Math for business and economics: compendium of essential formulas
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| Format: | Book |
| Language: | English |
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Springer
[2023]
|
| Edition: | Second edition |
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| Physical Description: | XXIV, 631 Seiten Diagramme |
| ISBN: | 9783662669747 3662669749 |
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| 100 | 1 | |a Peren, Franz W. |d 1959- |e Verfasser |0 (DE-588)170930858 |4 aut | |
| 245 | 1 | 0 | |a Math for business and economics |b compendium of essential formulas |c Franz W. Peren |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin |b Springer |c [2023] | |
| 300 | |a XXIV, 631 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Wirtschaftsmathematik |0 (DE-588)4066472-7 |2 gnd |9 rswk-swf |
| 653 | |a Mathematical signs and symbols | ||
| 653 | |a Financial mathematics | ||
| 653 | |a Annuity calculation | ||
| 653 | |a Sinking fund calculation | ||
| 653 | |a Investment calculation | ||
| 653 | |a Optimisation of linear models | ||
| 653 | |a Differential calculus | ||
| 653 | |a Integral calculus | ||
| 653 | |a Economic functions | ||
| 653 | |a Elasticities | ||
| 653 | |a Market equilibrium | ||
| 653 | |a The Peren Theorem | ||
| 653 | |a Combinatorics | ||
| 653 | |a Linear algebra | ||
| 653 | |a Arithmetic | ||
| 653 | |a Logic | ||
| 655 | 7 | |0 (DE-588)4155008-0 |a Formelsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Wirtschaftsmathematik |0 (DE-588)4066472-7 |D s |
| 689 | 0 | |5 DE-604 | |
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CONTENTS
LIST
OF
ABBREVIATIONS
XXI
1
MATHEMATICAL
SIGNS
AND
SYMBOLS
1
1.1
PRAGMATIC
SIGNS
.
1
1.2
GENERAL
ARITHMETIC
RELATIONS
AND
LINKS
.
1
1.3
SETS
OF
NUMBERS
.
2
1.4
SPECIAL
NUMBERS
AND
LINKS
.
3
1.5
LIMIT
.
3
1.6
EXPONENTIAL
FUNCTIONS,
LOGARITHM
.
4
1.7
TRIGONOMETRIC
FUNCTIONS,
HYPERBOLIC
FUNCTIONS
.
4
1.8
VECTORS,
MATRICES
.
5
1.9
SETS
.
6
1.10
RELATIONS
.
7
1.11
FUNCTIONS
.
7
1.12
ORDER
STRUCTURES
.
7
1.13
SI
MULTIPLYING
AND
DIVIDING
PREFIXES
.
8
1.14
GREEK
ALPHABET
.
9
IX
X
CONTENTS
2
LOGIC
11
2.1
MATHEMATICAL
LOGIC
.
11
2.2
PROPOSITIONAL
LOGIC
.
11
2.2.1
PROPOSITIONAL
VARIABLE
.
11
2.2.2
TRUTH
TABLES
.
12
3
ARITHMETIC
15
3.1
SETS
.
15
3.1.1
GENERAL
.
15
3.1.2
SET
RELATIONS
.
16
3.1.3
SET
OPERATIONS
.
17
3.1.4
RELATIONS,
LAWS,
RULES
OF
CALCULATION
FOR
SETS
19
3.1.5
INTERVALS
.
21
3.1.6
NUMERAL
SYSTEMS
.
22
3.1.6.1
DECIMAL
SYSTEM
(DECADIC
SYSTEM)
23
3.1.6.2
DUAL
SYSTEM
(BINARY
SYSTEM)
.
23
3.1.6.3
ROMAN
NUMERAL
SYSTEM
.
24
3.2
ELEMENTARY
CALCULUS
.
24
3.2.1
ELEMENTARY
FOUNDATIONS
.
24
3.2.1.1
AXIOMS
.
25
3.2.1.2
FACTORISATION
.
25
3.2.1.3
RELATIONS
.
26
3.2.1.4 ABSOLUTE
VALUE,
SIGNUM
.
26
3.2.1.5
FRACTIONS
.
27
3.2.1.6
POLYNOMIAL
DIVISION
.
27
3.2.1.7
HORNER
'
S
SCHEME
(HORNER
'
S
METHOD)
29
3.2.2
CONVERSIONS
OF
TERMS
.
30
3.2.2.1
BINOMIAL
FORMULAS
.
30
3.2.2.2
BINOMIAL
THEOREM
.
31
3.2.2.3
GENERAL
BINOMIAL
THEOREM
FOR
NAT
URAL
EXPONENTS
31
3.2.2.4
GENERAL
BINOMIAL
THEOREM
FOR
REAL
EXPONENTS
.
31
3.2.2.5
POLYNOMIAL
TERMS
.
32
3.2.3
SUMMATION
AND
PRODUCT
NOTATION
.
32
3.2.3.1
SUMMATION
NOTATION
.
32
CONTENTS
XI
3.2.3.2
PRODUCT
NOTATION
.
33
3.2.4
POWERS,
ROOTS
.
34
3.2.5
LOGARITHMS
.
37
3.2.6
FACTORIAL
.
39
3.2.7
BINOMIAL
COEFFICIENT
.
40
3.3
SEQUENCES
.
41
3.3.1
DEFINITION
.
41
3.3.2
LIMIT
OF
A
SEQUENCE
.
44
3.3.3
ARITHMETIC
AND
GEOMETRIC
SEQUENCES
.
46
3.4
SERIES
.
47
3.4.1
DEFINITION
.
47
3.4.2
ARITHMETIC
AND
GEOMETRIC
SERIES
.
47
4
ALGEBRA
51
4.1
FUNDAMENTAL
TERMS
.
51
4.2
LINEAR
EQUATIONS
.
53
4.2.1
LINEAR
EQUATIONS
WITH
ONE
VARIABLE
.
53
4.2.2
LINEAR
INEQUATIONS
WITH
ONE
VARIABLE
.
56
4.2.3
LINEAR
EQUATIONS
WITH
MULTIPLE
VARIABLES
.
56
4.2.4
SYSTEMS
OF
LINEAR
EQUATIONS
.
57
4.2.5
LINEAR
INEQUATIONS
WITH
MULTIPLE
VARIABLES
.
