Kolman / Shapiro Algebra for College Students

1. Auflage 2014
ISBN: 978-1-4832-7121-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 550 Seiten, Web PDF

Algebra for College Students, Revised and Expanded Edition is a complete and self-contained presentation of the fundamentals of algebra which has been designed for use by the student. The book provides sufficient materials for use in many courses in college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, sets and set notation, matrices and their application in solving linear systems, and notation of functions. The theory of polynomial equations, formulas for factoring a sum and a difference of cubes, roots of polynomials, and the geometric definition of each conic are likewise included in the book. College students will find the book very useful and invaluable.

Autoren/Hrsg.

Kolman, Bernard

Shapiro, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;Algebra for College Students
;2
3;Copyright Page
;3
4;Table of Contents;4
5;Dedication;12
6;PREFACE;8
7;ACKNOWLEDGMENTS;10
8;CHAPTER ONE. THE REAL NUMBER SYSTEM;14
8.1;1.1 THE REAL NUMBER SYSTEM;14
8.2;1.2 ARITHMETIC OPERATIONS: FRACTIONS;19
8.3;1.3 ALGEBRAIC EXPRESSIONS;29
8.4;1.4 OPERATING WITH SIGNED NUMBERS;32
8.5;1.5 PROPERTIES OF REAL NUMBERS;37
8.6;1.6 ABSOLUTE VALUE AND INEQUALITIES;41
9;CHAPTER
TWO.
POLYNOMIALS;54
9.1;2.1 POLYNOMIALS;54
9.2;2.2 ADDITION AND SUBTRACTION OF POLYNOMIALS;61
9.3;2.3 MULTIPLICATION OF POLYNOMIALS;65
9.4;2.4 FACTORING;70
9.5;2.5 SPECIAL FACTORS;76
10;CHAPTER THREE. LINEAR EQUATIONS AND INEQUALITlES;82
10.1;3.1 LINEAR EQUATIONS IN ONE VARIABLE;82
10.2;3.2 APPLICATIONS;86
10.3;3.3 LINEAR INEQUALITIES;92
10.4;3.4 ABSOLUTE VALUE IN EQUATIONS AND INEQUALITIES;97
11;CHAPTER
FOUR.
WORD
PROBLEMS;104
11.1;4.1 FROM WORDS TO ALGEBRA;104
11.2;4.2 COIN PROBLEMS;108
11.3;4.3 INVESTMENT PROBLEMS;112
11.4;4.4 DISTANCE (UNIFORM MOTION) PROBLEMS;115
11.5;4 5 MIXTURE PROBLEMS;119
12;CHAPTER FIVE. ALGEBRAIC FRACTIONS;126
12.1;5.1 MULTIPLICATION AND DIVISION OF FRACTIONS;127
12.2;5.2 ADDITION AND SUBTRACTION OF FRACTIONS;132
12.3;5.3 COMPLEX FRACTIONS;138
12.4;5.4 RATIO AND PROPORTION;141
12.5;5.5 EQUATONS AND INEQUALITIES WITH FRACTIONS;145
12.6;5.6 APPLICATIONS; WORK PROBLEMS;149
13;CHAPTER SIX. FUNCTIONS;158
13.1;6.1 RECTANGULAR COORDINATE SYSTEMS;158
13.2;6.2 FUNCTIONS AMD FUNCTION ....TI..;168
13.3;6.3 GRAPHS OF FUNCTIONS;179
