Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2007
|
| Subjects: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=2821315&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015037484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | X, 312 S. graph. Darst. |
| ISBN: | 1846285607 9781846285608 1846285615 |
Staff View
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| 245 | 1 | 0 | |a Elements of mathematics for economics and finance |c Vassilis C. Mavron and Timothy N. Phillips |
| 264 | 1 | |a London |b Springer |c 2007 | |
| 300 | |a X, 312 S. |b graph. Darst. | ||
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| 650 | 4 | |a Schulmathematik | |
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Record in the Search Index
| DE-BY-UBR_call_number | 40/QH 110 M461 |
|---|---|
| DE-BY-UBR_katkey | 4247663 |
| DE-BY-UBR_location | UB Lesesaal Wirtschaft |
| DE-BY-UBR_media_number | 069034498682 |
| _version_ | 1835085961527033857 |
| adam_text | Contents
1.
Essential Skills
.............................................. 1
1.1
Introduction
............................................. 1
1.2
Numbers
................................................ 2
1.2.1
Addition and Subtraction
........................... 3
1.2.2
Multiplication and Division
.......................... 3
1.2.3
Evaluation of Arithmetical Expressions
................ 4
1.3
Fractions
................................................ 5
1.3.1
Multiplication and Division
.......................... 7
1.4
Decimal Representation of Numbers
........................ 8
1.4.1
Standard Form
..................................... 10
1.5
Percentages
.............................................. 10
1.6
Powers and Indices
....................................... 12
1.7
Simplifying Algebraic Expressions
.......................... 16
1.7.1
Multiplying Brackets
................................ 16
1.7.2
Factorization
...................................... 18
2.
Linear Equations
........................................... 23
2.1
Introduction
............................................. 23
2.2
Solution of Linear Equations
............................... 24
2.3
Solution of Simultaneous Linear Equations
................... 27
2.4
Graphs of Linear Equations
................................ 30
2.4.1
Slope of a Straight Line
............................. 34
2.5
Budget Lines
............................................ 37
2.6
Supply and Demand Analysis
.............................. 40
2.6.1
Multicommodity Markets
............................ 44
v¡¡¡
Contents
3.
Quadratic Equations
........................................ 49
3.1
Introduction
............................................. 49
3.2
Graphs of Quadratic Functions
............................. 50
3.3
Quadratic Equations
...................................... 56
3.4
Applications to Economics
................................. 61
4.
Functions of a Single Variable
.............................. 69
4.1
Introduction
............................................. 69
4.2
Limits
.................................................. 72
4.3
Polynomial Functions
..................................... 72
4.4
Reciprocal Functions
...................................... 75
4.5
Inverse Functions
......................................... 81
5.
The Exponential and Logarithmic Functions
................ 87
5.1
Introduction
............................................. 87
5.2
Exponential Functions
.................................... 88
5.3
Logarithmic Functions
.................................... 90
5.4
Returns to Scale of Production Functions
.................... 95
5.4.1
Cobb-Douglas Production Functions
.................. 97
5.5
Compounding of Interest
.................................. 98
5.6
Applications of the Exponential Function in
Economic Modelling
......................................102
6.
Differentiation
..............................................109
6.1
Introduction
.............................................109
6.2
Rules of Differentiation
....................................113
6.2.1
Constant Functions
.................................113
6.2.2
Linear Functions
...................................114
6.2.3
Power Functions
...................................114
6.2.4
Sums and Differences of Functions
....................114
6.2.5
Product of Functions
...............................116
6.2.6
Quotient of Functions
...............................117
6.2.7
The Chain Rule
....................................117
6.3
Exponential and Logarithmic Functions
.....................119
6.4
Marginal Functions in Economics
...........................121
6.4.1
Marginal Revenue and Marginal Cost
.................121
6.4.2
Marginal Propensities
...............................123
6.5
Approximation to Marginal Functions
.......................125
6.6
Higher Order Derivatives
..................................127
6.7
Production Functions
.....................................129
Contents ix
7.
Maxima
and Minima
.......................................137
7.1
Introduction
.............................................137
7.2
Local Properties of Functions
..............................138
7.2.1
Increasing and Decreasing Functions
..................138
7.2.2
Concave and Convex Functions
......................138
7.3
Local or Relative
Extrema
.................................139
7.4
Global or Absolute
Extrema
...............................144
7.5
Points of Inflection
.......................................145
7.6
Optimization of Production Functions
.......................146
7.7
Optimization of Profit Functions
...........................151
7.8
Other Examples
..........................................154
8.