61
4.3
NON-LINEAR
EQUATIONS
.
62
4.3.1
QUADRATIC
EQUATIONS
WITH
ONE
VARIABLE
.
62
4.3.2
CUBIC
EQUATIONS
WITH
ONE
VARIABLE
.
65
4.3.3
BIQUADRATIC
EQUATIONS
.
67
4.3.4
EQUATIONS
OF
THE
NTH
DEGREE
.
68
4.3.5
RADICAL
EQUATIONS
.
69
4.4
TRANSCENDENTAL
EQUATIONS
.
71
4.4.1
EXPONENTIAL
EQUATIONS
.
71
4.4.2
LOGARITHMIC
EQUATIONS
.
73
4.5
APPROXIMATION
METHODS
.
75
4.5.1
REGULA
FALSI
(SECANT
METHOD)
.
75
4.5.2
NEWTON
'
S
METHOD
(TANGENT
METHOD)
.
77
XII
CONTENTS
4.5.3
GENERAL
APPROXIMATION
METHOD
(FIXED-POINT
ITERATION)
.
80
5
LINEAR
ALGEBRA
87
5.1
FUNDAMENTAL
TERMS
.
87
5.1.1
MATRIX
.
87
5.1.2
EQUALITY/INEQUALITY
OF
MATRICES
.
88
5.1.3
TRANSPOSED
MATRIX
.
89
5.1.4
VECTOR
.
89
5.1.5
SPECIAL
MATRICES
AND
VECTORS
.
92
5.2
OPERATIONS
WITH
MATRICES
.
94
5.2.1
ADDITION
OF
MATRICES
.
94
5.2.2
MULTIPLICATION
OF
MATRICES
.
96
5.2.2.1
MULTIPLICATION
OF
A
MATRIX
WITH
A
SCALAR
.
96
5.2.2.2
THE
SCALAR
PRODUCT
OF
TWO
VEC
TORS
.
98
5.2.2.3
MULTIPLICATION
OF
A
MATRIX
BY
A
COL
UMN
VECTOR
.
100
5.2.2.4
MULTIPLICATION
OF
A
ROW
VECTOR
BY
A
MATRIX
.
102
5.2.2.5
MULTIPLICATION
OF
TWO
MATRICES
.
103
5.3
THE
INVERSE
OF
A
MATRIX
.
107
5.3.1
INTRODUCTION
.
107
5.3.2
DETERMINATION
OF
THE
INVERSE
WITH
THE
USAGE
OF
THE
GAUSSIAN
ELIMINATION
METHOD
.
109
5.4
THE
RANK
OF
A
MATRIX
.
113
5.4.1
DEFINITION
.
113
5.4.2
DETERMINATION
OF
THE
RANK
OF
A
MATRIX
.
113
5.5
THE
DETERMINANT
OF
A
MATRIX
.
117
5.5.1
DEFINITION
.
117
5.5.2
CALCULATION
OF
DETERMINANTS
.
118
5.5.3
CHARACTERISTICS
OF
DETERMINANTS
.
124
CONTENTS
XIII
5.6
THE
ADJOINT
OF
A
MATRIX
.
125
5.6.1
DEFINITION
.
125
5.6.2
DETERMINATION
OF
THE
INVERSE
WITH
THE
USAGE
OF
THE
ADJOINT
.
127
6
COMBINATORICS
129
6.1
INTRODUCTION
.
129
6.2
PERMUTATIONS
.
133
6.3
VARIATIONS
.
135
6.4
COMBINATIONS
.
136
7
FINANCIAL
MATHEMATICS
141
7.1
CALCULATION
OF
INTEREST
.
141
7.1.1
FUNDAMENTAL
TERMS
.
141
7.1.2
ANNUAL
INTEREST
.
142
7.1.2.1
SIMPLE
INTEREST
CALCULATION
.
142
7.1.2.2
COMPOUND
COMPUTATION
OF
INTER
EST
.
144
7.1.2.3
COMPOSITE
INTEREST
.
146
7.1.3
INTEREST
DURING
THE
PERIOD
.
158
7.1.3.1
SIMPLE
INTEREST
CALCULATION
(LINEAR)
159
7.1.3.2
SIMPLE
INTEREST
USING
THE
NOMI
NAL
ANNUAL
INTEREST
RATE
.
159
7.1.3.3
COMPOUND
INTEREST
(EXPONENTIAL)
.
160
7.1.3.4
INTEREST
WITH
COMPOUND
INTEREST
USING
A
CONFORMING
ANNUAL
INTER
EST
RATE
.
161
7.1.3.5
MIXED
INTEREST
.
162
7.1.3.6
STEADY
INTEREST
RATE
.
163
7.2
ANNUAL
PERCENTAGE
RATE
.
168
7.3
DEPRECIATION
.
173
7.3.1
TIME
DEPRECIATION
.
173
7.3.1.1
LINEAR
DEPRECIATION
.
173
XIV
CONTENTS
7.3.1.2
ARITHMETIC-DEGRESSIVE
DEPRECIATION
174
7.3.1.3
GEOMETRIC-DEGRESSIVE
DEPRECIA
TION
.
176
7.3.2
UNITS
OF
PRODUCTION
DEPRECIATION
.
178
7.3.3
EXTRAORDINARY
DEPRECIATION
.
179
7.4
ANNUITY
CALCULATION
.
180
7.4.1
FUNDAMENTAL
TERMS
.
180
7.4.2
FINITE,
REGULAR
ANNUITY
.
183
7.4.2.1
ANNUAL
ANNUITY
WITH
ANNUAL
INTEREST
183
7.4.2.2
ANNUAL
ANNUITY
WITH
SUB-ANNUAL
INTEREST
.
187
7.4.2.3
SUB-ANNUAL
ANNUITY
WITH
ANNUAL
INTEREST
.
190
7.4.2.4
SUB-ANNUAL
ANNUITY
WITH
SUB-ANNUAL
INTEREST
.
194
7.4.3
FINITE,
VARIABLE
ANNUITY
.
213
7.4.3.1
IRREGULAR
ANNUITY
.
213
7.4.3.2
ARITHMETIC
PROGRESSIVE
ANNUITY
.
220
7.4.3.3
GEOMETRIC
PROGRESSIVE
ANNUITY
.
