Mathematical Formulas for Economists

by Luderer, Bernd; Nollau, Volker; Vetters, Klaus

• ISBN13: 9783642040788
• ISBN10: 3642040780
• Edition: 4th
• Format: Paperback
• Copyright: 2010-01-03
• Publisher: Springer Verlag

Summary

The present collection of formulas has been composed for students of economics or management science at universities, colleges and trade schools. It contains basic knowledge in mathematics, financial mathematics and statistics in a compact and clearly arranged form. This volume is meant to be a reference work to be used by students of undergraduate courses together with a textbook, and by researchers in need of exact statements of mathematical results. People dealing with practical or applied problems will also find this collection to be an efficient and easy-to-use work of reference.This carefully revised and enlarged edition also presents methods of rank statistics and the analysis of variance (ANOVA) and covariance.

Table of Contents

Mathematical Symbols and Constants	p. 1
Notations and symbols	p. 1
Mathematical constants	p. 2
Sets and Propositions	p. 3
Notion of a set	p. 3
Relations between sets	p. 3
Operations with sets	p. 4
Rules for operations with sets	p. 5
Product sets and mappings	p. 6
Propositional calculus	p. 7
Number Systems and Their Arithmetic	p. 9
Natural, integer, rational, and real numbers	p. 9
Calculation with real numbers	p. 10
Absolute values	p. 11
Factorial and binomial coefficients	p. 12
Equations	p. 13
Inequalities	p. 14
Finite sums	p. 15
Powers and roots	p. 15
Logarithms	p. 16
Complex numbers	p. 17
Combinatorial Analysis	p. 19
Permutations	p. 19
Arrangements	p. 19
Combinations	p. 20
Sequences and Series	p. 21
Sequences of numbers	p. 21
Sequences of functions	p. 22
Infinite series	p. 23
Function and power series	p. 25
Taylor series	p. 27
Fourier series	p. 29
Mathematics of Finance	p. 31
Simple interest	p. 31
Compound interest	p. 33
Annuities	p. 36
Dynamic annuities	p. 38
Amortization calculus	p. 39
Price calculus	p. 41
Investment analysis	p. 42
Depreciations	p. 43
Numerical methods for the determination of zeros	p. 44
Functions of one Independent Variable	p. 45
Basic notions	p. 45
Linear functions	p. 47
Quadratic functions	p. 47
Power functions	p. 48
Polynomials	p. 49
Fractional rational functions, partial fraction decomposition	p. 50
Exponential functions	p. 51
Logarithmic functions	p. 52
Trigonometric functions	p. 53
Inverse trigonometric functions	p. 55
Hyperbolic functions	p. 56
Area-hyperbolic functions	p. 56
Some economic functions	p. 57
Functions of one Variable: Differential Calculus	p. 61
Limit of a function	p. 61
Continuity	p. 62
Differentiation	p. 63
Economic interpretation of the first derivative	p. 66
Rates of change and elasticities	p. 68
Mean value theorems	p. 70
Higher derivatives and Taylor expansion	p. 70
Description of function features by means of derivatives	p. 72
Investigation of economic functions, profit maximization	p. 75
Functions of one Variable: Integral Calculus	p. 79
Indefinite integral	p. 79
Definite integral	p. 80
Tables of indefinite integrals	p. 81
Improper integrals	p. 88
Parameter integrals	p. 88
Economic applications of integral calculus	p. 89
Differential Equations	p. 91
First-order differential equations	p. 91
Linear differential equations of n-th order	p. 92
First-order linear systems with constant coefficients	p. 95
Difference Equations	p. 97
First-order linear difference equations	p. 97
Economic models	p. 98
Linear second-order difference equations	p. 99
Economic models	p. 101
Linear difference equations of n-th order with constant coefficients	p. 102
Differential Calculus for Functions of Several Variables	p. 103
Basic notions	p. 103
Point sets of the space Rn	p. 103
Limit and continuity	p. 104
Differentiation of functions of several variables	p. 105
Total differential	p. 108
Unconstrained extreme value problems	p. 109
Constrained extreme value problems	p. 110
Least squares method	p. 112
Propagation of errors	p. 113
Economic applications	p. 114
Linear Algebra	p. 115
Vectors	p. 115
Equations of straight lines and planes	p. 117
Matrices	p. 119
Determinants	p. 121
Systems of linear equations	p. 122
Gaussian elimination	p. 123
Cramer's rule	p. 125
Exchange method	p. 125
Inverse matrix	p. 126
Eigenvalue problems for matrices	p. 126
Matrix models	p. 127
Linear Programming. Transportation Problem	p. 129
Normal form of a linear programming problem	p. 129
Simplex method	p. 130
Dual simplex method	p. 132
Generation of an initial simplex table	p. 133
Duality	p. 135
Transportation problem	p. 136
Descriptive Statistics	p. 139
Basic notions	p. 139
Univariate data analysis	p. 139
Statistical parameters	p. 140
Bivariate data analysis	p. 141
Ratios	p. 144
Inventory analysis	p. 145
Time series analysis	p. 147
Calculus of Probability	p. 149
Random events and their probabilities	p. 149
Conditional probabilities	p. 151
Random variables and their distributions	p. 153
Discrete distributions	p. 153
Continuous distributions	p. 155
Special continuous distributions	p. 156
Random vectors	p. 159
Inductive Statistics	p. 163
Sample	p. 163
Point estimates	p. 163
Confidence interval estimates	p. 165
Statistical tests	p. 167
Significance tests under normal distribution	p. 168
Rank statistics	p. 170
Analysis of variance (ANOVA)	p. 173
Analysis of covariance	p. 176
Tables	p. 179
Distribution function of the standard normal distribution	p. 179
Quantiles of the standard normal distribution	p. 181
Quantiles of the t-distribution	p. 181
Probability density of the standardized normal distribution	p. 182
Quantiles of the F-distribution	p. 183
Probabilities of the Poisson distribution	p. 187
Quantiles of the ¿2-distribution	p. 189
References	p. 191
Index	p. 193
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