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Preface                                                                page     ix
Introduction: Getting Started                                          1
Notes for students: how to use this book                           1
Getting started with Excel                                         3
Getting started with Maple                                         9
Notes for tutors: an author's apology                                      12

1  Linear Equations                                                            13
1.1 Graphs of linear equations                                             14
1.2 Algebraic solution of simultaneous linear equations           32
1.3 Supply and demand analysis                                             44
1.4 Algebra                                                                63
1.5 Transposition of formulae                                              84
1.6  National income determination                                         93

2  Non-linear Equations                                                      111
2.2 Revenue, cost and profit                                              125
2.3 Indices and logarithms                                                137
2.4 The exponential and natural logarithm functions                       158

3  Mathematics of Finance                                                    171
3.1 Percentages                                                           172
3.2 Compound interest                                                     189
3.3 Geometric series                                                      205
3.4 Investment appraisal                                                  215

4  Differentiation                                                           233
4.1  The derivative of a function                                         235
4.2  Rules of differentiation                                             247
4.3 Marginal functions                                                    256
4.4  Further rules of differentiation                                     270
4.5  Elasticity                                                           280
4.6 Optimization of economic functions                                    293

4.7 Further optimization of economic functions                            315
4.8 The derivative of the exponential and natural logarithm functions  326

5  Partial Differentiation                                                    337
5.1  Functions of several variables                                       338
5.2  Partial elasticity and marginal functions                            350
5.3 Comparative statics                                                   367
5.4  Unconstrained optimization                                           379
5.5 Constrained optimization                                              395
5.6 Lagrange multipliers                                                  407

6  Integration                                                               419
6.1 Indefinite integration                                                420
6.2  Definite integration                                                 435

7  Matrices                                                                  451
7.1  Basic matrix operations                                              452
7.2  Matrix inversion                                                    471
7.3 Cramer's rule                                                        492
7.4 Input-output analysis                                                 502

8  Linear Programming                                                        515
8.1  Graphical solution of linear programming problems                    516
8.2 Applications of linear programming                                    535

9  Dynamics                                                                  551
9.1  Difference equations                                                 552
9.2 Differential equations                                                569

Appendix Differentiation from First Principles                               587
Solutions to Problems                                                        591
Index                                                                        661

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Library of Congress Subject Headings for this publication: Economics, Mathematical, Business mathematics