Kolman / Shapiro Precalculus

Functions & Graphs
1. Auflage 2014
ISBN: 978-1-4832-6507-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 637 Seiten, Web PDF

Precalculus: Functions & Graphs provides a complete and self-contained presentation of the basic mathematical techniques and ideas required for the successful completion of a calculus course. The book emphasizes the learning and understanding of the concept of a function, using function notation, and being able to sketch graphs of functions with ease. The text employs a number of pedagogic devices that have been proven effective in teaching college mathematics. The mathematical concepts are presented in a style that is informal, supportive, and 'user-friendly'. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appr This textbook is intended for college students.

Autoren/Hrsg.

Kolman, Bernard

Shapiro, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;Precalculus: Functions & Graphs;6
3;Copyright Page;7
4;Table of Contents;8
5;Dedication;7
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;21
9.2;1.2 POLYNOMIALS AND FACTORING;31
9.3;1.3 EXPONENTS,RADICALS, ANDCOMPLEX NUMBERS;43
9.4;1.4 LINEAR EQUATIONS AND LINEAR INEQUALITIES IN ONE UNKNOWN;56
9.5;1.5 ABSOLUTE VALUE IN EQUATIONS AND INEQUALITIES;64
9.6;1.6 SECOND-DEGREE INEQUALITIES;67
10;CHAPTER 2. FUNCTIONS AND GRAPHS;76
10.1;2.1 THE RECTANGULAR COORDINATE SYSTEM;77
10.2;2.2 FUNCTIONS AND FUNCTION NOTATION;87
10.3;2.3 GRAPHS OF FUNCTIONS;93
10.4;2.4 AIDS IN GRAPHING;102
10.5;2.5 LINEAR FUNCTIONS;106
10.6;2.6 QUADRATIC EQUATIONS;117
10.7;2.7 QUADRATIC FUNCTIONS;129
10.8;2.8 COMBINING FUNCTIONS; INVERSE FUNCTIONS;133
11;CHAPTER 3. ROOTS OF POLYNOMIALS;148
11.1;3.1 SYNTHETIC DIVISION; THE REMAINDER AND FACTOR THEOREMS;149
11.2;3.2 GRAPHS OF POLYNOMIAL FUNCTIONS;155
11.3;3.3 THE RATIONAL ROOTTHEOREM AND THE DEPRESSED EQUATION;161
11.4;3.4 RATIONAL FUNCTIONSAND THEIR GRAPHS;168
11.5;3.5 PARTIAL FRACTIONS;178
12;CHAPTER 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS;188
12.1;4.1 EXPONENTIAL FUNCTIONS;189
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. TRIGONOMETRY: THE CIRCULAR FUNCTIONS;230
13.1;5.0 REVIEW OF GEOMETRY;231
13.2;5.1 THE WRAPPING FUNCTION;232
13.3;5.2 THE SINE, COSINE, AND TANGENT FUNCTIONS;243
13.4;5.3 GRAPHS OFSINE, COSINE,AND TANGENT;250
13.5;5.4 VALUES OFSINE, COSINE,AND TANGENT;255
13.6;5.5 GRAPHS:AMPLITUDE, PERIOD,AND PHASE SHIFT;258
13.7;5.6 SECANT, COSECANT,AND COTANGENT;265
13.8;5.7 THE INVERSE TRIGONOMETRIC FUNCTIONS;269
14;CHAPTER 6. ANGLES AND TRIANGLES;282
14.1;6.1 ANGLES AND THEIRMEASUREMENT;283
14.2;6.2 TRIGONOMETRIC FUNCTIONS OF ANGLES;290
14.3;6.3 RIGHT TRIANGLE TRIGONOMETRY;293
14.4;6.4 LAW OF COSINES;305
14.5;6.5 LAW OF SINES;309
15;CHAPTER 7. ANALYTIC TRIGONOMETRY;318
15.1;7.1 TRIGONOMETRIC IDENTITIES;319
15.2;7.2 THE ADDITION FORMULAS;325
15.3;7.3 DOUBLE- ANDHALF-ANGLE FORMULAS;332
15.4;7.4 THE PRODUCT-SUM FORMULAS;340
15.5;7.5 TRIGONOMETRIC EQUATIONS;344
16;CHAPTER 8. COMPLEX NUMBERS AND THE FUNDAMENTAL THEOREM OF ALGEBRA;352
16.1;8.1 COMPLEX NUMBERS AND THEIRPROPERTIES;353
16.2;8.2 TRIGONOMETRY AND COMPLEX NUMBERS;358
16.3;8.3 THE FUNDAMENTAL THEOREM OF ALGEBRA;365
16.4;8.4 DESCARTES'S RULE OF SIGNS;372
17;CHAPTER 9. ANALYTIC GEOMETRY: THE CONIC SECTIONS;380
17.1;9.1 ANALYTIC GEOMETRY;381
17.2;9.2 THE CIRCLE;384
17.3;9.3 THE PARABOLA;388
17.4;9.4 THE ELLIPSE;394
17.5;9.5 THE HYPERBOLA;400
17.6;9.6 TRANSLATION OF AXES;409
17.7;9.7 ROTATION OF AXES;415
17.8;9.8 POLAR COORDINATES;423
17.9;9.9 PARAMETRIC EQUATIONS;431
18;CHAPTER 10. SYSTEMS OF EQUATIONS AND INEQUALITIES;438
18.1;10.1 SYSTEMS OF EQUATIONS;439
18.2;10.2 SYSTEMS OF LINEAR INEQUALITIES;446
18.3;10.3 LINEAR PROGRAMMING (Optional);454
18.4;10.4 SYSTEMS OF LINEAR EQUATIONS IN THREE UNKNOWNS;460
18.5;10.5 MATRICES AND LINEAR SYSTEMS;465
18.6;10.6 MATRIX OPERATIONS AND APPLICATIONS (Optional);475
18.7;10.7 INVERSES OF MATRICES (Optional);484
18.8;10.8 DETERMINANTS AND CRAMER'S RULE;495
19;CHAPTER 11. SEQUENCES AND SERIES;512
19.1;11.1 SEQUENCES AND SIGMA NOTATION;513
19.2;11.2 ARITHMETIC SEQUENCES;521
19.3;11.3 GEOMETRIC SEQUENCES;527
19.4;11.4 MATHEMATICAL INDUCTION;536
19.5;11.5 THE BINOMIAL THEOREM;540
20;APPENDIX A: APPLICATIONS;550
21;APPENDIX B: LIMITS: A PREVIEW OF CALCULUS;558
22;TABLES APPENDIX;568
23;ANSWERS TO ODD-NUMBERED EXERCISES AND TO REVIEW EXERCISES AND PROGRESS TESTS;586
24;SOLUTIONS TO SELECTED REVIEW EXERCISES;650
25;INDEX;678