231
7.4.4
PERPETUITY
.
234
7.5
SINKING
FUND
CALCULATION
.
235
7.5.1
FUNDAMENTAL
TERMS
.
236
7.5.2
ANNUITY
REPAYMENT
.
238
7.5.3
REPAYMENT
BY
INSTALMENTS
.
241
7.5.4
REPAYMENT
WITH
PREMIUM
.
243
7.5.4.1
ANNUITY
REPAYMENT
WITH
PREMIUM
243
7.5.4.2
REPAYMENT
OF
AN
INSTALMENT
DEBT
WITH
PREMIUM
.
248
7.5.5
REPAYMENT
WITH
DISCOUNT
(DISAGIO)
.
249
7.5.5.1
ANNUITY
REPAYMENT
WITH
DISCOUNT
WHEN
IMMEDIATELY
BOOKED
AS
INTER
EST
EXPENSE
.
251
7.5.5.2
ANNUITY
REPAYMENT
WITH
DISCOUNT
WHEN
A
DISAGIO
IS
INCLUDED
IN
PRE
PAID
EXPENSES
.
253
7.5.5.3
INSTALMENT
REPAYMENT
WITH
DIS
COUNT
WHEN
IMMEDIATELY
BOOKED
AS
INTEREST
EXPENSE
.
253
CONTENTS
XV
7.5.5.4
INSTALMENT
REPAYMENT
WITH
DIS
COUNT
WHEN
A
DISAGIO
IS
INCLUDED
IN
PREPAID
EXPENSES
.
254
7.5.6
GRACE
PERIODS
.
255
7.5.7
ROUNDED
ANNUITIES
.
257
7.5.7.1
PERCENTAGE
ANNUITY
.
257
7.5.7.2
REPAYMENT
OF
BONDS
.
260
7.5.8
REPAYMENT
DURING
THE
YEAR
.
266
7.5.8.1
ANNUITY
REPAYMENT
DURING
THE
YEAR
266
7.5.8.2
REPAYMENT
BY
INSTALMENTS
DURING
THE
YEAR
.
274
7.6
INVESTMENT
CALCULATION
.
279
7.6.1
FUNDAMENTAL
TERMS
.
280
7.6.2
FUNDAMENTALS
OF
FINANCIAL
MATHEMATICS
.
283
7.6.3
METHODS
OF
STATIC
INVESTMENT
CALCULATION
.
286
7.6.4
METHODS
OF
DYNAMIC
INVESTMENT
CALCULA
TION
.
286
7.6.4.1
NET
PRESENT
VALUE
METHOD
(NET
PRESENT
VALUE,
AMOUNT
OF
CAPITAL,
FINAL
ASSET
VALUE)
.
287
7.6.4.2
ANNUITY
METHOD
.
290
7.6.4.3
INTERNAL
RATE
OF
RETURN
METHOD
.
293
8
OPTIMISATION
OF
LINEAR
MODELS
297
8.1
LAGRANGE
METHOD
.
297
8.1.1
INTRODUCTION
.
297
8.1.2
FORMATION
OF
THE
LAGRANGE
FUNCTION
.
297
8.1.3
DETERMINATION
OF
THE
SOLUTION
.
298
8.1.4
INTERPRETATION
OF
A
.
299
8.2
LINEAR
OPTIMISATION
.
302
8.2.1
INTRODUCTION
.
302
8.2.2
THE
LINEAR
PROGRAMMING
APPROACH
.
303
8.2.3
GRAPHICAL
SOLUTION
.
303
8.2.4
PRIMAL
SIMPLEX
ALGORITHM
.
308
8.2.5
SIMPLEX
TABLEAU
(BASIC
STRUCTURE)
.
308
8.2.6
DUAL
SIMPLEX
ALGORITHM
.
315
XVI
CONTENTS
9
FUNCTIONS
325
9.1
INTRODUCTION
.
325
9.1.1
COMPOSITION
OF
FUNCTIONS
.
329
9.1.2
INVERSE
FUNCTION
.
331
9.2
CLASSIFICATION
OF
FUNCTIONS
.
333
9.2.1
RATIONAL
FUNCTIONS
.
334
9.2.1.1
POLYNOMIAL
FUNCTIONS
.
334
9.2.1.2
BROKEN
RATIONAL
FUNCTIONS
.
334
9.2.2
NON-RATIONAL
FUNCTIONS
.
338
9.2.2.1
POWER
FUNCTIONS
.
338
9.2.2.2
ROOT
FUNCTION
.
341
9.2.2.3
TRANSCENDENTAL
FUNCTIONS
.
342
9.2.2.3.1
EXPONENTIAL
FUNCTIONS
.
342
9.2.2.3.2
LOGARITHMIC
FUNCTIONS
.
348
9.2.2.4
TRIGONOMETRIC
FUNCTIONS
(ANGLE
FUNC
TIONS/CIRCULAR
FUNCTIONS)
.
354
9.3
CHARACTERISTICS
OF
REAL
FUNCTIONS
.
382
9.3.1
BOUNDEDNESS
.
382
9.3.2
SYMMETRY
.
384
9.3.2.1
AXIAL
SYMMETRY
.
384
9.3.2.2
POINT
SYMMETRY
.
386
9.3.3
TRANSFORMATIONS
.
389
9.3.3.1
VERTEX
FORM
.
391
9.3.4
CONTINUITY
.
394
9.3.5
INFINITE
DISCONTINUITIES
.
394
9.3.6
REMOVABLE
DISCONTINUITIES
.
396
9.3.7
JUMP
DISCONTINUITIES
.
397
9.3.8
HOMOGENEITY
.
398
9.3.9
PERIODICITY
.
399
9.3.10
ZEROS
.
399
9.3.11
LOCAL
EXTREMES
.
400
9.3.12
MONOTONICITY
.
401
9.3.13
CONCAVITY
AND
CONVEXITY
|
INFLECTION
POINTS
.
402
9.3.14
ASYMPTOTES
.
404
9.3.14.1
HORIZONTAL
ASYMPTOTES
.
405
9.3.14.2
VERTICAL
ASYMPTOTE
.
407
9.3.14.3
OBLIQUE
ASYMPTOTE
.
408
9.3.14.4
ASYMPTOTIC
CURVE
.
