Mathematical Formulas for... | Buy

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.

Mathematical Symbols and Constants

1

(2)

Notations and symbols

1

(1)

Mathematical constants

2

(1)

Sets and Propositions

3

(6)

Notion of a set

3

(1)

Relations between sets

3

(1)

Operations with sets

4

(1)

Rules for operations with sets

5

(1)

Product sets and mappings

6

(1)

Propositional calculus

7

(2)

Number Systems and their Arithmetic

9

(10)

Natural, integer, rational, and real numbers

9

(1)

Calculation with real numbers

10

(1)

Absolute values

11

(1)

Factorial and binomial coefficients

12

(1)

Equations

13

(1)

Inequalities

14

(1)

Finite sums

15

(1)

Powers and roots

15

(1)

Logarithms

16

(1)

Complex numbers

17

(2)

Combinatorial Analysis

19

(2)

Permutations

19

(1)

Arrangements

19

(1)

Combinations

20

(1)

Sequences and Series

21

(10)

Sequences of numbers

21

(1)

Sequences of functions

22

(1)

Infinite series

23

(2)

Function and power series

25

(2)

Taylor series

27

(2)

Fourier series

29

(2)

Mathematics of Finance

31

(14)

Simple interest

31

(2)

Compound interest

33

(3)

Annuities

36

(2)

Dynamic annuities

38

(1)

Amortization calculus

39

(2)

Price calculus

41

(1)

Investment analysis

42

(1)

Depreciations

43

(1)

Numerical methods for the determination of zeros

44

(1)

Functions of one Independent Variable

45

(16)

Basic notions

45

(2)

Linear functions

47

(1)

Quadratic functions

47

(1)

Power functions

48

(1)

Polynomials

49

(1)

Fractional rational functions, partial fraction decomposition

50

(1)

Exponential functions

51

(1)

Logarithmic functions

52

(1)

Trigonometric functions

53

(2)

Inverse trigonometric functions

55

(1)

Hyperbolic functions

56

(1)

Area-hyperbolic functions

56

(1)

Some economic functions

57

(4)

Functions of one Variable: Differential Calculus

61

(18)

Limit of a function

61

(1)

Continuity

62

(1)

Differentiation

63

(3)

Economic interpretation of the first derivative

66

(2)

Rates of change and elasticities

68

(2)

Mean value theorems

70

(1)

Higher derivatives and Taylor expansion

70

(2)

Description of function features by means of derivatives

72

(3)

Investigation of economic functions, profit maximization

75

(4)

Functions of one Variable: Integral Calculus

79

(12)

Indefinite integral

79

(1)

Definite integral

80

(1)

Tables of indefinite integrals

81

(7)

Improper integrals

88

(1)

Parameter integrals

88

(1)

Economic applications of integral calculus

89

(2)

Differential Equations

91

(6)

First-order differential equations

91

(1)

Linear differential equations of n-th order

92

(3)

First-order linear systems with constant coefficients

95

(2)

Difference Equations

97

(6)

First-order linear difference equations

97

(1)

Economic models

98

(1)

Linear second-order difference equations

99

(2)

Economic models

101

(1)

Linear difference equations of n-th order with constant coefficients

102

(1)

Differential Calculus for Functions of Several Variables

103

(12)

Basic notions

103

(1)

Point sets of the space Rn

103

(1)

Limit and continuity

104

(1)

Differentiation of functions of several variables

105

(3)

Total differential

108

(1)

Unconstrained extreme value problems

109

(1)

Constrained extreme value problems

110

(2)

Least squares method

112

(1)

Propagation of errors

113

(1)

Economic applications

114

(1)

Linear Algebra

115

(14)

Vectors

115

(2)

Equations of straight lines and planes

117

(2)

Matrices

119

(2)

Determinants

121

(1)

Systems of linear equations

122

(1)

Gaussian elimination

123

(2)

Cramer's rule

125

(1)

Exchange method

125

(1)

Inverse matrix

126

(1)

Eigenvalue problems for matrices

126

(1)

Matrix models

127

(2)

Linear Programming. Transportation Problem

129

(10)

Normal form of a linear programming problem

129

(1)

Simplex method

130

(2)

Dual simplex method

132

(1)

Generation of an initial simplex table

133

(2)

Duality

135

(1)

Transportation problem

136

(3)

Descriptive Statistics

139

(10)

Basic notions

139

(1)

Univariate data analysis

139

(1)

Statistical parameters

140

(1)

Bivariate data analysis

141

(3)

Ratios

144

(1)

Inventory analysis

145

(2)

Time series analysis

147

(2)

Calculus of Probability

149

(14)

Random events and their probabilities

149

(2)

Conditional probabilities

151

(2)

Random variables and their distributions

153

(1)

Discrete distributions

153

(2)

Continuous distributions

155

(1)

Special continuous distributions

156

(3)

Random vectors

159

(4)

Inductive Statistics

163

(18)

Sample

163

(1)

Point estimates

163

(2)

Confidence interval estimates

165

(2)

Statistical tests

167

(1)

Significance tests under normal distribution

168

(2)

Tables

170

(11)

References

181

(2)

Index

183

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