Additional Information
Book Details
Abstract
Mathematics for Economics and Business, 9e is the essential resource you need when studying mathematics as part of your economics, management or business course.
Whatever your level of prior mathematical knowledge, ability or confidence, this book will guide you step-by-step through the key mathematical concepts and techniques you need to succeed. Starting with the basics, the book is designed to allow you to progress at your own pace, with a wealth of examples, practice exercises and self-test questions to check your understanding along the way.
Worked examples throughout each chapter illustrate how mathematical concepts and techniques relate to the business world and encourage you to solve real problems yourself.
Over 200 new questions have been added to this new edition, with answers provided, making it a fantastic resource for revision purposes.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Inside Front Cover | IFC | ||
| Title Page | iii | ||
| Copyright Page | iv | ||
| Dedication | v | ||
| Contents | vi | ||
| Preface | xi | ||
| INTRODUCTION: Getting Started | 1 | ||
| Notes for students: how to use this text | 1 | ||
| Chapter 1 Linear Equations | 5 | ||
| 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 | ||
| 1.2 Further algebra | 22 | ||
| 1.2.1 Fractions | 22 | ||
| 1.2.2 Equations | 29 | ||
| 1.2.3 Inequalities | 33 | ||
| Key Terms | 36 | ||
| Exercise 1.2 | 36 | ||
| Exercise 1.2* | 38 | ||
| 1.3 Graphs of linear equations | 40 | ||
| Key Terms | 51 | ||
| Exercise 1.3 | 52 | ||
| Exercise 1.3* | 53 | ||
| 1.4 Algebraic solution of simultaneous linear equations | 55 | ||
| Key Term | 65 | ||
| Exercise 1.4 | 65 | ||
| Exercise 1.4* | 66 | ||
| 1.5 Supply and demand analysis | 67 | ||
| Key Terms | 80 | ||
| Exercise 1.5 | 80 | ||
| Exercise 1.5* | 82 | ||
| 1.6 Transposition of formulae | 84 | ||
| Key Terms | 91 | ||
| Exercise 1.6 | 91 | ||
| Exercise 1.6* | 92 | ||
| 1.7 National income determination | 93 | ||
| Key Terms | 105 | ||
| Exercise 1.7 | 105 | ||
| Exercise 1.7* | 106 | ||
| Formal mathematics | 109 | ||
| Multiple choice questions | 112 | ||
| Examination questions | 116 | ||
| Chapter 2 Non-linear Equations | 121 | ||
| 2.1 Quadratic functions | 122 | ||
| Key Terms | 136 | ||
| Exercise 2.1 | 137 | ||
| Exercise 2.1* | 138 | ||
| 2.2 Revenue, cost and profit | 140 | ||
| Key Terms | 148 | ||
| Exercise 2.2 | 148 | ||
| Exercise 2.2* | 150 | ||
| 2.3 Indices and logarithms | 151 | ||
| 2.3.1 Index notation | 151 | ||
| 2.3.2 Rules of indices | 155 | ||
| 2.3.3 Logarithms | 161 | ||
| 2.3.4 Summary | 167 | ||
| Key Terms | 168 | ||
| Exercise 2.3 | 168 | ||
| Exercise 2.3* | 170 | ||
| 2.4 The exponential and natural logarithm functions | 172 | ||
| Key Terms | 182 | ||
| Exercise 2.4 | 182 | ||
| Exercise 2.4* | 183 | ||
| Formal mathematics | 186 | ||
| Multiple choice questions | 189 | ||
