Elements of mathematical economics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Mifflin
1965
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 413 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents
PART I: Introduction
1 Variables, Functions, and Equations 3
1.1 Introduction 3
1.2 Variables 5
1.3 Functions and Their Graphic Representation 6
1.4 Equations and Their Graphic Representation 10
Exercises 1 20
2 Fundamental Functions and Series 23
2.1 Power and Exponential Functions 23
2.2 Logarithmic Functions 28
2.3 Trigonometric Functions 30
2.4 The X) Notation 37
2.5 The JJ Notation 42
2.6 Sequence and Series 43
Exercises 2 46
3 Some Basic Functional Equations in Economics 51
3.1 Demand 51
3.2 Supply 57
3.3 Market Equilibrium 60
3.4 Lange s Model 66
3.5 Kaldor s Model 71
Exercises 3 74
PART II: Differential and Integral Calculus
4 Sets, Limits, and Continuity 79
4.1 Sets 79
4.2 Functions 83
ix
x CONTENTS
4.3 Limits and Limit Theorems 85
4.4 Continuity 89
4.5 Definition and Meaning of Derivatives 90
4.6 Tangent Lines, Continuity, and Differentiation 92
Exercises 4 93
5 Derivatives and Economic Applications 97
5.1 The Rules of Derivatives 97
5.2 The Rules of Differentiation 98
5.3 Complete Criteria for Maxima and Minima 108
5.4 Keynes Aggregate Supply Function 117
5.5 Profit Maximization Concept 119
5.6 The Concept of Elasticity 122
Exercises 5 128
6 Partial Derivatives and Economic Application 131
6.1 Functions of More Than Two Variables in Economics 131
6.2 The Meaning of Partial Derivatives 134
6.3 Some Criteria for Maxima and Minima 139
6.4 Homogeneous Functions and Euler s Theorem 145
6.5 Income Distribution Model 150
Exercises 6 153
7 Differentials and Differentiation in Economics 155
7.1 The Variation and Differential of Two or More Variables 155
7.2 The Rules of Differentiation 160
7.3 Differentiation of Implicit Functions 163
7.4 The Neo Classical Growth Model 168
Exercises 7 172
8 Integrals and Integrations 175
8.1 The Meaning and Technique of Integration 175
8.2 Some Properties of Definite Integrals 181
8.3 Expansions: Maclaurin and Taylor s Theorems 183
8.4 Complex Numbers 194
8.5 The Theory of Investment 199
Exercises 8 203
CONTENTS xi
PART III: Differential and Difference Equations
9 Linear Differential Equations in Economics 209
9.1 Solutions and Constants of Integration 210
9.2 Differential Equations of the First Order and Degree 212
9.3 The Solution of Higher Order Linear Differential Equations
with Constant Coefficients 219
9.4 Some Continuous Dynamic Models 229
9.5 The Stability of Competitive Equilibrium 239
Exercises 9 248
10 Linear Difference Equations in Economics 250
10.1 Difference Equations and Their Properties 250
10.2 Solution of a Linear First Order Difference Equation 252
10.3 Solution of a Linear Second Order Homogeneous Difference
Equation 256
10.4 Complete Solution of the Complete Linear Second Order
Difference Equation 257
10.5 Some Dynamic Models 260
10.6 Duesenberry s Growth and Cycle Model 268
Exercises 10 273
PART IV: Programming, Games, and Activity
Analysis
11 Matrix and Vector Analysis 277
11.1 Introduction 277
11.2 Vectors in the Plane 278
11.3 Matrices 279
11.4 Addition and Subtraction of Matrices 284
11.5 Matrix Multiplication 284
11.6 Determinants and Matrices 287
11.7 The Adjoint Matrix 292
11.8 The Inverse of a Square Matrix 292
11.9 The Rank of a Matrix 293
11.10 Elementary Transformations 294
Exercises 11 295
12 Mathematical Analysis for Programming 297
12.1 Linear Equations in Matrix Notation 297
12.2 Linear Transformation 298
xii CONTENTS
12.3 Consistent and Inconsistent Systems of Equations 298
12.4 The Condition Which Renders a System of Linear Equations
Consistent 300
12.5 The Linear Dependency of Vectors and Matrices 303
12.6 Bilinear Forms 306
12.7 Quadratic Forms 308
12.8 A Necessary and Sufficient Condition for Positive Definiteness 313
12.9 Orthogonal Matrices 321
12.10 The Characteristic Roots of a Characteristic Equation 321
12.11 Matrices, Differential Equations and Application 326
Exercises 12 336
13 The Simplex and Dual Methods in Programming 338
13.1 Introduction 338
13.2 Linear Programming Problems 339
13.3 Example and Geometry 340
13.4 Matrix Notation and Linear Programming 343
13.5 The Simplex Method 345
13.6 The Basic Feasible Solution and Artificial Base 349
13.7 Duality Problem 359
Exercises 13 361
14 Linear Programming and Activity Analysis 362
14.1 Production Function 362
14.2 A Continuous Production Function 363
14.3 The Technology, Commodities, and Activities; Basic Concepts
of Activity Analysis 370
14.4 Efficiency and Allocation 373
15 Linear Programming and the Theory of Games 379
15.1 Definitions and Terminologies 380
15.2 Saddle Points and Minimax 382
15.3 Two Person Zero Sum Games with Saddle Points 384
15.4 The Fundamental Theorems for Two Person Zero Sum Games 387
15.5 Linear Programming and the Theory of Games 393
Answers to Selected Exercises 397
A Selected Bibliography 403
index 407
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| indexdate | 2024-07-09T15:53:55Z |
| institution | BVB |
| language | English |
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| physical | XII, 413 S. graph. Darst. |
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| spelling | Kooros, Ahmed Verfasser aut Elements of mathematical economics A. Kooros Boston [u.a.] Mifflin 1965 XII, 413 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001956757&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kooros, Ahmed Elements of mathematical economics Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 |
| title | Elements of mathematical economics |
| title_auth | Elements of mathematical economics |
| title_exact_search | Elements of mathematical economics |
| title_full | Elements of mathematical economics A. Kooros |
| title_fullStr | Elements of mathematical economics A. Kooros |
| title_full_unstemmed | Elements of mathematical economics A. Kooros |
| title_short | Elements of mathematical economics |
| title_sort | elements of mathematical economics |
| topic | Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Economics, Mathematical Wirtschaftsmathematik |
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