Contents
Preface ix
Introduction: Getting Started 1
Notes for students: how to use this book 1
Getting started with MyMathLab
Getting started with Excel 3
Getting started with Maple 9
1 Linear Equations 13
1.1 Introduction to algebra
1.2 Further algebra
1.3 Graphs of linear equations 15
1.4 Algebraic solution of simultaneous linear equations 35
1.5 Supply and demand analysis 47
1.6 Transposition of formulae 87
1.7 National income determination 96
2 Non-linear Equations 113
2.1 Quadratic functions 115
2.2 Revenue, cost and profit 129
2.3 Indices and logarithms 141
2.4 The exponential and natural logarithm functions 162
3 Mathematics of Finance 175
3.1 Percentages 177
3.2 Compound interest 194
3.3 Geometric series 209
3.4 Investment appraisal 220
4 Differentiation 237
4.1 The derivative of a function 239
4.2 Rules of differentiation 251
4.3 Marginal functions 261
4.4 Further rules of differentiation 275
4.5 Elasticity 284
4.6 Optimization of economic functions 298
4.7 Further optimization of economic functions 320
4.8 The derivative of the exponential and natural logarithm functions 331
5 Partial Differentiation 341
5.1 Functions of several variables 343
5.2 Partial elasticity and marginal functions 356
5.3 Comparative statics 374
5.4 Unconstrained optimization 386
5.5 Constrained optimization 400
5.6 Lagrange multipliers 411
6 Integration 421
6.1 Indefinite integration 423
6.2 Definite integration 437
7 Matrices 451
7.1 Basic matrix operations 453
7.2 Matrix inversion 472
7.3 Cramer's rule 492
7.4 Input output analysis 502
Glossary 663
Index 673
THE FOLLOWING ADDITIONAL MATERIAL CAN BE FOUND ON THE WEBSITE (www.pearsoned.co.uk/jacques):
Additional Topic 1 Linear Programming 515
T.1.1 Graphical solution of linear programming problems 517
T.2.1 Applications of linear programming 535
Additional Topic 2 Dynamics 551
T.2.1 Difference equations 553
T.2.2 Differential equations 569
Appendix 1 Differentiation from First Principles 587
Appendix 2 Implicit Differentiation 591
Appendix 3 Hessians 594
Solutions to Problems 598
WEB BOX
Contents
Preface ix
Introduction: Getting Started 1
Notes for students: how to use this book 1
Getting started with MyMathLab
Getting started with Excel 3
Getting started with Maple 9
1 Linear Equations 13
1.1 Introduction to algebra
1.2 Further algebra
1.3 Graphs of linear equations 15
1.4 Algebraic solution of simultaneous linear equations 35
1.5 Supply and demand analysis 47
1.6 Transposition of formulae 87
1.7 National income determination 96
2 Non-linear Equations 113
2.1 Quadratic functions 115
2.2 Revenue, cost and profit 129
2.3 Indices and logarithms 141
2.4 The exponential and natural logarithm functions 162
3 Mathematics of Finance 175
3.1 Percentages 177
3.2 Compound interest 194
3.3 Geometric series 209
3.4 Investment appraisal 220
4 Differentiation 237
4.1 The derivative of a function 239
4.2 Rules of differentiation 251
4.3 Marginal functions 261
4.4 Further rules of differentiation 275
4.5 Elasticity 284
4.6 Optimization of economic functions 298
4.7 Further optimization of economic functions 320
4.8 The derivative of the exponential and natural logarithm functions 331
5 Partial Differentiation 341
5.1 Functions of several variables 343
5.2 Partial elasticity and marginal functions 356
5.3 Comparative statics 374
5.4 Unconstrained optimization 386
5.5 Constrained optimization 400
5.6 Lagrange multipliers 411
6 Integration 421
6.1 Indefinite integration 423
6.2 Definite integration 437
7 Matrices 451
7.1 Basic matrix operations 453
7.2 Matrix inversion 472
7.3 Cramer's rule 492
7.4 Input output analysis 502
Glossary 663
Index 673
THE FOLLOWING ADDITIONAL MATERIAL CAN BE FOUND ON THE WEBSITE (www.pearsoned.co.uk/jacques):
Additional Topic 1 Linear Programming 515
T.1.1 Graphical solution of linear programming problems 517
T.2.1 Applications of linear programming 535
Additional Topic 2 Dynamics 551
T.2.1 Difference equations 553
T.2.2 Differential equations 569
Appendix 1 Differentiation from First Principles 587
Appendix 2 Implicit Differentiation 591
Appendix 3 Hessians 594
Solutions to Problems 598
WEB BOX