Elementary Functions and Analytic Geometry (eBook)

Harley Flanders (Autor)

eBook Download: PDF

2014 | 1. Auflage
402 Seiten
Elsevier Science (Verlag)
978-1-4832-7196-5 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Elementary Functions and Analytic Geometry 4
Copyright Page 5
Table of Contents 8
Dedication 6
PREFACE 12
CHAPTER 1. FUNCTIONS AND GRAPHS 18
1. INTRODUCTION 18
2. REAL NUMBERS 19
3. COORDINATES ON THE LINE AND PLANE 21
4. FUNCTIONS 25
5. CONSTRUCTION OF FUNCTIONS 30
CHAPTER 2. LINEAR AND QUADRATIC FUNCTIONS 33
1. LINEAR FUNCTIONS 33
2. QUADRATIC FUNCTIONS 40
3. SOME APPLICATIONS 47
4. TIPS ON GRAPHING 50
CHAPTER 3. POLYNOMIAL FUNCTIONS 55
1. ALGEBRA OF POLYNOMIALS 55
2. GRAPHS OF POLYNOMIALS 60
3. ZEROS AND ROOTS 66
4. ZEROS OF HIGHER DEGREE POLYNOMIALS 71
5. GRAPHS OF FACTORED POLYNOMIALS 76
CHAPTER 4. RATIONAL FUNCTIONS 81
1. BASIC PROPERTIES 81
2. ALGEBRAIC OPERATIONS 85
3. GRAPHS OF RATIONAL FUNCTIONS 88
4. DIVISION WITH REMAINDER 99
5. PARTIAL FRACTIONS 103
CHAPTER 5. EXPONENTIAL AND LOGARITHM FUNCTIONS 108
1. REVIEW OF EXPONENTS 108
2. EXPONENTIAL FUNCTIONS 111
3. LOGARITHM FUNCTIONS 117
4. ACCURACY AND TABLES [Optional] 122
5. LOG TABLES [Optional] 125
6. COMPUTATIONS WITH LOGARITHMS [Optional] 128
7. POWER FUNCTIONS 133
CHAPTER 6. TRIGONOMETRIC FUNCTIONS 141
1. INTRODUCTION 141
2. DISTANCES AND ANGLES 141
3. SINE AND COSINE 147
4. OTHER TRIGONOMETRIC FUNCTIONS 152
5. GRAPHS OF SINE AND COSINE 156
6. GRAPHS OF THE OTHER FUNCTIONS 162
CHAPTER 7. IDENTITIES AND INVERSE FUNCTIONS 169
1. IDENTITIES 169
2. FURTHER IDENTITIES 175
3. INVERSE FUNCTIONS 180
4. TRIGONOMETRIC EQUATIONS 187
CHAPTER 8. TRIGONOMETRY 190
1. RIGHT TRIANGLES 190
2. LAWS OF COSINES AND SINES 195
3. OBLIQUE TRIANGLES [Optional] 199
CHAPTER 9. VECTORS 204
1. VECTOR ALGEBRA 204
2. LINES 210
3. LENGTH AND INNER PRODUCT 216
4. NORMAL FORM 222
CHAPTER 10. ANALYTIC GEOMETRY 231
1. TRANSLATION OF AXES 231
2. THE CIRCLE 233
3. TANGENTS AND LOCI 239
5. CONICS THE PARABOLA
6. THE ELLIPSE 257
7. THE HYPERBOLA 263
8. ROTATION OF AXES [Optional] 268
9. ADDITIONAL EXERCISES ON CONICS [Optional] 277
CHAPTER 11. SOLID ANALYTIC GEOMETRY 280
1. COORDINATES AND VECTORS 280
2. LINES AND PLANES 288
3. LINEAR SYSTEMS AND INTERSECTIONS 294
4. POLYNOMIALS IN SEVERAL VARIABLES 300
5. QUADRIC SURFACES 304
6. CYLINDERS AND CONES 309
CHAPTER 12. COMPLEX NUMBERS 312
1. COMPLEX ARITHMETIC 312
2. THE COMPLEX PLANE 318
3. ZEROS OF POLYNOMIALS 325
4. DE MOIVRE'S THEOREM AND ROOTS OF UNITY 329
CHAPTER 13. INDUCTION AND THE BINOMIAL THEOREM 337
1. MATHEMATICAL INDUCTION 337
2. BINOMIAL COEFFICIENTS 343
3. BINOMIAL THEOREM 346
ANSWERS TO ODD-NUMBERED EXERCISES 352
TABLES 382
1. 4-place logarithm 383
2. 4-place antilogarithm 385
3. Powers and roots 387
4. Trigonometric (degrees) 389
5. Trigonometric (radians) 393
6. Log-trig (degrees) 395
7. Trigonometric (p radians) 399
INDEX 400

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 1-4832-7196-X / 148327196X
• ISBN-13: 978-1-4832-7196-5 / 9781483271965