATIONS;361
17.2;9.2 SOLVING BY ELIMINATION;366
17.3;9.3 APPLICATIONS;369
17.4;9.4 SYSTEMS OF LINEAR EQUATIONS IN THREE UNKNOWNS;377
17.5;9.5 SYSTEMS INVOLVING NONLINEAR EQUATIONS;382
17.6;9.6 SYSTEMS OF LINEAR INEQUALITIES IN TWO VARIABLES;386
17.7;KEY IDEAS FOR REVIEW;395
18;CHAPTER 10. MATRICES AND DETERMINANTS;400
18.1;10.1 MATRICES AND LINEAR SYSTEMS;400
18.2;10.2 MATRIX OPERATIONS AND APPLICATIONS (Optional);409
18.3;10.3 INVERSES OF MATRICES (Optional);417
18.4;10.4 DETERMINANTS AND CRAMER'S RULE;427
18.5;KEY IDEAS FOR REVIEW;437
19;CHAPTER 11. ROOTS OF POLYNOMIALS;443
19.1;11.1 POLYNOMIAL DIVISION AND SYNTHETIC DIVISION;444
19.2;11.2 THE REMAINDER AND FACTOR THEOREMS;448
19.3;11.3 FACTORS AND ROOTS;452
19.4;11.4 REAL AND RATIONAL ROOTS;461
19.5;11.5 RATIONAL FUNCTIONS AND THEIR GRAPHS;467
19.6;KEY IDEAS FOR REVIEW;477
20;CHAPTER 12. TOPICS IN ALGEBRA;481
20.1;12.1 ARITHMETIC PROGRESSIONS;482
20.2;12.2 GEOMETRIC PROGRESSIONS;489
20.3;12.3 MATHEMATICAL INDUCTION;497
20.4;12.4 THE BINOMIAL THEOREM;500
20.5;12.5 COUNTING: PERMUTATIONS AND COMBINATIONS;505
20.6;12.6 PROBABILITY;514
20.7;KEY IDEAS FOR REVIEW;521
21;APPENDIX/TABLE;526
22;ANSWERS TO ODD-NUMBERED EXERCISES, REVIEW EXERCISES, AND PROGRESS TESTS;544
23;INDEX;614