商务与经济数学 英文PDF格式文档图书下载

INTRODUCTION： Getting Started 1

NOTES FOR STUDENTS： HOW TO USE THIS BOOK 1

CHAPTER 1 Linear Equations 5

SECTION 1.1 Introduction to algebra 6

1.1.1 Negative numbers 7

1.1.2 Expressions 9

1.1.3 Brackets 12

Key Terms 17

Exercise 1.1 18

Exercise 1.1 20

SECTION 1.2 Further algebra 21

1.2.1 Fractions 21

1.2.2 Equations 28

1.2.3 Inequalities 32

Key Terms 35

Exercise 1.2 35

Exercise 1.2 36

SECTION 1.3 Graphs of linear equations 39

Key Terms 49

Exercise 1.3 49

Exercise 1.3 50

SECTION 1.4 Algebraic solution of simultaneous linear equations 51

Key Term 61

Exercise 1.4 61

Exercise 1.4 62

SECTION 1.5 Supply and demand analysis 63

Key Terms 75

Exercise 1.5 75

Exercise 1.5 77

SECTION 1.6 Transposition of formulae 79

Key Terms 86

Exercise 1.6 86

Exercise 1.6 87

SECTION 1.7 National income determination 89

Key Terms 101

Exercise 1.7 101

Exercise 1.7 102

Formal mathematics 104

key Terms 106

CHAPTER 2 Non-linear Equations 109

SECTION 2.1 Quadratic functions 110

Key Terms 124

Exercise 2.1 125

Exercise 2.1 125

SECTION 2.2 Revenue， cost and profit 127

Key Terms 135

Exercise 2.2 135

Exercise 2.2 137

SECTION 2.3 Indices and logarithms 138

2.3.1 Index notation 138

2.3.2 Rules of indices 142

2.3.3 Logarithms 148

2.3.4 Summary 154

Key Terms 155

Exercise 2.3 156

Exercise 2.3 157

SECTION 2.4 The exponential and natural logarithm functions 159

Key Terms 169

Exercise 2.4 169

Exercise 2.4 170

Formal mathematics 172

key Terms 174

CHAPTER 3 Mathematics of Finance 177

SECTION 3.1 Percentages 178

3.1.1 Index numbers 184

3.1.2 Inflation 187

Key Terms 190

Exercise 3.1 190

Exercise 3.1 192

SECTION 3.2 Compound interest 195

Key Terms 205

Exercise 3.2 206

Exercise 3.2 207

SECTION 3.3 Geometric series 209

Key Terms 217

Exercise 3.3 217

Exercise 3.3 218

SECTION 3.4 Investment appraisal 220

Key Terms 232

Exercise 3.4 233

Exercise 3.4 233

Formal mathematics 235

key Terms 236

CHAPTER 4 Differentiation 239

SECTION 4.1 The derivative of a function 240

Key Terms 249

Exercise 4.1 249

Exercise 4.1 250

SECTION 4.2 Rules of differentiation 251

Rule 1 The constant rule 251

Rule 2 The sum rule 252

Rule 3 The difference rule 253

Key Terms 258

Exercise 4.2 258

Exercise 4.2 260

SECTION 4.3 Marginal functions 261

4.3.1 Revenue and cost 261

4.3.2 Production 268

4.3.3 Consumption and savings 271

Key Terms 272

Exercise 4.3 273

Exercise 4.3 274

SECTION 4.4 Further rules of differentiation 275

Rule 4 The chain rule 276

Rule 5 The product rule 278

Rule 6 The quotient rule 281

Exercise 4.4 283

Exercise 4.4 284

SECTION 4.5 Elasticity 285

Key Terms 297

Exercise 4.5 298

Exercise 4.5 298

SECTION 4.6 Optimisation of economic functions 300

Key Terms 316

Exercise 4.6 316

Exercise 4.6 318

SECTION 4.7 Further optimisation of economic functions 319

Exercise 4.7 328

SECTION 4.8 The derivative of the exponential and natural logarithm functions 330

Exercise 4.8 339

Exercise 4.8 340

Formal mathematics 342

CHAPTER5 Partial Differentiation 347

SECTION 5.1 Functions of several variables 348

Key Terms 359

Exercise 5.1 360

Exercise 5.1 361

SECTION 5.2 Partial elasticity and marginal functions 362

5.2.1 Elasticity of demand 362

5.2.2 Utility 365

5.2.3 Production 371

Key Terms 373

Exercise 5.2 374

Exercise 5.2 375

SECTION 5.3 Comparative statics 377

Key Terms 386

Exercise 5.3 387

SECTION 5.4 Unconstrained optimisation 390

Key Terms 401

Exercise 5.4 401

Exercise 5.4 402

SECTION 5.5 Constrained optimisation 403

Key Terms 412

Exercise 5.5 413

Exercise 5.5 414

SECTION 5.6 Lagrange multipliers 415

Key Terms 424

Exercise 5.6 424

Exercise 5.6 425

Formal mathematics 427

CHAPTER 6 Integration 431

SECTION 6.1 Indefinite integration 432

Key Terms 441

Exercise 6.1 442

Exercise 6.1 442

SECTION 6.2 Definite integration 444

6.2.1 Consumer's surplus 448

6.2.2 Producer's surplus 449

6.2.3 Investment flow 451

6.2.4 Discounting 453

Key Terms 454

Exercise 6.2 454

Exercise 6.2 455

Formal mathematics 457

CHAPTER 7 Matrices 461

SECTION 7.1 Basic matrix operations 462

7.1.1 Transposition 464

7.1.2 Addition and subtraction 466

7.1.3 Scalar multiplication 468

7.1.4 Matrix multiplication 469

7.1.5 Summary 477

Key Terms 477

Exercise 7.1 478

Exercise 7.1 480

SECTION 7.2 Matrix inversion 482

Key Terms 497

Exercise 7.2 497

Exercise 7.2 498

SECTION 7.3 Cramer's rule 500

Key Term 508

Exercise 7.3 508

Exercise 7.3 509

Formal mathematics 512

CHAPTER 8 Linear Programming 515

SECTION 8.1 Graphical solution of linear programming problems 516

Key Terms 531

Exercise 8.1 531

Exercise 8.1 532

SECTION 8.2 Applications of linear programming 534

Key Term 544

Exercise 8.2 544

Exercise 8.2 545

Formal mathematics 547

CHAPTER 9 Dynamics 549

SECTION 9.1 Difference equations 550

9.1.1 National income determination 556

9.1.2 Supply and demand analysis 558

Key Terms 561

Exercise 9.1 561

Exercise 9.1 563

SECTION 9.2 Differential equations 565

9.2.1 National income determination 571

9.2.2 Supply and demand analysis 573

Key Terms 575

Exercise 9.2 576

Exercise 9.2 577

Formal mathematics 579

Answers 580

Chapter 1 580

Chapter 2 588

Chapter 3 595

Chapter 4 598

Chapter 5 607

Chapter 6 611

Chapter 7 613

Chapter 8 618

Chapter 9 621

GLOSSARY 624

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