| Examination questions | 193 | ||
| Chapter 3 Mathematics of Finance | 197 | ||
| 3.1 Percentages | 198 | ||
| 3.1.1 Index numbers | 204 | ||
| 3.1.2 Inflation | 208 | ||
| Key Terms | 210 | ||
| Exercise 3.1 | 210 | ||
| Exercise 3.1* | 213 | ||
| 3.2 Compound interest | 216 | ||
| Key Terms | 226 | ||
| Exercise 3.2 | 226 | ||
| Exercise 3.2* | 228 | ||
| 3.3 Geometric series | 230 | ||
| Key Terms | 238 | ||
| Exercise 3.3 | 238 | ||
| Exercise 3.3* | 239 | ||
| 3.4 Investment appraisal | 241 | ||
| Key Terms | 253 | ||
| Exercise 3.4 | 253 | ||
| Exercise 3.4* | 255 | ||
| Formal mathematics | 257 | ||
| Multiple choice questions | 259 | ||
| Examination questions | 263 | ||
| Chapter 4 Differentiation | 267 | ||
| 4.1 The derivative of a function | 268 | ||
| Key Terms | 277 | ||
| Exercise 4.1 | 277 | ||
| Exercise 4.1* | 278 | ||
| 4.2 Rules of differentiation | 279 | ||
| Rule 1 The constant rule | 279 | ||
| Rule 2 The sum rule | 280 | ||
| Rule 3 The difference rule | 281 | ||
| Key Terms | 286 | ||
| Exercise 4.2 | 286 | ||
| Exercise 4.2* | 288 | ||
| 4.3 Marginal functions | 290 | ||
| 4.3.1 Revenue and cost | 290 | ||
| 4.3.2 Production | 297 | ||
| 4.3.3 Consumption and savings | 299 | ||
| Key Terms | 301 | ||
| Exercise 4.3 | 301 | ||
| Exercise 4.3* | 302 | ||
| 4.4 Further rules of differentiation | 304 | ||
| Rule 4 The chain rule | 305 | ||
| Rule 5 The product rule | 307 | ||
| Rule 6 The quotient rule | 310 | ||
| Exercise 4.4 | 312 | ||
| Exercise 4.4* | 313 | ||
| 4.5 Elasticity | 314 | ||
| Key Terms | 326 | ||
| Exercise 4.5 | 326 | ||
| Exercise 4.5* | 327 | ||
| 4.6 Optimisation of economic functions | 329 | ||
| Key Terms | 345 | ||
| Exercise 4.6 | 345 | ||
| Exercise 4.6* | 347 | ||
| 4.7 Further optimisation of economic functions | 348 | ||
| Key Term | 359 | ||
| Exercise 4.7* | 359 | ||
| 4.8 The derivative of the exponential and natural logarithm functions | 361 | ||
| Exercise 4.8 | 370 | ||
| Exercise 4.8* | 371 | ||
| Formal mathematics | 373 | ||
| Multiple choice questions | 376 | ||
| Examination questions | 382 | ||
| Chapter 5 Partial Differentiation | 389 | ||
| 5.1 Functions of several variables | 390 | ||
| Key Terms | 400 | ||
| Exercise 5.1 | 401 | ||
| Exercise 5.1* | 402 | ||
| 5.2 Partial elasticity and marginal functions | 404 | ||
| 5.2.1 Elasticity of demand | 404 | ||
| 5.2.2 Utility | 407 | ||
| 5.2.3 Production | 413 | ||
| Key Terms | 415 | ||
| Exercise 5.2 | 416 | ||
| Exercise 5.2* | 418 | ||
| 5.3 Comparative statics | 420 | ||
| Key Terms | 429 | ||
| Exercise 5.3* | 429 | ||
| 5.4 Unconstrained optimisation | 433 | ||
| Key Terms | 444 | ||
| Exercise 5.4 | 444 | ||
| Exercise 5.4* | 445 | ||
| 5.5 Constrained optimisation | 447 | ||
| Key Terms | 456 | ||
| Exercise 5.5 | 457 | ||
| Exercise 5.5* | 458 | ||
| 5.6 Lagrange multipliers | 460 | ||
| Key Terms | 468 | ||
| Exercise 5.6 | 469 | ||
| Exercise 5.6* | 470 | ||
