Contents	6
	Preface	10
	Preface to Second Edition	12
	Acknowledgements	13
	1 Introduction	14
	1.1 Why study mathematics?	14
	1.2 Calculators and computers	16
	1.3 Using the book	18
	2 Arithmetic	21
	2.1 Revision of basic concepts	21
	2.2 Multiple operations	22
	2.3 Brackets	24
	2.4 Fractions	25
	2.5 Elasticity of demand	28
	2.6 Decimals	31
	2.7 Negative numbers	34
	2.8 Powers	36
	2.9 Roots and fractional powers	39
	2.10 Logarithms	42
	3 Introduction to algebra	47
	3.1 Representation	47
	3.2 Evaluation	49
	3.3 Simplification: addition and subtraction	51
	3.4 Simplification: multiplication	53
	3.5 Simplification: factorizing	58
	3.6 Simplification: division	62
	3.7 Solving simple equations	64
	3.8 The summation sign	69
	3.9 Inequality signs	72
	4 Graphs and functions	76
	4.1 Functions	76
	4.2 Inverse functions	78
	4.3 Graphs of linear functions	81
	4.4 Fitting linear functions	86
	4.5 Slope	89
	4.6 Budget constraints	94
	4.7 Non-linear functions	99
	4.8 Composite functions	103
	4.9 Using Excel to plot functions	108
	4.10 Functions with two independent variables	112
	4.11 Summing functions horizontally	117
	5 Linear equations	122
	5.1 Simultaneous linear equation systems	122
	5.2 Solving simultaneous linear equations	123
	5.3 Graphical solution	123
	5.4 Equating to same variable	125
	5.5 Substitution	128
	5.6 Row operations	129
	5.7 More than two unknowns	131
	5.8 Which method?	134
	5.9 Comparative statics and the reduced form of an economic model	139
	5.10 Price discrimination	148
	5.11 Multiplant monopoly	154
	Appendix: linear programming	161
	6 Quadratic equations	181
	6.1 Solving quadratic equations	181
	6.2 Graphical solution	182
	6.3 Factorization	186
	6.4 The quadratic formula	189
	6.5Quadratic simultaneous equations	191
	6.6 Polynomials	195
	7 Financial mathematics	202
	7.1 Discrete and continuous growth	202
	7.2 Interest	204
	7.3 Part year investment and the annual equivalent rate	209
	7.4 Time periods, initial amounts and interest rates	215
	7.5 Investment appraisal: net present value	220
	7.6 The internal rate of return	231
	7.7 Geometric series and annuities	237
	7.8 Perpetual annuities	243
	7.9 Loan repayments	247
	7.10 Other applications of growth and decline	253
	8 Introduction to calculus	260
	8.1 The differential calculus	260
	8.2 Rules for differentiation	262
	8.3 Marginal revenue and total revenue	265
	8.4 Marginal cost and total cost	271
	8.5 Profit maximization	274
	8.6 Respecifying functions	276
	8.7 Point elasticity of demand	278
	8.8 Tax yield	280
	8.9 The Keynesian multiplier	282
	9 Unconstrained optimization	285
	9.1 First-order conditions for a maximum	285
	9.2 Second-order condition for a maximum	286
	9.3 Second-order condition for a minimum	289
	9.4 Summary of second-order conditions	290
	9.5 Profit maximization	293
	9.6 Inventory control	295
	9.7 Comparative static effects of taxes	298
	10 Partial differentiation	304
	10.1 Partial differentiation and the marginal product	304
	10.2 Further applications of partial differentiation	309
	10.3 Second-order partial derivatives	320
	10.4 Unconstrained optimization: functions with two variables	325
	10.5 Total differentials and total derivatives	338
	11 Constrained optimization	347
	11.1 Constrained optimization and resource allocation	347
	11.2 Constrained optimization by substitution	347
	11.3 The Lagrange multiplier: constrained maximization with two variables	355
	11.4 The Lagrange multiplier: second-order conditions	361
	11.5 Constrained minimization using the Lagrange multiplier	363
	11.6 Constrained optimization with more than two variables	368
	12 Further topics in calculus	377
	12.1 Overview	377
	12.2 The chain rule	377
	12.3 The product rule	385
	12.4 The quotient rule	390
	12.5 Individual labour supply	394
	12.6 Integration	397
	12.7 Definite integrals	401
	13 Dynamics and difference equations	408
	13.1 Dynamic economic analysis	408
	13.2 The cobweb: iterative solutions	409
	13.3 The cobweb: difference equation solutions	418
	13.4 The lagged Keynesian macroeconomic model	427
	13.5 Duopoly price adjustment	439
	14 Exponential functions, continuous growth and differential equations	445
	14.1 Continuous growth and the exponential function	445
	14.2 Accumulated final values after continuous growth	447
	14.3 Continuous growth rates and initial amounts	450
	14.4 Natural logarithms	453
	14.5 Differentiation of logarithmic functions	459
	14.6 Continuous time and differential equations	460
	14.7 Solution of homogeneous differential equations	461
	14.8 Solution of non-homogeneous differential equations	465
	14.9 Continuous adjustment of market price	469
	14.10 Continuous adjustment in a Keynesian macroeconomic model	474
	15 Matrix algebra	478
	15.1 Introduction to matrices and vectors	478
	15.2 Basic principles of matrix multiplication	482
	15.3 Matrix multiplication – the general case	485
	15.4 The matrix inverse and the solution of simultaneous equations	491
	15.5 Determinants	494
	15.6 Minors, cofactors and the Laplace expansion	497
	15.7 The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula	500
	15.8 Application of the matrix inverse to the solution of linear simultaneous equations	505
	15.9 Cramer’s rule	510
	15.10 Second-order conditions and the Hessian matrix	512
	15.11 Constrained optimization and the bordered Hessian	518
	Answers	523
	Symbols and terminology	536
	Index	538
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