Flanders / Price Introductory College Mathematics

with Linear Algebra and Finite Mathematics
1. Auflage 2014
ISBN: 978-1-4832-6295-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 486 Seiten, Web PDF

Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction. Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction 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;Introductory College Mathematics: With Linear Algebra and Finite Mathematics;6
3;Copyright Page;7
4;Table of Contents;10
5;Dedication;8
6;PREFACE;14
7;CHAPTER 1. FUNCTIONS AND GRAPHS;20
7.1;1. INTRODUCTION;20
7.2;2. REAL NUMBERS;21
7.3;3. COORDINATES ON THE LINE AND PLANE;23
7.4;4. FUNCTIONS;27
7.5;5. CONSTRUCTION OF FUNCTIONS;32
7.6;TEST;34
8;CHAPTER 2. LINEAR AND QUADRATIC FUNCTIONS;35
8.1;1. LINEAR FUNCTIONS;35
8.2;2. QUADRATIC FUNCTIONS;42
8.3;3. SOME APPLICATIONS;49
8.4;4. TIPS ON GRAPHING;52
8.5;TEST;56
9;CHAPTER 3. POLYNOMIAL FUNCTIONS;57
9.1;1. ALGEBRA OF POLYNOMIALS;57
9.2;2. GRAPHS OF POLYNOMIALS;62
9.3;3. ZEROS AND ROOTS;68
9.4;4. ZEROS OF HIGHER DEGREE POLYNOMIALS;73
9.5;5. GRAPHS OF FACTORED POLYNOMIALS;78
9.6;TEST;81
10;CHAPTER 4. RATIONAL FUNCTIONS;83
10.1;1. BASIC PROPERTIES;83
10.2;2. ALGEBRAIC OPERATIONS;87
10.3;3. GRAPHS OF RATIONAL FUNCTIONS;90
10.4;4. DIVISION WITH REMAINDER;101
10.5;5. PARTIAL FRACTIONS;105
10.6;TEST;109
11;CHAPTER 5. EXPONENTIAL AND LOGARITHM FUNCTIONS;110
11.1;1. REVIEW OF EXPONENTS;110
11.2;2. EXPONENTIAL FUNCTIONS;113
11.3;3. LOGARITHM FUNCTIONS;119
11.4;4. ACCURACY AND TABLES [Optional];124
11.5;5. LOG TABLES [Optional];127
11.6;6. COMPUTATIONS WITH LOGARITHMS [Optional];130
11.7;7. POWER FUNCTIONS;135
11.8;TEST;142
12;CHAPTER 6. TRIGONOMETRIC FUNCTIONS;143
12.1;1. INTRODUCTION;143
12.2;2. DISTANCES AND ANGLES;143
12.3;3. SINE AND COSINE;149
12.4;4. OTHER TRIGONOMETRIC FUNCTIONS;154
12.5;5. GRAPHS OF SINE AND COSINE;158
12.6;6. GRAPHS OF THE OTHER FUNCTIONS;164
12.7;TEST;169
13;CHAPTER 7. IDENTITIES AND INVERSE FUNCTIONS;171
13.1;1. IDENTITIES;171
13.2;2. FURTHER IDENTITIES;177
13.3;3. INVERSE FUNCTIONS;182
13.4;4. TRIGONOMETRIC EQUATIONS;189
13.5;TEST;191
14;CHAPTER 8. TRIGONOMETRY;192
14.1;1. RIGHT TRIANGLES;192
14.2;2. LAWS OF COSINES AND SINES;197
14.3;3. OBLIQUE TRIANGLES [Optional];201
14.4;TEST;205
15;CHAPTER 9. VECTORS;206
15.1;1. VECTOR ALGEBRA;206
15.2;2. LINES;212
15.3;3. LENGTH AND INNER PRODUCT;218
15.4;4. NORMAL FORM;224
15.5;TEST;232
16;CHAPTER 10. ANALYTIC GEOMETRY;233
16.1;1. TRANSLATION OF AXES;233
16.2;2. THE CIRCLE;235
16.3;3. TANGENTS AND LOCI;241
16.4;4. POLAR COORDINATES;246
16.5;5. CONICS; THE PARABOLA;255
16.6;6. THE ELLIPSE;259
16.7;7. THE HYPERBOLA;265
16.8;8. ROTATION OF AXES [Optional];270
16.9;9. ADDITIONAL EXERCISES ON CONICS [Optional];279
16.10;TEST;281
17;CHAPTER 11. VECTORS AND MATRICES;282
17.1;1. COLUMN VECTORS AND INNER PRODUCTS;282
17.2;2. MATRICES;290
17.3;3. 3 x 3 MATRICES;295
17.4;4. DETERMINANTS;298
17.5;5. LINEAR SYSTEMS;305
17.6;6. INVERSES AND CRAMER'S RULE;311
17.7;TEST;315
18;CHAPTER 12. GEOMETRY OF SPACE;317
18.1;1. LINES AND PLANES;317
18.2;2. THE CROSS PRODUCT;320
18.3;3. LINEAR INDEPENDENCE;326
18.4;4. SOME APPLICATIONS;331
18.5;5. POLYNOMIALS IN SEVERAL VARIABLES;337
18.6;6. QUADRIC SURFACES;340
18.7;7. CYLINDERS AND CONES;345
18.8;TEST;347
19;CHAPTER 13. LINEAR TRANSFORMATIONS;348
19.1;1. BASIC PROPERTIES;348
19.2;2. EXAMPLES IN THE PLANE;351
19.3;3. ROTATIONS AND REFLECTIONS;355
19.4;4. EXAMPLES IN SPACE;360
19.5;TEST;364
20;CHAPTER 14. COMPLEX NUMBERS;366
20.1;1. COMPLEX ARITHMETIC;366
20.2;2. THE COMPLEX PLANE;372
20.3;3. ZEROS OF POLYNOMIALS;379
20.4;4. DE MOIVRE'S THEOREM AND ROOTS OF UNITY;383
20.5;5. COMPLEX MATRICES [Optional];390
20.6;TEST;394
21;CHAPTER 15. FINITE MATHEMATICS;395
21.1;1. SEQUENCES;395
21.2;2. EVALUATION OF SUMS;402
21.3;3. COUNTING;408
21.4;4. PERMUTATIONS AND COMBINATIONS;411
21.5;5. BINOMIAL THEOREM;417
21.6;6. MATHEMATICAL INDUCTION;419
21.7;TEST;426
22;ANSWERS TO ODD-NUMBERED EXERCISES;428
23;TABLES;466
24;INDEX;484