Flanders Elementary Functions and Analytic Geometry

1. Auflage 2014
ISBN: 978-1-4832-7196-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 402 Seiten, Web PDF

Elementary Functions and Analytic Geometry is an introduction to college mathematics, with emphasis on elementary functions and analytic geometry. 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; and complex numbers, mathematical induction, and the binomial theorem. Comprised of 13 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 trigonometry are also explored, together with complex numbers and solid analytic geometry. The book concludes by considering mathematical induction, binomial coefficients, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Autoren/Hrsg.

Flanders, Harley

Inhaltsverzeichnis

1;Front Cover;1
2;Elementary Functions and Analytic Geometry;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;12
7;CHAPTER 1. FUNCTIONS AND GRAPHS;18
7.1;1. INTRODUCTION;18
7.2;2. REAL NUMBERS;19
7.3;3. COORDINATES ON THE LINE AND PLANE;21
7.4;4. FUNCTIONS;25
7.5;5. CONSTRUCTION OF FUNCTIONS;30
8;CHAPTER 2. LINEAR AND QUADRATIC FUNCTIONS;33
8.1;1. LINEAR FUNCTIONS;33
8.2;2. QUADRATIC FUNCTIONS;40
8.3;3. SOME APPLICATIONS;47
8.4;4. TIPS ON GRAPHING;50
9;CHAPTER 3. POLYNOMIAL FUNCTIONS;55
9.1;1. ALGEBRA OF POLYNOMIALS;55
9.2;2. GRAPHS OF POLYNOMIALS;60
9.3;3. ZEROS AND ROOTS;66
9.4;4. ZEROS OF HIGHER DEGREE POLYNOMIALS;71
9.5;5. GRAPHS OF FACTORED POLYNOMIALS;76
10;CHAPTER 4. RATIONAL FUNCTIONS;81
10.1;1. BASIC PROPERTIES;81
10.2;2. ALGEBRAIC OPERATIONS;85
10.3;3. GRAPHS OF RATIONAL FUNCTIONS;88
10.4;4. DIVISION WITH REMAINDER;99
10.5;5. PARTIAL FRACTIONS;103
11;CHAPTER 5. EXPONENTIAL AND LOGARITHM FUNCTIONS;108
11.1;1. REVIEW OF EXPONENTS;108
11.2;2. EXPONENTIAL FUNCTIONS;111
11.3;3. LOGARITHM FUNCTIONS;117
11.4;4. ACCURACY AND TABLES [Optional];122
11.5;5. LOG TABLES [Optional];125
11.6;6. COMPUTATIONS WITH LOGARITHMS [Optional];128
11.7;7. POWER FUNCTIONS;133
12;CHAPTER 6. TRIGONOMETRIC FUNCTIONS;141
12.1;1. INTRODUCTION;141
12.2;2. DISTANCES AND ANGLES;141
12.3;3. SINE AND COSINE;147
12.4;4. OTHER TRIGONOMETRIC FUNCTIONS;152
12.5;5. GRAPHS OF SINE AND COSINE;156
12.6;6. GRAPHS OF THE OTHER FUNCTIONS;162
13;CHAPTER 7. IDENTITIES AND INVERSE FUNCTIONS;169
13.1;1. IDENTITIES;169
13.2;2. FURTHER IDENTITIES;175
13.3;3. INVERSE FUNCTIONS;180
13.4;4. TRIGONOMETRIC EQUATIONS;187
14;CHAPTER 8. TRIGONOMETRY;190
14.1;1. RIGHT TRIANGLES;190
14.2;2. LAWS OF COSINES AND SINES;195
14.3;3. OBLIQUE TRIANGLES [Optional];199
15;CHAPTER 9. VECTORS;204
15.1;1. VECTOR ALGEBRA;204
15.2;2. LINES;210
15.3;3. LENGTH AND INNER PRODUCT;216
15.4;4. NORMAL FORM;222
16;CHAPTER 10. ANALYTIC GEOMETRY;231
16.1;1. TRANSLATION OF AXES;231
16.2;2. THE CIRCLE;233
16.3;3. TANGENTS AND LOCI;239
16.4;5. CONICS; THE PARABOLA;253
16.5;6. THE ELLIPSE;257
16.6;7. THE HYPERBOLA;263
16.7;8. ROTATION OF AXES [Optional];268
16.8;9. ADDITIONAL EXERCISES ON CONICS [Optional];277
17;CHAPTER 11. SOLID ANALYTIC GEOMETRY;280
17.1;1. COORDINATES AND VECTORS;280
17.2;2. LINES AND PLANES;288
17.3;3. LINEAR SYSTEMS AND INTERSECTIONS;294
17.4;4. POLYNOMIALS IN SEVERAL VARIABLES;300
17.5;5. QUADRIC SURFACES;304
17.6;6. CYLINDERS AND CONES;309
18;CHAPTER 12. COMPLEX NUMBERS;312
18.1;1. COMPLEX ARITHMETIC;312
18.2;2. THE COMPLEX PLANE;318
18.3;3. ZEROS OF POLYNOMIALS;325
18.4;4. DE MOIVRE'S THEOREM AND ROOTS OF UNITY;329
19;CHAPTER 13. INDUCTION AND THE BINOMIAL THEOREM;337
19.1;1. MATHEMATICAL INDUCTION;337
19.2;2. BINOMIAL COEFFICIENTS;343
19.3;3. BINOMIAL THEOREM;346
20;ANSWERS TO ODD-NUMBERED EXERCISES;352
21;TABLES;382
21.1;1. 4-place logarithm;383
21.2;2. 4-place antilogarithm;385
21.3;3. Powers and roots;387
21.4;4. Trigonometric (degrees);389
21.5;5. Trigonometric (radians);393
21.6;6. Log-trig (degrees);395
21.7;7. Trigonometric (p radians);399
22;INDEX;400