| Formal mathematics | 472 | ||
| Multiple choice questions | 474 | ||
| Examination questions | 477 | ||
| Chapter 6 Integration | 483 | ||
| 6.1 Indefinite integration | 484 | ||
| Key Terms | 495 | ||
| Exercise 6.1 | 496 | ||
| Exercise 6.1* | 497 | ||
| 6.2 Definite integration | 499 | ||
| 6.2.1 Consumer’s surplus | 503 | ||
| 6.2.2 Producer’s surplus | 504 | ||
| 6.2.3 Investment flow | 506 | ||
| 6.2.4 Discounting | 508 | ||
| Key Terms | 509 | ||
| Exercise 6.2 | 509 | ||
| Exercise 6.2* | 510 | ||
| Formal mathematics | 513 | ||
| Multiple choice questions | 515 | ||
| Examination questions | 518 | ||
| Chapter 7 Matrices | 523 | ||
| 7.1 Basic matrix operations | 524 | ||
| 7.1.1 Transposition | 526 | ||
| 7.1.2 Addition and subtraction | 527 | ||
| 7.1.3 Scalar multiplication | 530 | ||
| 7.1.4 Matrix multiplication | 531 | ||
| 7.1.5 Summary | 539 | ||
| Key Terms | 539 | ||
| Exercise 7.1 | 540 | ||
| Exercise 7.1* | 542 | ||
| 7.2 Matrix inversion | 545 | ||
| Key Terms | 560 | ||
| Exercise 7.2 | 560 | ||
| Exercise 7.2* | 561 | ||
| 7.3 Cramer’s rule | 564 | ||
| Key Term | 572 | ||
| Exercise 7.3 | 572 | ||
| Exercise 7.3* | 573 | ||
| Formal mathematics | 576 | ||
| Multiple choice questions | 577 | ||
| Examination questions | 581 | ||
| Chapter 8 Linear Programming | 585 | ||
| 8.1 Graphical solution of linear programming problems | 586 | ||
| Key Terms | 600 | ||
| Exercise 8.1 | 601 | ||
| Exercise 8.1* | 602 | ||
| 8.2 Applications of linear programming | 604 | ||
| Key Terms | 612 | ||
| Exercise 8.2 | 612 | ||
| Exercise 8.2* | 614 | ||
| Formal mathematics | 617 | ||
| Multiple choice questions | 618 | ||
| Examination questions | 623 | ||
| Chapter 9 Dynamics | 627 | ||
| 9.1 Difference equations | 628 | ||
| 9.1.1 National income determination | 634 | ||
| 9.1.2 Supply and demand analysis | 636 | ||
| Key Terms | 639 | ||
| Exercise 9.1 | 639 | ||
| Exercise 9.1* | 640 | ||
| 9.2 Differential equations | 643 | ||
| 9.2.1 National income determination | 649 | ||
| 9.2.2 Supply and demand analysis | 651 | ||
| Key Terms | 653 | ||
| Exercise 9.2 | 654 | ||
| Exercise 9.2* | 655 | ||
| Formal mathematics | 658 | ||
| Multiple choice questions | 659 | ||
| Examination questions | 662 | ||
| Answers to Problems | 664 | ||
| Chapter 1 | 664 | ||
| Chapter 2 | 674 | ||
| Chapter 3 | 683 | ||
| Chapter 4 | 687 | ||
| Chapter 5 | 698 | ||
| Chapter 6 | 705 | ||
| Chapter 7 | 709 | ||
| Chapter 8 | 715 | ||
| Chapter 9 | 719 | ||
| Glossary | 723 | ||
| Index | 730 | ||
| A | 730 | ||
| B | 730 | ||
| C | 730 | ||
| D | 731 | ||
| E | 732 | ||
| F | 732 | ||
| G | 733 | ||
| H | 733 | ||
| I | 733 | ||
| L | 734 | ||
| M | 734 | ||
| N | 735 | ||
| O | 736 | ||
| P | 736 | ||
| Q | 736 | ||
| R | 736 | ||
| S | 737 | ||
| T | 737 | ||
| U | 738 | ||
| V | 738 | ||
| W | 738 | ||
| X | 738 | ||
| Y | 738 | ||
| Z | 738 | ||
| Back Cover | Back Cover |