Partial Differentiation
......................................159
8.1
Introduction
.............................................159
8.2
Functions of Two or More Variables
........................160
8.3
Partial Derivatives
........................................160
8.4
Higher Order Partial Derivatives
...........................163
8.5
Partial Rate of Change
....................................165
8.6
The Chain Rule and Total Derivatives
......................168
8.7
Some Applications of Partial Derivatives
....................171
8.7.1
Implicit Differentiation
..............................171
8.7.2
Elasticity of Demand
...............................173
8.7.3
Utility
............................................176
8.7.4
Production
........................................179
8.7.5
Graphical Representations
...........................181
9.
Optimization
...............................................185
9.1
Introduction
.............................................185
9.2
Unconstrained Optimization
...............................186
9.3
Constrained Optimization
.................................193
9.3.1
Substitution Method
................................193
9.3.2
Lagrange Multipliers
................................197
9.3.3
The Lagrange Multiplier A: An Interpretation
..........201
9.4
Iso Curves
...............................................204
10.
Matrices and Determinants
.................................209
10.1
Introduction
.............................................209
10.2
Matrix Operations
........................................209
10.2.1
Scalar Multiplication
................................211
10.2.2
Matrix Addition
....................................212
10.2.3
Matrix Multiplication
...............................212
10.3
Solutions of Linear Systems of Equations
....................220
x
Contents
10.4
Cramer s Rule
...........................................222
10.5
More Determinants
.......................................223
10.6
Special Cases
............................................230
11.
Integration
.................................................233
11.1
Introduction
.............................................233
11.2
Rules of Integration
.......................................236
11.3
Definite Integrals
.........................................241
11.4
Definite Integration: Area and Summation
...................243
11.5
Producer s Surplus
.......................................250
11.6
Consumer s Surplus
.......................................251
12.
Linear Difference Equations
................................261
12.1
Introduction
.............................................261
12.2
Difference Equations
......................................261
12.3
First Order Linear Difference Equations
.....................264
12.4
Stability
.................................................267
12.5
The Cobweb Model
.......................................270
12.6
Second Order Linear Difference Equations
...................273
12.6.1
Complementary Solutions
...........................274
12.6.2
Particular Solutions
................................277
12.6.3
Stability
..........................................282
13.
Differential Equations
......................................287
13.1
Introduction
.............................................287
13.2
First Order Linear Differential Equations
....................288
13.2.1
Stability
..........................................292
13.3
Nonlinear First Order Differential Equations
.................292
13.3.1
Separation of Variables
..............................294
13.4
Second Order Linear Differential Equations
..................296
13.4.1
The Homogeneous Case
.............................297
13.4.2
The General Case
..................................300
13.4.3
Stability
..........................................302
A. Differentials
................................................305
Index
...........................................................309
|
| any_adam_object | 1 |
| author | Mavron, Vassilis C. Phillips, Timothy N. |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV021825407 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:42:55Z |
| institution | BVB |
| isbn | 1846285607 9781846285608 1846285615 |
| language | English |
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| spellingShingle | Mavron, Vassilis C. Phillips, Timothy N. Elements of mathematics for economics and finance Schulmathematik Mathematisches Modell Wirtschaft Business mathematics Economics Mathematical models Economics, Mathematical Finance Mathematical models Schulmathematik (DE-588)4153188-7 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4153188-7 (DE-588)4001865-9 (DE-588)4151278-9 |
| title | Elements of mathematics for economics and finance |
| title_auth | Elements of mathematics for economics and finance |
| title_exact_search | Elements of mathematics for economics and finance |
| title_full | Elements of mathematics for economics and finance Vassilis C. Mavron and Timothy N. Phillips |
| title_fullStr | Elements of mathematics for economics and finance Vassilis C. Mavron and Timothy N. Phillips |
| title_full_unstemmed | Elements of mathematics for economics and finance Vassilis C. Mavron and Timothy N. Phillips |
| title_short | Elements of mathematics for economics and finance |
| title_sort | elements of mathematics for economics and finance |
| topic | Schulmathematik Mathematisches Modell Wirtschaft Business mathematics Economics Mathematical models Economics, Mathematical Finance Mathematical models Schulmathematik (DE-588)4153188-7 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Schulmathematik Mathematisches Modell Wirtschaft Business mathematics Economics Mathematical models Economics, Mathematical Finance Mathematical models Analysis Einführung Einführung - Analysis |
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