409
CONTENTS
XVII
9.3.15
TANGENT
LINES
TO
A
CURVE
.
410
9.3.16
NORMAL
LINES
TO
A
CURVE
.
411
9.4
EXERCISES
.
412
10
DIFFERENTIAL
CALCULUS
417
10.1
DIFFERENTIATION
OF
FUNCTIONS
WITH
ONE
INDEPENDENT
VARIABLE
.
417
10.1.1
GENERAL
.
417
10.1.2
FIRST
DERIVATIVE
OF
ELEMENTARY
FUNCTIONS
.
420
10.1.3
DERIVATION
RULES
.
422
10.1.4
HIGHER
DERIVATIONS
.
424
10.1.5
DIFFERENTIATION
OF
FUNCTIONS
WITH
PARAME
TERS
.
425
10.1.6
CURVE
SKETCHING
.
425
10.2
DIFFERENTIATION
OF
FUNCTIONS
WITH
MORE
THAN
ONE
IN
DEPENDENT
VARIABLE
.
435
10.2.1
PARTIAL
DERIVATIVES
(1
ST
ORDER)
.
435
10.2.2
PARTIAL
DERIVATIVES
(2ND
ORDER)
.
438
10.2.3
LOCAL
EXTREMA
OF
THE
FUNCTION
F
=
F{X,
Y)
.
440
10.2.3.1
RELATIVE
EXTREMA
WITHOUT
CONSTRAINT
OF
THE
FUNCTION
F
=
F(X,
Y)
.
440
1
0.2.3.2
RELATIVE
EXTREMA
WITH
M
CONSTRAINTS
OF
THE
FUNCTION
F
=
F(XI,X
N
)
WITH
M N
.
449
10.2.4
DIFFERENTIALS
OF
THE
FUNCTION
F
=
F(XI,
.,
X
N
)
453
10.3
THEOREMS
OF
DIFFERENTIABLE
FUNCTIONS
.
455
10.3.1
MEAN
VALUE
THEOREM
FOR
DIFFERENTIAL
CAL
CULUS
.
455
10.3.2
GENERALIZED
MEAN
VALUE
THEOREM
FOR
DIF
FERENTIAL
CALCULUS
.
456
10.3.3
ROLLE
'
S
THEOREM
.
456
10.3.4
LHOSPITAL
'
S
RULE
.
457
10.3.5
BOUNDS
THEOREM
FOR
DIFFERENTIAL
CALCULUS
.
458
XVIII
CONTENTS
11
INTEGRAL
CALCULUS
459
11.1
INTRODUCTION
.
459
11.2
THE
INDEFINITE
INTEGRAL
.
460
11.2.1
DEFINITION/DETERMINING
THE
ANTIDERIVATIVE
.
460
11.2.2
ELEMENTARY
CALCULATION
RULES
FOR
THE
INDEFI
NITE
INTEGRAL
.
463
11.3
THE
DEFINITE
INTEGRAL
.
464
11.3.1
INTRODUCTION
.
464
11.3.2
RELATIONSHIP
BETWEEN
THE
DEFINITE
AND
THE
INDEFINITE
INTEGRAL
.
468
11.3.3
SPECIAL
TECHNIQUES
OF
INTEGRATION
.
473
11.3.3.1
PARTIAL
INTEGRATION
.
473
11.3.3.2
INTEGRATION
BY
SUBSTITUTION
.
475
11.4
MULTIPLE
INTEGRALS
.
476
11.5
INTEGRAL
CALCULUS
AND
ECONOMIC
PROBLEMS
.
477
11.5.1
COST
FUNCTIONS
.
477
11.5.2
REVENUE
FUNCTION
(=
SALES
FUNCTION)
.
479
11.5.3
PROFIT
FUNCTIONS
.
480
12
ELASTICITIES
485
12.1
DEFINITION
OF
ELASTICITY
.
485
12.2
ARC
ELASTICITY
.
486
12.3
POINT
ELASTICITY
.
491
12.4
PRICE
ELASTICITY
OF
DEMAND
EXP
.
494
12.5
CROSS
ELASTICITY
OF
DEMAND
E
X
A
P
B
.
499
12.6
INCOME
ELASTICITY
OF
DEMAND
EXY
.
501
13
ECONOMIC
FUNCTIONS
503
CONTENTS
XIX
13.1
SUPPLY
FUNCTION
.
503
13.2
DEMAND
FUNCTION
/
INVERSE
DEMAND
FUNCTION
.
505
13.3
MARKET
EQUILIBRIUM
.
507
13.4
BUYER'S
MARKET
AND
SELLER
'
S
MARKET
.
508
13.5
SUPPLY
GAP
.
509
13.6
DEMAND
GAP
.
509
13.7
REVENUE
FUNCTION
.
511
13.8
COST
FUNCTIONS
.
517
13.9
NEOCLASSICAL
COST
FUNCTION
.
525
13.10
COST
FUNCTION
ACCORDING
TO
THE
LAW
OF
DIMINISHING
RETURNS
.
533
13.11
DIRECT
COSTS
VERSUS
INDIRECT
COSTS
.
546
13.11.1
ONE-DIMENSIONAL
COST
ALLOCATION
PRINCIPLES
549
13.11.2
MULTI-DIMENSIONAL
COST
ALLOCATION
PRINCIPLES
551
13.12
PROFIT
FUNCTION
.
554
14
THE
PEREN
THEOREM
THE
MATHEMATICAL
FRAME
IN
WHICH
WE
LIVE
563
A
FINANCIAL
MATHEMATICAL
FACTORS
571
B
BIBLIOGRAPHY
617
INDEX
625 |
| adam_txt |
CONTENTS
LIST
OF
ABBREVIATIONS
XXI
1
MATHEMATICAL
SIGNS
AND
SYMBOLS
1
1.1
PRAGMATIC
SIGNS
.
1
1.2
GENERAL
ARITHMETIC
RELATIONS
AND
LINKS
.
1
1.3
SETS
OF
NUMBERS
.
2
1.4
SPECIAL
NUMBERS
AND
LINKS
.
3
1.5
LIMIT
.
3
1.6
EXPONENTIAL
FUNCTIONS,
LOGARITHM
.
