Flanders / Price Algebra and Trigonometry

1. Auflage 2014
ISBN: 978-1-4832-7104-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 442 Seiten, Web PDF

Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered. Comprised of 11 chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions: polynomial, rational, exponential, logarithm, and trigonometric. Trigonometry and the inverse trigonometric functions and identities are also presented. The book concludes with a review of progressions, permutations, combinations, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Autoren/Hrsg.

Flanders, Harley

Price, Justin J.

Inhaltsverzeichnis

1;Front Cover;1
2;Algebra and Trigonometry;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;12
7;CHAPTER 1. BASIC ALGEBRA;18
7.1;1. THE NATURE OF ALGEBRA;18
7.2;2. ALGEBRAIC NOTATION;20
7.3;3. THE RULES OF ALGEBRA;22
7.4;4. INTEGERS AND RATIONALS;29
7.5;5. INTEGRAL EXPONENTS;35
7.6;6. ROOTS AND RADICALS;40
7.7;7. RATIONAL EXPONENTS;45
7.8;8. POLYNOMIALS;48
7.9;9. POLYNOMIALS IN SEVERAL VARIABLES;52
7.10;10. FACTORING;55
7.11;11. RATIONAL EXPRESSIONS;59
7.12;12. COMMON ERRORS IN ALGEBRA;63
7.13;Test 1;65
7.14;Test 2;65
8;CHAPTER 2. EQUATIONS AND INEQUALITIES;66
8.1;1. EQUATIONS AND IDENTITIES;66
8.2;2. LINEAR EQUATIONS;69
8.3;3. QUADRATIC EQUATIONS;74
8.4;4. OTHER TYPES OF EQUATIONS;80
8.5;5. APPLICATIONS;83
8.6;6. ORDER;89
8.7;7. ABSOLUTE VALUES;95
8.8;8. INEQUALITIES;100
8.9;Test 1;105
8.10;Test 2;105
9;CHAPTER 3. FUNCTIONS AND GRAPHS;106
9.1;1. INTRODUCTION;106
9.2;2. COORDINATES IN THE PLANE;107
9.3;3. FUNCTIONS;110
9.4;4. CONSTRUCTION OF FUNCTIONS;116
9.5;5. LINEAR FUNCTIONS;118
9.6;6. QUADRATIC FUNCTIONS;126
9.7;7. TIPS ON GRAPHING;133
9.8;Test 1;138
9.9;Test 2;139
10;CHAPTER 4. POLYNOMIAL AND RATIONAL FUNCTIONS;140
10.1;1. INTRODUCTION;140
10.2;2. GRAPHS OF POLYNOMIALS;140
10.3;3. GRAPHS OF FACTORED POLYNOMIALS;147
10.4;4. RATIONAL FUNCTIONS;151
10.5;5. GRAPHS OF RATIONAL FUNCTIONS;154
10.6;6. FACTORED RATIONAL FUNCTIONS;159
10.7;Test 1;165
10.8;Test 2;165
11;CHAPTER 5. EXPONENTIALS AND LOGARITHMS;166
11.1;1. EXPONENTIAL FUNCTIONS;166
11.2;2. LOGARITHM FUNCTIONS;170
11.3;3. POWER FUNCTIONS;177
11.4;4. ACCURACY AND ROUND-OFF;184
11.5;5. TABLES AND INTERPOLATION;186
11.6;6. COMPUTATIONS WITH LOGARITHMS [optional];189
11.7;7. COMPUTATIONS' WITH A SMALL CALCULATOR [optional];194
11.8;8. APPLICATIONS;200
11.9;9. BUSINESS APPLICATIONS [optional];203
11.10;Test 1 [without optional material];209
11.11;Test 2;209
12;CHAPTER 6. TRIGONOMETRIC FUNCTIONS;210
12.1;1. INTRODUCTION;210
12.2;2. DISTANCES AND ANGLES;211
12.3;3. SINE AND COSINE;216
12.4;4. OTHER TRIGONOMETRIC FUNCTIONS;222
12.5;5. GRAPHS OF SINE AND COSINE;226
12.6;6. GRAPHS OF THE OTHER FUNCTIONS;232
12.7;Test 1;238
12.8;Test 2;239
13;CHAPTER 7. IDENTITIES AND INVERSE FUNCTIONS;240
13.1;1. BASIC IDENTITIES;240
13.2;2. THE ADDITION LAWS;245
13.3;3. FURTHER IDENTITIES;248
13.4;4. INVERSE FUNCTIONS;253
13.5;5. APPLICATIONS;260
13.6;Test 1;267
13.7;Test 2;267
14;CHAPTER 8. TRIGONOMETRY;268
14.1;1. RIGHT TRIANGLES;268
14.2;2. OBLIQUE TRIANGLES;273
14.3;3. NUMERICAL SOLUTION;277
14.4;4. APPLICATIONS TO GEOMETRY;284
14.5;5. VECTORS [optional];289
14.6;6. LENGTH AND INNER PRODUCT [optional];295
14.7;Test 1;301
14.8;Test 2;301
15;CHAPTER 9. TOPICS IN ALGEBRA;302
15.1;1. DIVISION OF POLYNOMIALS;302
15.2;2. ZEROS OF POLYNOMIALS;308
15.3;3. PARTIAL FRACTIONS;316
15.4;4. SYSTEMS OF LINEAR EQUATIONS;322
15.5;5. DETERMINANTS;329
15.6;Test 1;336
15.7;Test 2;337
16;CHAPTER 10. COMPLEX NUMBERS;338
16.1;1. COMPLEX ARITHMETIC;338
16.2;2. THE COMPLEX PLANE;343
16.3;3. ZEROS OF POLYNOMIALS;350
16.4;4. DE MOIVRE'S THEOREM AND ROOTS OF UNITY;354
16.5;Test 1;361
16.6;Test 2;361
17;CHAPTER 11. DISCRETE ALGEBRA;362
17.1;1. SEOUENCES;362
17.2;2. PERMUTATIONS AND COMBINATIONS;367
17.3;3. BINOMIAL THEOREM;371
17.4;4. SUMMATION;374
17.5;5. MATHEMATICAL INDUCTION;381
17.6;Test 1;386
17.7;Test 2;387
18;ANSWERS TO ODD-NUMBERED EXERCISES;388
19;TABLES;420
20;INDEX;438