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