4
1.7
TRIGONOMETRIC
FUNCTIONS,
HYPERBOLIC
FUNCTIONS
.
4
1.8
VECTORS,
MATRICES
.
5
1.9
SETS
.
6
1.10
RELATIONS
.
7
1.11
FUNCTIONS
.
7
1.12
ORDER
STRUCTURES
.
7
1.13
SI
MULTIPLYING
AND
DIVIDING
PREFIXES
.
8
1.14
GREEK
ALPHABET
.
9
IX
X
CONTENTS
2
LOGIC
11
2.1
MATHEMATICAL
LOGIC
.
11
2.2
PROPOSITIONAL
LOGIC
.
11
2.2.1
PROPOSITIONAL
VARIABLE
.
11
2.2.2
TRUTH
TABLES
.
12
3
ARITHMETIC
15
3.1
SETS
.
15
3.1.1
GENERAL
.
15
3.1.2
SET
RELATIONS
.
16
3.1.3
SET
OPERATIONS
.
17
3.1.4
RELATIONS,
LAWS,
RULES
OF
CALCULATION
FOR
SETS
19
3.1.5
INTERVALS
.
21
3.1.6
NUMERAL
SYSTEMS
.
22
3.1.6.1
DECIMAL
SYSTEM
(DECADIC
SYSTEM)
23
3.1.6.2
DUAL
SYSTEM
(BINARY
SYSTEM)
.
23
3.1.6.3
ROMAN
NUMERAL
SYSTEM
.
24
3.2
ELEMENTARY
CALCULUS
.
24
3.2.1
ELEMENTARY
FOUNDATIONS
.
24
3.2.1.1
AXIOMS
.
25
3.2.1.2
FACTORISATION
.
25
3.2.1.3
RELATIONS
.
26
3.2.1.4 ABSOLUTE
VALUE,
SIGNUM
.
26
3.2.1.5
FRACTIONS
.
27
3.2.1.6
POLYNOMIAL
DIVISION
.
27
3.2.1.7
HORNER
'
S
SCHEME
(HORNER
'
S
METHOD)
29
3.2.2
CONVERSIONS
OF
TERMS
.
30
3.2.2.1
BINOMIAL
FORMULAS
.
30
3.2.2.2
BINOMIAL
THEOREM
.
31
3.2.2.3
GENERAL
BINOMIAL
THEOREM
FOR
NAT
URAL
EXPONENTS
31
3.2.2.4
GENERAL
BINOMIAL
THEOREM
FOR
REAL
EXPONENTS
.
31
3.2.2.5
POLYNOMIAL
TERMS
.
32
3.2.3
SUMMATION
AND
PRODUCT
NOTATION
.
32
3.2.3.1
SUMMATION
NOTATION
.
32
CONTENTS
XI
3.2.3.2
PRODUCT
NOTATION
.
33
3.2.4
POWERS,
ROOTS
.
34
3.2.5
LOGARITHMS
.
37
3.2.6
FACTORIAL
.
39
3.2.7
BINOMIAL
COEFFICIENT
.
40
3.3
SEQUENCES
.
41
3.3.1
DEFINITION
.
41
3.3.2
LIMIT
OF
A
SEQUENCE
.
44
3.3.3
ARITHMETIC
AND
GEOMETRIC
SEQUENCES
.
46
3.4
SERIES
.
47
3.4.1
DEFINITION
.
47
3.4.2
ARITHMETIC
AND
GEOMETRIC
SERIES
.
47
4
ALGEBRA
51
4.1
FUNDAMENTAL
TERMS
.
51
4.2
LINEAR
EQUATIONS
.
53
4.2.1
LINEAR
EQUATIONS
WITH
ONE
VARIABLE
.
53
4.2.2
LINEAR
INEQUATIONS
WITH
ONE
VARIABLE
.
56
4.2.3
LINEAR
EQUATIONS
WITH
MULTIPLE
VARIABLES
.
56
4.2.4
SYSTEMS
OF
LINEAR
EQUATIONS
.
57
4.2.5
LINEAR
INEQUATIONS
WITH
MULTIPLE
VARIABLES
.
61
4.3
NON-LINEAR
EQUATIONS
.
62
4.3.1
QUADRATIC
EQUATIONS
WITH
ONE
VARIABLE
.
62
4.3.2
CUBIC
EQUATIONS
WITH
ONE
VARIABLE
.
65
4.3.3
BIQUADRATIC
EQUATIONS
.
67
4.3.4
EQUATIONS
OF
THE
NTH
DEGREE
.
68
4.3.5
RADICAL
EQUATIONS
.
69
4.4
TRANSCENDENTAL
EQUATIONS
.
71
4.4.1
EXPONENTIAL
EQUATIONS
.
71
4.4.2
LOGARITHMIC
EQUATIONS
.
73
4.5
APPROXIMATION
METHODS
.
75
4.5.1
REGULA
FALSI
(SECANT
METHOD)
.
75
4.5.2
NEWTON
'
S
METHOD
(TANGENT
METHOD)
.
77
XII
CONTENTS
4.5.3
GENERAL
APPROXIMATION
METHOD
(FIXED-POINT
ITERATION)
.
80
5
LINEAR
ALGEBRA
87
5.1
FUNDAMENTAL
TERMS
.
87
5.1.1
MATRIX
.
87
5.1.2
EQUALITY/INEQUALITY
OF
MATRICES
.
88
5.1.3
TRANSPOSED
MATRIX
.
89
5.1.4
VECTOR
.
89
5.1.5
SPECIAL
MATRICES
AND
VECTORS
.
92
5.2
OPERATIONS
WITH
MATRICES
.
94
5.2.1
ADDITION
OF
MATRICES
.
94
5.2.2
MULTIPLICATION
OF
MATRICES
.
96
5.2.2.1
MULTIPLICATION
OF
A
MATRIX
WITH
A
SCALAR
.
96
5.2.2.2
THE
SCALAR
PRODUCT
OF
TWO
VEC
TORS
.
98
5.2.2.3
MULTIPLICATION
OF
A
MATRIX
BY
A
COL
UMN
VECTOR
.
100
5.2.2.4
MULTIPLICATION
OF
A
ROW
VECTOR
BY
A
MATRIX
.
102
5.2.2.5
MULTIPLICATION
OF
TWO
MATRICES
.
