Flanders / Price Algebra

1. Auflage 2014
ISBN: 978-1-4832-6508-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 324 Seiten, Web PDF

Algebra presents the essentials of algebra 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, together with exponentials and logarithms. Comprised of eight 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 of algebra: polynomial, rational, exponential, and logarithm. The book concludes with a review of sequences, permutations and combinations, and the binomial theorem, as well as summation and mathematical induction. 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;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;12
7;CHAPTER 1. BASIC ALGEBRA;16
7.1;1. THE NATURE OF ALGEBRA;16
7.2;2. ALGEBRAIC NOTATION;18
7.3;3. THE RULES OF ALGEBRA;20
7.4;4. INTEGERS AND RATIONALS;27
7.5;5. INTEGRAL EXPONENTS;33
7.6;6. ROOTS AND RADICALS;38
7.7;7. RATIONAL EXPONENTS;43
7.8;8. POLYNOMIALS;46
7.9;9. POLYNOMIALS IN SEVERAL VARIABLES;50
7.10;10. FACTORING;53
7.11;11. RATIONAL EXPRESSIONS;57
7.12;12. COMMON ERRORS IN ALGEBRA;61
7.13;Test;63
8;CHAPTER 2. EQUATIONS AND INEQUALITIES;64
8.1;1. EQUATIONS AND IDENTITIES;64
8.2;2. LINEAR EQUATIONS;67
8.3;3. QUADRATIC EQUATIONS;72
8.4;4. OTHER TYPES OF EQUATIONS;78
8.5;5. APPLICATIONS;81
8.6;6. ORDER;87
8.7;7. ABSOLUTE VALUES;93
8.8;8. INEQUALITIES;98
8.9;Test;103
9;CHAPTER 3. FUNCTIONS AND GRAPHS;104
9.1;1. INTRODUCTION;104
9.2;2. COORDINATES IN THE PLANE;105
9.3;3. FUNCTIONS;108
9.4;4. CONSTRUCTION OF FUNCTIONS;114
9.5;5. LINEAR FUNCTIONS;116
9.6;6. QUADRATIC FUNCTIONS;124
9.7;7. TIPS ON GRAPHING;131
9.8;Test;136
10;CHAPTER 4. POLYNOMIAL AND RATIONAL FUNCTIONS;138
10.1;1. INTRODUCTION;138
10.2;2. GRAPHS OF POLYNOMIALS;138
10.3;3. GRAPHS OF FACTORED POLYNOMIALS;145
10.4;4. RATIONAL FUNCTIONS;149
10.5;5. GRAPHS OF RATIONAL FUNCTIONS;152
10.6;6. FACTORED RATIONAL FUNCTIONS;157
10.7;Test;163
11;CHAPTER 5. EXPONENTIALS AND LOGARITHMS;164
11.1;1. EXPONENTIAL FUNCTIONS;164
11.2;2. LOGARITHM FUNCTIONS;168
11.3;3. POWER FUNCTIONS;175
11.4;4. ACCURACY AND ROUND-OFF;182
11.5;5. TABLES AND INTERPOLATION;184
11.6;6. COMPUTATIONS WITH LOGARITHMS [optional];187
11.7;7. COMPUTATIONS WITH A SMALL CALCULATOR [optional];192
11.8;8. APPLICATIONS;198
11.9;9. BUSINESS APPLICATIONS [optional];201
11.10;Test;207
12;CHAPTER 6. TOPICS IN ALGEBRA;208
12.1;1. DIVISION OF POLYNOMIALS;208
12.2;2. ZEROS OF POLYNOMIALS;214
12.3;3. PARTIAL FRACTIONS;222
12.4;4. SYSTEMS OF LINEAR EQUATIONS;228
12.5;5. DETERMINANTS;235
12.6;Test;242
13;CHAPTER 7. COMPLEX NUMBERS;244
13.1;1. THE COMPLEX NUMBER SYSTEM;244
13.2;2. COMPLEX ARITHMETIC;246
13.3;3. QUADRATIC EQUATIONS;253
13.4;4. ZEROS OF POLYNOMIALS;256
13.5;Test;263
14;CHAPTER 8. DISCRETE ALGEBRA;264
14.1;1. SEOUENCES;264
14.2;2. PERMUTATIONS AND COMBINATIONS;269
14.3;3. BINOMIAL THEOREM;273
14.4;4. SUMMATION;276
14.5;5. MATHEMATICAL INDUCTION;283
14.6;Teat;288
15;ANSWERS TO ODD-NUMBERED EXERCISES;290
16;TABLES;314
16.1;1. 4-place logarithm;315
16.2;2. 4-place antilogarithm;317
16.3;3. Powers and roots;319
17;INDEX;322