13.4;6.4 INCREASING AND DECREASING FUNCTIONS;186
13.5;6.5 DIRECT AND INVERSE VARIATION;189
14;CHAPTER SEVEN. THE STRAIGHT LINE;200
14.1;7.1 SLOPE OF THE STRAIGHT LINE;200
14.2;7.2 EQUATIONS OF THE STRAIGHT LINE;205
14.3;7.3 FURTHER PROPERTIES OF THE STRAIGHT LINE;212
14.4;7.4 LINEAR INEQUALITIES IN TWO VARIABLES;220
15;CHAPTER EIGHT. EXPONENTS, RADICALS, AND COMPLEX NUMBERS;228
15.1;8.1 POSITIVE INTEGER ....NENTS;228
15.2;8.2 INTEGER EXPONENTS;233
15.3;8.3 RATIONAL EXPONENTS AND RADICALS;237
15.4;8.4 EVALUATING AND SIMPLIFYING RADICALS;243
15.5;8.5 OPERATIONS WITH RADICALS;248
15.6;8.6 COMPLEX NUMBERS;251
16;CHAPTER ..N.. SECOND-DEGREE EQUATIONS AND INEQUALITIES;262
16.1;9.1 SOLVING QUADRATIC EQUATIONS;262
16.2;9.2 THE QUADRATIC FORMULA;268
16.3;9.3 ROOTS OF A QUADRATIC EQUATION: THE DISCRIMINANT;272
16.4;9.4 APPLICATIONS;275
16.5;9.5 FORMS LEADING TO QUADRATICS;279
16.6;9.6 SECOND-DEGREE INEQUALITIES;283
17;CHAPTER
TEN.
ROOTS
OF
POLYNOMIALS;292
17.1;10.1 POLYNOMIAL DIVISION AND SYNTHETIC DIVISION;293
17.2;10.2 THE REMAINDER AND FACTOR THEOREMS;297
17.3;10.3 FACTORS AND ROOTS;301
17.4;10.4 REAL AND RATIONAL ROOTS;309
18;CHAPTER ELEVEN. EXPONENTIAL AND LOGARITHMIC FUNCTIONS;320
18.1;11.1 COMBINING FUNCTIONS; INVERSE FUNCTIONS;321
18.2;11.2 EXPONENTIAL FUNCTIONS;332
18.3;11.3 LOGARITHMIC FUNCTIONS;340
18.4;11.4 PROPERTIES OF LOGARITHMS;347
18.5;11.5 COMPUTING WITH LOGARITHMS;353
18.6;11.6 EXPONENTIAL AND LOGARITHMIC EQUATIONS;359
19;CHAPTER TWELVE. ANALYTIC GEOMETRY: THE CONIC SECTIONS;366
19.1;12.1 THE DISTANCE AND MIDPOINT FORMULAS;366
19.2;12.2 SYMMETRY;372
19.3;12.3 THE CIRCLE;375
19.4;12.4 THE PARABOLA;379
19.5;12.5 THE ELLIPSE AND HYPERBOLA;385
19.6;12.6 IDENTIFYING THE CONIC SECTIONS;393
20;CHAPTER THIRTEEN. SYSTEMS OF EQUATIONS;400
20.1;13.1 SYSTEMS OF LINEAR EQUATIONS;400
20.2;13.2 SOLVING BY ELIMINATION;408
20.3;13.3 APPLICATIONS;412
20.4;13.4 SYSTEMS OF LINEAR EQUATIONS IN THREE UNKNOWNS;421
20.5;13.5 SYSTEMS INVOLVING NONLINEAR EQUATIONS;424
21;CHAPTER
FOURTEEN.
MATRICES
AND
DETERMINANTS;432
21.1;14.1 MATRICES AND LINEAR SYSTEMS;432
21.2;14.2 DETERMINANTS;441
21.3;14.3 CRAMER'S RULE;446
22;CHAPTER FIFTEEN. TOPICS IN ALGEBRA;454
22.1;15.1 .RITH...IC PROGRESSIONS;454
22.2;15.2 GEOMETRIC PROGRESSIONS;462
22.3;15.3 THE BINOMIAL THEOREM;469
22.4;15.4 COUNTING: PERMUTATIONS AND COMBINATIONS;474
23;APPENDIX/TABLES;486
24;ANSWERS TO ODD-NUMBERED EXERCISES AND PROGRESS TESTS;494
25;INDEX;546