103
5.3
THE
INVERSE
OF
A
MATRIX
.
107
5.3.1
INTRODUCTION
.
107
5.3.2
DETERMINATION
OF
THE
INVERSE
WITH
THE
USAGE
OF
THE
GAUSSIAN
ELIMINATION
METHOD
.
109
5.4
THE
RANK
OF
A
MATRIX
.
113
5.4.1
DEFINITION
.
113
5.4.2
DETERMINATION
OF
THE
RANK
OF
A
MATRIX
.
113
5.5
THE
DETERMINANT
OF
A
MATRIX
.
117
5.5.1
DEFINITION
.
117
5.5.2
CALCULATION
OF
DETERMINANTS
.
118
5.5.3
CHARACTERISTICS
OF
DETERMINANTS
.
124
CONTENTS
XIII
5.6
THE
ADJOINT
OF
A
MATRIX
.
125
5.6.1
DEFINITION
.
125
5.6.2
DETERMINATION
OF
THE
INVERSE
WITH
THE
USAGE
OF
THE
ADJOINT
.
127
6
COMBINATORICS
129
6.1
INTRODUCTION
.
129
6.2
PERMUTATIONS
.
133
6.3
VARIATIONS
.
135
6.4
COMBINATIONS
.
136
7
FINANCIAL
MATHEMATICS
141
7.1
CALCULATION
OF
INTEREST
.
141
7.1.1
FUNDAMENTAL
TERMS
.
141
7.1.2
ANNUAL
INTEREST
.
142
7.1.2.1
SIMPLE
INTEREST
CALCULATION
.
142
7.1.2.2
COMPOUND
COMPUTATION
OF
INTER
EST
.
144
7.1.2.3
COMPOSITE
INTEREST
.
146
7.1.3
INTEREST
DURING
THE
PERIOD
.
158
7.1.3.1
SIMPLE
INTEREST
CALCULATION
(LINEAR)
159
7.1.3.2
SIMPLE
INTEREST
USING
THE
NOMI
NAL
ANNUAL
INTEREST
RATE
.
159
7.1.3.3
COMPOUND
INTEREST
(EXPONENTIAL)
.
160
7.1.3.4
INTEREST
WITH
COMPOUND
INTEREST
USING
A
CONFORMING
ANNUAL
INTER
EST
RATE
.
161
7.1.3.5
MIXED
INTEREST
.
162
7.1.3.6
STEADY
INTEREST
RATE
.
163
7.2
ANNUAL
PERCENTAGE
RATE
.
168
7.3
DEPRECIATION
.
173
7.3.1
TIME
DEPRECIATION
.
173
7.3.1.1
LINEAR
DEPRECIATION
.
173
XIV
CONTENTS
7.3.1.2
ARITHMETIC-DEGRESSIVE
DEPRECIATION
174
7.3.1.3
GEOMETRIC-DEGRESSIVE
DEPRECIA
TION
.
176
7.3.2
UNITS
OF
PRODUCTION
DEPRECIATION
.
178
7.3.3
EXTRAORDINARY
DEPRECIATION
.
179
7.4
ANNUITY
CALCULATION
.
180
7.4.1
FUNDAMENTAL
TERMS
.
180
7.4.2
FINITE,
REGULAR
ANNUITY
.
183
7.4.2.1
ANNUAL
ANNUITY
WITH
ANNUAL
INTEREST
183
7.4.2.2
ANNUAL
ANNUITY
WITH
SUB-ANNUAL
INTEREST
.
187
7.4.2.3
SUB-ANNUAL
ANNUITY
WITH
ANNUAL
INTEREST
.
190
7.4.2.4
SUB-ANNUAL
ANNUITY
WITH
SUB-ANNUAL
INTEREST
.
194
7.4.3
FINITE,
VARIABLE
ANNUITY
.
213
7.4.3.1
IRREGULAR
ANNUITY
.
213
7.4.3.2
ARITHMETIC
PROGRESSIVE
ANNUITY
.
220
7.4.3.3
GEOMETRIC
PROGRESSIVE
ANNUITY
.
231
7.4.4
PERPETUITY
.
234
7.5
SINKING
FUND
CALCULATION
.
235
7.5.1
FUNDAMENTAL
TERMS
.
236
7.5.2
ANNUITY
REPAYMENT
.
238
7.5.3
REPAYMENT
BY
INSTALMENTS
.
241
7.5.4
REPAYMENT
WITH
PREMIUM
.
243
7.5.4.1
ANNUITY
REPAYMENT
WITH
PREMIUM
243
7.5.4.2
REPAYMENT
OF
AN
INSTALMENT
DEBT
WITH
PREMIUM
.
248
7.5.5
REPAYMENT
WITH
DISCOUNT
(DISAGIO)
.
249
7.5.5.1
ANNUITY
REPAYMENT
WITH
DISCOUNT
WHEN
IMMEDIATELY
BOOKED
AS
INTER
EST
EXPENSE
.
251
7.5.5.2
ANNUITY
REPAYMENT
WITH
DISCOUNT
WHEN
A
DISAGIO
IS
INCLUDED
IN
PRE
PAID
EXPENSES
.
253
7.5.5.3
INSTALMENT
REPAYMENT
WITH
DIS
COUNT
WHEN
IMMEDIATELY
BOOKED
AS
INTEREST
EXPENSE
.
253
CONTENTS
XV
7.5.5.4
INSTALMENT
REPAYMENT
WITH
DIS
COUNT
WHEN
A
DISAGIO
IS
INCLUDED
IN
PREPAID
EXPENSES
.
254
7.5.6
GRACE
PERIODS
.
255
7.5.7
ROUNDED
ANNUITIES
.
257
7.5.7.1
PERCENTAGE
ANNUITY
.
257
7.5.7.2
REPAYMENT
OF
BONDS
.
260
7.5.8
REPAYMENT
DURING
THE
YEAR
.
266
7.5.8.1
ANNUITY
REPAYMENT
DURING
THE
YEAR
266
7.5.8.2
REPAYMENT
BY
INSTALMENTS
DURING
THE
YEAR
.
274
7.6
INVESTMENT
CALCULATION
.
279
7.6.1
FUNDAMENTAL
TERMS
.
