經(jīng)濟(jì)數(shù)學(xué)和金融數(shù)學(xué)

內(nèi)容概要

This book is an introduction to calculus and linear algebra for students of disciplines such as economics, finance, business, management, and accounting. It is intended for readers who may have already encountered some differential calculus, and it will also be appropriate for those with less experience, possibly used in conjunction with one of the many more elementary texts on basic mathematics.

書籍目錄

1. Mathematical models in economics  1.1 Introduction  1.2 A model of the market  1.3 Market equilibrium  1.4 Excise tax  1.5 Comments  Worked examples  Main topics/Key terms, notations and formulae  Exercises2. Mathematical terms and notations  2.1 Sets  2.2 Functions  2.3 Composite functions  2.4 Graphs and equations  Worked examples  Main topics/Key terms, notations and formulae  Exercises3. Sequences, recurrences, limits  3.1 Sequences  3.2 The first-order recurrence  3.3 Limits  3.4 Special cases  Worked examples  Main topics/Key terms, notations and formulae  Exercises4. The elements of finance  4.1 Interest and capital growth  4.2 Income generation  4.3 The interval of compounding  Worked examples  Main topics/Key terms, notations and formulae  Exercises5. The cobweb model  5.1 How stable is market equilibrium  5.2 An example  5.3 The general linear case  5.4 Economic interpretation  Worked examples  Main topics/Key terms, notations and formulae  Exercises6. Introduction to calculus  6.1 The rate of change of a function  6.2 Rules for finding the derivative  6.3 Marginal cost as a derivative  6.4 The derivative of a composite function  6.5 The derivative of an inverse function  Worked examples  Main topics/Key terms, notations and formulae  Exercises7. Some special functions  7.1 Powers  7.2 The exponential function and its properties  7.3 Continuous compounding of interest  7.4 The logarithm function  7.5 Trigonometrical functions  Worked examples  Main topics/Key terms, notations and formulae  Exercises8. Introduction to optimisation  8.1 Profit maximisation  8.2 Critical points  8.3 Optimisation in an interval  8.4 Infinite intervals  Worked examples  Main topics/Key terms, notations and formulae  Exercises9. The derivative in economics--I  9.1 Elasticity of demand  9.2 Profit maximisation again  9.3 Competition versus monopoly  Worked examples  Main topics/Key terms, notations and formulae  Exercises10. The derivative in economics--II  10.1 The efficient small firm  10.2 Startup and breakeven points  Worked examples  Main topics/Key terms, notations and formulae  Exercises11. Partial derivatives  11.1 Functions of several variables  11.2 Partial derivatives  11.3 The chain rule  Worked examples  Main topics/Key terms, notations and formulae  Exercises12. Applications of partial derivatives  12.1 Functions defined implicitly  12.2 The derivative of an implicit function  12.3 Contours and isoquants  12.4 Scale effects and homogeneous functions  Worked examples  Main topics/Key terms, notations and formulae  Exercises13. Optimisation in two variables  13.1 Profit maximisation again  13.2 How prices are related to quantities  13.3 Critical points  13.4 Maxima, minima, and saddle points  13.5 Classification of critical points - introduction  13.6 The classification of critical points in general  Worked examples  Main topics/Key terms, notations and formulae  Exercises14. Vectors, preferences and convexity  14.1 Vectors and bundles  14.2 Prices and budgets  14.3 Preferences, utility, and indifference curves  14.4 Linear and convex combinations  14.5 Choosing optimal bundles  Worked examples  Main topics/Key terms, notations and formulae  Exercises15. Matrix algebra  15.1 What is a matrix  ……16. Linear equations--I17. Linear equations--II18. Inverse matrices19. The input-output model20. Determinants21. Constrained optimisation22. Lagrangeans and the consumer23. Second-order recurrence equations24. Macroeconomic applications25. Areas and integrals26. Techniques of integration27. First-order differential equations28. Second-order differential equationsSolutions to selected exercisesIndex

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