新视野中学数学读本：高中年级版PDF电子书下载

Chapter 1 Sets 1

1.1 Equality of Sets 1

1.2 Empty Set,Subsets 2

1.3 Venn Diagrams 2

1.4 Operations on Sets 3

1.5 Number of Elements in a Finite Set 5

1.6 Worked Examples 5

1.7 Exercises 6

Chapter 2 Real Number System 9

2.1 Integers 9

2.2 Rational Numbers 10

2.3 Irrational Numbers 11

2.4 Operations and Their Properties 12

2.5 The Real Number Line 16

2.6 Ordering the Real Numbers 16

2.7 The Absolute Value of a Real Number 17

2.8 Worked Examples 17

2.9 Exercises 20

Chapter 3 The Language of Algebra 23

3.1 Describing Situation with Algebra 24

3.2 Formulas 26

3.3 Explicit and Recursive Formulas for Sequences 28

3.4 Solving Equations and Inequalities 31

3.5 Worked Examples 33

3.6 Exercises 35

Chapter 4 Statement Calculus 37

4.1 Composition of Statements 37

4.2 Equivalent Formulae 39

4.3 Valid Formulae and Falsities 40

4.4 Universal Quantifier and Existential Quantifier 42

4.5 Worked Examples 43

4.6 Exercises 44

Chapter 5 Functions 46

5.1 Introduction to Coordinates 46

5.2 Functions 48

5.3 Composition of Functions 53

5.4 Some Special Real Functions 56

5.5 Some Examples of Real Functions 60

5.6 Worked Examples 63

5.7 Exercises 69

Chapter 6 Power,Exponential and Logarithmic Functions 75

6.1 nth Root Functions 76

6.2 Rational Power Functions 79

6.3 Exponential Functions 82

6.4 Logarithmic Functions 86

6.5 e and Natural Logarithms 89

6.6 Properties of Logarithms 92

6.7 Solving Exponential Equations 94

6.8 The Scientific Calculator 95

6.9 Worked Examples 100

6.10 Exercises 103

Chapter 7 Polynomial Functions 105

7.1 Polynomial Models 105

7.2 Finding Polynomial Models 110

7.3 The Factor Theorem 111

7.4 Complex Numbers 113

7.5 The Fundamental Theorem of Algebra 115

7.6 Roots and Coefficients of Polynomials 118

7.7 Modeling Data with Polynomials 120

7.8 Worked Examples 122

7.9 Exercises 125

Chapter 8 Sequences,Series and Counting Principles 127

8.1 Arithmetic and Geometric Sequences 127

8.2 Limits of Sequences 130

8.3 Arithmetic and Geometric Series 133

8.4 Mathematical Induction 141

8.5 The Binomial Theorem 146

8.6 Worked Examples 153

8.7 Exercises 156

Chapter 9 Trigonometry 161

9.1 Radian and Degree Measure 162

9.2 Lengths of Arc and Areas of Sectors 164

9.3 Trigonometric Ratios of Acute Angeles 165

9.4 The Sine,Cosine and Tangent Functions 167

9.5 Graphs of the Sine,Cosine and Tangent Functions 170

9.6 Properties of Sines,Cosines and Tangents 174

9.7 The Law of Sines and Cosines 177

9.8 From Washington to Beijing 179

9.9 The Secant,Cosecant and Cotangent Functions 187

9.10 Inverse Trigonometric Functions 187

9.11 Analytic Trigonometry 189

9.12 Trigonometric Form of a Complex Number 193

9.13 Worked Examples 197

9.14 Exercises 201

Chapter 10 Matrices 204

10.1 Storing Data in Matrices 205

10.2 Matrix Multiplication 207

10.3 Size Changes 211

10.4 Scale Changes 213

10.5 Reflections 215

10.6 Transformations and Matrices 216

10.7 Rotations 217

10.8 Perpendicular Lines 221

10.9 Matrix Addition 222

10.10 Worked Examples 225

10.11 Exercises 229

Chapter 11 Linear Programming 231

11.1 Solving Linear Inequalities in Two Variables Graphically 231

11.2 Linear Programming Ⅰ 237

11.3 Linear Programming Ⅱ 243

11.4 Worked Examples 246

11.5 Exercises 249

Chapter 12 Inequalities 251

12.1 Elementary Properties 251

12.2 Arithmetic Mean and Geometric Mean 252

12.3 Cauchy-Schwarz Inequality 254

12.4 Absolute Values 255

12.5 Worked Examples 256

12.6 Exercises 260

Chapter 13 Complex Numbers 262

13.1 Operations on Complex Numbers 263

13.2 Complex Conjugate 264

13.3 Argand Diagram 265

13.4 Modulus of a Complex Number 265

13.5 Argument of a Complex Number 267

13.6 Vectorial Representation of a Complex Number 268

13.7 Geometric Application of Complex Numbers 269

13.8 De Moivre's Theorem 270

13.9 The Mandelbrot Set 271

13.10 Worked Examples 273

13.11 Exercises 276

Chapter 14 Two Dimensional Coordinate Geometry 279

14.1 Straight Lines 280

14.2 Circles 282

14.3 Quadratic Relation 283

14.4 Parabolae 285

14.5 Ellipses 286

14.6 Hyperbolae 288

14.7 Worked Examples 290

14.8 Exercises 294

Chapter 15 Probability and Statistics 296

15.1 Fundamental Properties of Probability 296

15.2 Descriptive Statistics 300

15.3 Probability Distributions 302

15.4 Binomial Probabilities 305

15.5 Binomial Probability Distributions 307

15.6 Mean and Standard Deviation of a Binomial Distribution 310

15.7 Representing Probabilities by Areas 313

15.8 The Parent of the Normal Curve 314

15.9 The Standard Normal Distribution 318

15.10 Using Probability to Make Judgments 320

15.11 Worked Examples 323

15.12 Exercises 330

Chapter 16 Calculus 334

16.1 Limit of a Sequence 334

16.2 Limit of a Function at Infinity 345

16.3 Limit ofa Function at a Point 347

16.4 Two Important Limits 349

16.5 Left and Right Hand Limits 349

16.6 Continuous Functions 350

16.7 Properties of Continuous Functions 352

16.8 Worked Examples Ⅰ 353

16.9 Exercises Ⅰ 356

16.10 Derivatives 357

16.11 Differentiability 360

16.12 Rules of Differentiation 362

16.13 Mean Value Theorem 364

16.14 Applications of Differential Calculus 366

16.15 Worked Examples Ⅱ 372

16.16 Exercises Ⅱ 375

16.17 Indefinite Integrals 376

16.18 Definite Integrals 377

16.19 Applications of Definite Integrals 381

16.20 Worked Examples Ⅲ 383

16.21 Exercises Ⅲ 384

GLOSSARY 385