新视野中学数学读本：高中年级版PDF|Epub|txt|kindle电子书版本网盘下载

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Chapter 1 Sets1

1.1 Equality of Sets1

1.2 Empty Set,Subsets2

1.3 Venn Diagrams2

1.4 Operations on Sets3

1.5 Number of Elements in a Finite Set5

1.6 Worked Examples5

1.7 Exercises6

Chapter 2 Real Number System9

2.1 Integers9

2.2 Rational Numbers10

2.3 Irrational Numbers11

2.4 Operations and Their Properties12

2.5 The Real Number Line16

2.6 Ordering the Real Numbers16

2.7 The Absolute Value of a Real Number17

2.8 Worked Examples17

2.9 Exercises20

Chapter 3 The Language of Algebra23

3.1 Describing Situation with Algebra24

3.2 Formulas26

3.3 Explicit and Recursive Formulas for Sequences28

3.4 Solving Equations and Inequalities31

3.5 Worked Examples33

3.6 Exercises35

Chapter 4 Statement Calculus37

4.1 Composition of Statements37

4.2 Equivalent Formulae39

4.3 Valid Formulae and Falsities40

4.4 Universal Quantifier and Existential Quantifier42

4.5 Worked Examples43

4.6 Exercises44

Chapter 5 Functions46

5.1 Introduction to Coordinates46

5.2 Functions48

5.3 Composition of Functions53

5.4 Some Special Real Functions56

5.5 Some Examples of Real Functions60

5.6 Worked Examples63

5.7 Exercises69

Chapter 6 Power,Exponential and Logarithmic Functions75

6.1 nth Root Functions76

6.2 Rational Power Functions79

6.3 Exponential Functions82

6.4 Logarithmic Functions86

6.5 e and Natural Logarithms89

6.6 Properties of Logarithms92

6.7 Solving Exponential Equations94

6.8 The Scientific Calculator95

6.9 Worked Examples100

6.10 Exercises103

Chapter 7 Polynomial Functions105

7.1 Polynomial Models105

7.2 Finding Polynomial Models110

7.3 The Factor Theorem111

7.4 Complex Numbers113

7.5 The Fundamental Theorem of Algebra115

7.6 Roots and Coefficients of Polynomials118

7.7 Modeling Data with Polynomials120

7.8 Worked Examples122

7.9 Exercises125

Chapter 8 Sequences,Series and Counting Principles127

8.1 Arithmetic and Geometric Sequences127

8.2 Limits of Sequences130

8.3 Arithmetic and Geometric Series133

8.4 Mathematical Induction141

8.5 The Binomial Theorem146

8.6 Worked Examples153

8.7 Exercises156

Chapter 9 Trigonometry161

9.1 Radian and Degree Measure162

9.2 Lengths of Arc and Areas of Sectors164

9.3 Trigonometric Ratios of Acute Angeles165

9.4 The Sine,Cosine and Tangent Functions167

9.5 Graphs of the Sine,Cosine and Tangent Functions170

9.6 Properties of Sines,Cosines and Tangents174

9.7 The Law of Sines and Cosines177

9.8 From Washington to Beijing179

9.9 The Secant,Cosecant and Cotangent Functions187

9.10 Inverse Trigonometric Functions187

9.11 Analytic Trigonometry189

9.12 Trigonometric Form of a Complex Number193

9.13 Worked Examples197

9.14 Exercises201

Chapter 10 Matrices204

10.1 Storing Data in Matrices205

10.2 Matrix Multiplication207

10.3 Size Changes211

10.4 Scale Changes213

10.5 Reflections215

10.6 Transformations and Matrices216

10.7 Rotations217

10.8 Perpendicular Lines221

10.9 Matrix Addition222

10.10 Worked Examples225

10.11 Exercises229

Chapter 11 Linear Programming231

11.1 Solving Linear Inequalities in Two Variables Graphically231

11.2 Linear Programming Ⅰ237

11.3 Linear Programming Ⅱ243

11.4 Worked Examples246

11.5 Exercises249

Chapter 12 Inequalities251

12.1 Elementary Properties251

12.2 Arithmetic Mean and Geometric Mean252

12.3 Cauchy-Schwarz Inequality254

12.4 Absolute Values255

12.5 Worked Examples256

12.6 Exercises260

Chapter 13 Complex Numbers262

13.1 Operations on Complex Numbers263

13.2 Complex Conjugate264

13.3 Argand Diagram265

13.4 Modulus of a Complex Number265

13.5 Argument of a Complex Number267

13.6 Vectorial Representation of a Complex Number268

13.7 Geometric Application of Complex Numbers269

13.8 De Moivre's Theorem270

13.9 The Mandelbrot Set271

13.10 Worked Examples273

13.11 Exercises276

Chapter 14 Two Dimensional Coordinate Geometry279

14.1 Straight Lines280

14.2 Circles282

14.3 Quadratic Relation283

14.4 Parabolae285

14.5 Ellipses286

14.6 Hyperbolae288

14.7 Worked Examples290

14.8 Exercises294

Chapter 15 Probability and Statistics296

15.1 Fundamental Properties of Probability296

15.2 Descriptive Statistics300

15.3 Probability Distributions302

15.4 Binomial Probabilities305

15.5 Binomial Probability Distributions307

15.6 Mean and Standard Deviation of a Binomial Distribution310

15.7 Representing Probabilities by Areas313

15.8 The Parent of the Normal Curve314

15.9 The Standard Normal Distribution318

15.10 Using Probability to Make Judgments320

15.11 Worked Examples323

15.12 Exercises330

Chapter 16 Calculus334

16.1 Limit of a Sequence334

16.2 Limit of a Function at Infinity345

16.3 Limit ofa Function at a Point347

16.4 Two Important Limits349

16.5 Left and Right Hand Limits349

16.6 Continuous Functions350

16.7 Properties of Continuous Functions352

16.8 Worked Examples Ⅰ353

16.9 Exercises Ⅰ356

16.10 Derivatives357

16.11 Differentiability360

16.12 Rules of Differentiation362

16.13 Mean Value Theorem364

16.14 Applications of Differential Calculus366

16.15 Worked Examples Ⅱ372

16.16 Exercises Ⅱ375

16.17 Indefinite Integrals376

16.18 Definite Integrals377

16.19 Applications of Definite Integrals381

16.20 Worked Examples Ⅲ383

16.21 Exercises Ⅲ384

GLOSSARY385