280
7.6.2
FUNDAMENTALS
OF
FINANCIAL
MATHEMATICS
.
283
7.6.3
METHODS
OF
STATIC
INVESTMENT
CALCULATION
.
286
7.6.4
METHODS
OF
DYNAMIC
INVESTMENT
CALCULA
TION
.
286
7.6.4.1
NET
PRESENT
VALUE
METHOD
(NET
PRESENT
VALUE,
AMOUNT
OF
CAPITAL,
FINAL
ASSET
VALUE)
.
287
7.6.4.2
ANNUITY
METHOD
.
290
7.6.4.3
INTERNAL
RATE
OF
RETURN
METHOD
.
293
8
OPTIMISATION
OF
LINEAR
MODELS
297
8.1
LAGRANGE
METHOD
.
297
8.1.1
INTRODUCTION
.
297
8.1.2
FORMATION
OF
THE
LAGRANGE
FUNCTION
.
297
8.1.3
DETERMINATION
OF
THE
SOLUTION
.
298
8.1.4
INTERPRETATION
OF
A
.
299
8.2
LINEAR
OPTIMISATION
.
302
8.2.1
INTRODUCTION
.
302
8.2.2
THE
LINEAR
PROGRAMMING
APPROACH
.
303
8.2.3
GRAPHICAL
SOLUTION
.
303
8.2.4
PRIMAL
SIMPLEX
ALGORITHM
.
308
8.2.5
SIMPLEX
TABLEAU
(BASIC
STRUCTURE)
.
308
8.2.6
DUAL
SIMPLEX
ALGORITHM
.
315
XVI
CONTENTS
9
FUNCTIONS
325
9.1
INTRODUCTION
.
325
9.1.1
COMPOSITION
OF
FUNCTIONS
.
329
9.1.2
INVERSE
FUNCTION
.
331
9.2
CLASSIFICATION
OF
FUNCTIONS
.
333
9.2.1
RATIONAL
FUNCTIONS
.
334
9.2.1.1
POLYNOMIAL
FUNCTIONS
.
334
9.2.1.2
BROKEN
RATIONAL
FUNCTIONS
.
334
9.2.2
NON-RATIONAL
FUNCTIONS
.
338
9.2.2.1
POWER
FUNCTIONS
.
338
9.2.2.2
ROOT
FUNCTION
.
341
9.2.2.3
TRANSCENDENTAL
FUNCTIONS
.
342
9.2.2.3.1
EXPONENTIAL
FUNCTIONS
.
342
9.2.2.3.2
LOGARITHMIC
FUNCTIONS
.
348
9.2.2.4
TRIGONOMETRIC
FUNCTIONS
(ANGLE
FUNC
TIONS/CIRCULAR
FUNCTIONS)
.
354
9.3
CHARACTERISTICS
OF
REAL
FUNCTIONS
.
382
9.3.1
BOUNDEDNESS
.
382
9.3.2
SYMMETRY
.
384
9.3.2.1
AXIAL
SYMMETRY
.
384
9.3.2.2
POINT
SYMMETRY
.
386
9.3.3
TRANSFORMATIONS
.
389
9.3.3.1
VERTEX
FORM
.
391
9.3.4
CONTINUITY
.
394
9.3.5
INFINITE
DISCONTINUITIES
.
394
9.3.6
REMOVABLE
DISCONTINUITIES
.
396
9.3.7
JUMP
DISCONTINUITIES
.
397
9.3.8
HOMOGENEITY
.
398
9.3.9
PERIODICITY
.
399
9.3.10
ZEROS
.
399
9.3.11
LOCAL
EXTREMES
.
400
9.3.12
MONOTONICITY
.
401
9.3.13
CONCAVITY
AND
CONVEXITY
|
INFLECTION
POINTS
.
402
9.3.14
ASYMPTOTES
.
404
9.3.14.1
HORIZONTAL
ASYMPTOTES
.
405
9.3.14.2
VERTICAL
ASYMPTOTE
.
407
9.3.14.3
OBLIQUE
ASYMPTOTE
.
408
9.3.14.4
ASYMPTOTIC
CURVE
.
409
CONTENTS
XVII
9.3.15
TANGENT
LINES
TO
A
CURVE
.
410
9.3.16
NORMAL
LINES
TO
A
CURVE
.
411
9.4
EXERCISES
.
412
10
DIFFERENTIAL
CALCULUS
417
10.1
DIFFERENTIATION
OF
FUNCTIONS
WITH
ONE
INDEPENDENT
VARIABLE
.
417
10.1.1
GENERAL
.
417
10.1.2
FIRST
DERIVATIVE
OF
ELEMENTARY
FUNCTIONS
.
420
10.1.3
DERIVATION
RULES
.
422
10.1.4
HIGHER
DERIVATIONS
.
424
10.1.5
DIFFERENTIATION
OF
FUNCTIONS
WITH
PARAME
TERS
.
425
10.1.6
CURVE
SKETCHING
.
425
10.2
DIFFERENTIATION
OF
FUNCTIONS
WITH
MORE
THAN
ONE
IN
DEPENDENT
VARIABLE
.
435
10.2.1
PARTIAL
DERIVATIVES
(1
ST
ORDER)
.
435
10.2.2
PARTIAL
DERIVATIVES
(2ND
ORDER)
.
438
10.2.3
LOCAL
EXTREMA
OF
THE
FUNCTION
F
=
F{X,
Y)
.
440
10.2.3.1
RELATIVE
EXTREMA
WITHOUT
CONSTRAINT
OF
THE
FUNCTION
F
=
F(X,
Y)
.
440
1
0.2.3.2
RELATIVE
EXTREMA
WITH
M
CONSTRAINTS
OF
THE
FUNCTION
F
=
F(XI,X
N
)
WITH
M N
.
449
10.2.4
DIFFERENTIALS
OF
THE
FUNCTION
F
=
F(XI,
.,
X
N
)
453
10.3
THEOREMS
OF
DIFFERENTIABLE
FUNCTIONS
.
455
10.3.1
MEAN
VALUE
THEOREM
FOR
DIFFERENTIAL
CAL
CULUS
.
455
10.3.2
GENERALIZED
MEAN
VALUE
THEOREM
FOR
DIF
FERENTIAL
CALCULUS
.
