Basic Mathematics for Economists

Автор(ы):Rosser M.
06.10.2007
Год изд.:2003
Издание:2
Описание: Economics students will welcome the new edition of this excellent textbook. Given that many students come into economics courses without having studied mathematics for a number of years, this clearly written book will help to develop quantitative skills in even the least numerate student up to the required level for a general Economics or Business Studies course. All explanations of mathematical concepts are set out in the context of applications in economics. This new edition incorporates several new features, including new sections on: financial mathematics; continuous growth; matrix algebra.
Оглавление:
Basic Mathematics for Economists — обложка книги.
1 Introduction
  1.1 Why study mathematics?
  1.2 Calculators and computers
  1.3 Using the book
2 Arithmetic
  2.1 Revision of basic concepts
  2.2 Multiple operations
  2.3 Brackets
  2.4 Fractions
  2.5 Elasticity of demand
  2.6 Decimals
  2.7 Negative numbers
  2.8 Powers
  2.9 Roots and fractional powers
  2.10 Logarithms
3 Introduction to algebra
  3.1 Representation
  3.2 Evaluation
  3.3 Simplification: addition and subtraction
  3.4 Simplification: multiplication
  3.5 Simplification: factorizing
  3.6 Simplification: division
  3.7 Solving simple equations
  3.8 The summation sign J2
  3.9 Inequality signs
4 Graphs and functions
  4.1 Functions
  4.2 Inverse functions
  4.3 Graphs of linear functions
  4.4 Fitting linear functions
  4.5 Slope
  4.6 Budget constraints
  4.7 Non-linear functions
  4.8 Composite functions
  4.9 Using Excel to plot functions
  4.10 Functions with two independent variables
  4.11 Summing functions horizontally
5 Linear equations
  5.1 Simultaneous linear equation systems
  5.2 Solving simultaneous linear equations
  5.3 Graphical solution
  5.4 Equating to same variable
  5.5 Substitution
  5.6 Row operations
  5.7 More than two unknowns
  5.8 Which method?
  5.9 Comparative statics and the reduced form of an economic model
  5.10 Price discrimination
  5.11 Multiplant monopoly Appendix: linear programming
6 Quadratic equations
  6.1 Solving quadratic equations
  6.2 Graphical solution
  6.3 Factorization
  6.4 The quadratic formula
  6.5 Quadratic simultaneous equations
  6.6 Polynomials
7 Financial mathematics: series, time and investment
  7.1 Discrete and continuous growth
  7.2 Interest
  7.3 Part year investment and the annual equivalent rate
  7.4 Time periods, initial amounts and interest rates
  7.5 Investment appraisal: net present value
  7.6 The internal rate of return
  7.7 Geometric series and annuities
  7.8 Perpetual annuities
  7.9 Loan repayments
  7.10 Other applications of growth and decline
8 Introduction to calculus
  8.1 The differential calculus
  8.2 Rules for differentiation
  8.3 Marginal revenue and total revenue
  8.4 Marginal cost and total cost
  8.5 Profit maximization
  8.6 Respecifying functions
  8.7 Point elasticity of demand
  8.8 Tax yield
  8.9 The Keynesian multiplier
9 Unconstrained optimization
  9.1 First-order conditions for a maximum
  9.2 Second-order condition for a maximum
  9.3 Second-order condition for a minimum
  9.4 Summary of second-order conditions
  9.5 Profit maximization
  9.6 Inventory control
  9.7 Comparative static effects of taxes
10 Partial differentiation
  10.1 Partial differentiation and the marginal product
  10.2 Further applications of partial differentiation
  10.3 Second-order partial derivatives
  10.4 Unconstrained optimization: functions with two variables
  10.5 Total differentials and total derivatives
11 Constrained optimization
  11.1 Constrained optimization and resource allocation
  11.2 Constrained optimization by substitution
  11.3 The Lagrange multiplier: constrained maximization with two variables
  11.4 The Lagrange multiplier: second-order conditions
  11.5 Constrained minimization using the Lagrange multiplier
  11.6 Constrained optimization with more than two variables
12 Further topics in calculus
  12.1 Overview
  12.2 The chain rule
  12.3 The product rule
  12.4 The quotient rule
  12.5 Individual labour supply
  12.6 Integration
  12.7 Definite integrals
13 Dynamics and difference equations
  13.1 Dynamic economic analysis
  13.2 The cobweb: iterative solutions
  13.3 The cobweb: difference equation solutions
  13.4 The lagged Keynesian macroeconomic model
  13.5 Duopoly price adjustment
14 Exponential functions, continuous growth and differential equations
  14.1 Continuous growth and the exponential function
  14.2 Accumulated final values after continuous growth
  14.3 Continuous growth rates and initial amounts
  14.4 Natural logarithms
  14.5 Differentiation of logarithmic functions
  14.6 Continuous time and differential equations
  14.7 Solution of homogeneous differential equations
  14.8 Solution of non-homogeneous differential equations
  14.9 Continuous adjustment of market price
  14.10 Continuous adjustment in a Keynesian macroeconomic model
15 Matrix algebra
  15.7 Introduction to matrices and vectors
  15.2 Basic principles of matrix multiplication
  15.3 Matrix multiplication - the general case
  15.4 The matrix inverse and the solution of simultaneous equations
  15.5 Determinants
  15.6 Minors, cofactors and the Laplace expansion
  15.7 The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula
  15.8 Application of the matrix inverse to the solution of linear simultaneous equations
  15.9 Cramer's rule
  15.10 Second-order conditions and the Hessian matrix
  15.11 Constrained optimization and the bordered Hessian
Answers
Symbols and terminology
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