456
10.3.3
ROLLE
'
S
THEOREM
.
456
10.3.4
LHOSPITAL
'
S
RULE
.
457
10.3.5
BOUNDS
THEOREM
FOR
DIFFERENTIAL
CALCULUS
.
458
XVIII
CONTENTS
11
INTEGRAL
CALCULUS
459
11.1
INTRODUCTION
.
459
11.2
THE
INDEFINITE
INTEGRAL
.
460
11.2.1
DEFINITION/DETERMINING
THE
ANTIDERIVATIVE
.
460
11.2.2
ELEMENTARY
CALCULATION
RULES
FOR
THE
INDEFI
NITE
INTEGRAL
.
463
11.3
THE
DEFINITE
INTEGRAL
.
464
11.3.1
INTRODUCTION
.
464
11.3.2
RELATIONSHIP
BETWEEN
THE
DEFINITE
AND
THE
INDEFINITE
INTEGRAL
.
468
11.3.3
SPECIAL
TECHNIQUES
OF
INTEGRATION
.
473
11.3.3.1
PARTIAL
INTEGRATION
.
473
11.3.3.2
INTEGRATION
BY
SUBSTITUTION
.
475
11.4
MULTIPLE
INTEGRALS
.
476
11.5
INTEGRAL
CALCULUS
AND
ECONOMIC
PROBLEMS
.
477
11.5.1
COST
FUNCTIONS
.
477
11.5.2
REVENUE
FUNCTION
(=
SALES
FUNCTION)
.
479
11.5.3
PROFIT
FUNCTIONS
.
480
12
ELASTICITIES
485
12.1
DEFINITION
OF
ELASTICITY
.
485
12.2
ARC
ELASTICITY
.
486
12.3
POINT
ELASTICITY
.
491
12.4
PRICE
ELASTICITY
OF
DEMAND
EXP
.
494
12.5
CROSS
ELASTICITY
OF
DEMAND
E
X
A
P
B
.
499
12.6
INCOME
ELASTICITY
OF
DEMAND
EXY
.
501
13
ECONOMIC
FUNCTIONS
503
CONTENTS
XIX
13.1
SUPPLY
FUNCTION
.
503
13.2
DEMAND
FUNCTION
/
INVERSE
DEMAND
FUNCTION
.
505
13.3
MARKET
EQUILIBRIUM
.
507
13.4
BUYER'S
MARKET
AND
SELLER
'
S
MARKET
.
508
13.5
SUPPLY
GAP
.
509
13.6
DEMAND
GAP
.
509
13.7
REVENUE
FUNCTION
.
511
13.8
COST
FUNCTIONS
.
517
13.9
NEOCLASSICAL
COST
FUNCTION
.
525
13.10
COST
FUNCTION
ACCORDING
TO
THE
LAW
OF
DIMINISHING
RETURNS
.
533
13.11
DIRECT
COSTS
VERSUS
INDIRECT
COSTS
.
546
13.11.1
ONE-DIMENSIONAL
COST
ALLOCATION
PRINCIPLES
549
13.11.2
MULTI-DIMENSIONAL
COST
ALLOCATION
PRINCIPLES
551
13.12
PROFIT
FUNCTION
.
554
14
THE
PEREN
THEOREM
THE
MATHEMATICAL
FRAME
IN
WHICH
WE
LIVE
563
A
FINANCIAL
MATHEMATICAL
FACTORS
571
B
BIBLIOGRAPHY
617
INDEX
625 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Peren, Franz W. 1959- |
| author_GND | (DE-588)170930858 |
| author_facet | Peren, Franz W. 1959- |
| author_role | aut |
| author_sort | Peren, Franz W. 1959- |
| author_variant | f w p fw fwp |
| building | Verbundindex |
| bvnumber | BV049082687 |
| classification_rvk | QH 212 QH 100 |
| ctrlnum | (OCoLC)1394992064 (DE-599)DNB1279528885 |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| edition | Second edition |
| format | Book |
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| genre_facet | Formelsammlung |
| id | DE-604.BV049082687 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T22:28:09Z |
| indexdate | 2024-12-09T13:07:58Z |
| institution | BVB |
| institution_GND | (DE-588)1065168780 |
| isbn | 9783662669747 3662669749 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034344573 |
| oclc_num | 1394992064 |
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| owner | DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-355 DE-BY-UBR |
| physical | XXIV, 631 Seiten Diagramme |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Springer |
| record_format | marc |
| spelling | Peren, Franz W. 1959- Verfasser (DE-588)170930858 aut Math for business and economics compendium of essential formulas Franz W. Peren Second edition Berlin Springer [2023] XXIV, 631 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Mathematical signs and symbols Financial mathematics Annuity calculation Sinking fund calculation Investment calculation Optimisation of linear models Differential calculus Integral calculus Economic functions Elasticities Market equilibrium The Peren Theorem Combinatorics Linear algebra Arithmetic Logic (DE-588)4155008-0 Formelsammlung gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-662-66975-4 Vorangegangen ist 978-3-662-63248-2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=e8fe241d224142129af2a00d50a8a0f4&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB https://link.springer.com/978-3-662-66974-7 Auszug B:DE-101 application/pdf https://d-nb.info/1279528885/04 Verlag Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034344573&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20230130 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Peren, Franz W. 1959- Math for business and economics compendium of essential formulas Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4155008-0 |
| title | Math for business and economics compendium of essential formulas |
| title_auth | Math for business and economics compendium of essential formulas |
| title_exact_search | Math for business and economics compendium of essential formulas |
| title_exact_search_txtP | Math for business and economics compendium of essential formulas |
| title_full | Math for business and economics compendium of essential formulas Franz W. Peren |
| title_fullStr | Math for business and economics compendium of essential formulas Franz W. Peren |
| title_full_unstemmed | Math for business and economics compendium of essential formulas Franz W. Peren |
| title_short | Math for business and economics |
| title_sort | math for business and economics compendium of essential formulas |
| title_sub | compendium of essential formulas |
| topic | Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Wirtschaftsmathematik Formelsammlung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=e8fe241d224142129af2a00d50a8a0f4&prov=M&dok_var=1&dok_ext=htm https://link.springer.com/978-3-662-66974-7 https://d-nb.info/1279528885/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034344573&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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