Introductory mathematics for economic analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Glenview, Ill. [u.a.]
Scott, Foresman
1971
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 502 S. graph. Darst. |
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MARC
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| 100 | 1 | |a KIM, THOMAS K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory mathematics for economic analysis |c Thomas K. Kim |
| 264 | 1 | |a Glenview, Ill. [u.a.] |b Scott, Foresman |c 1971 | |
| 300 | |a 502 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Economics |x Mathematical models | |
| 650 | 4 | |a Economics, Mathematical | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003958592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003958592 | ||
Record in the Search Index
| _version_ | 1804120480696762368 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
SELECTED DEFINITIONS 2
Constants 2
Variables: Continuous and Discrete 3
Auxiliary Symbols 4
THE NATURE OF ECONOMIC THEORIZING 4
The Definition of the Problem and the Statement of Assumptions 4
The Hypothesis 6
Theory 6
THE FUNCTION OF MATHEMATICS 7
2 REVIEW OF ELEMENTARY MATHEMATICS 9
BASIC OPERATIONS AND ASSUMPTIONS OF ALGEBRA 9
LAWS OF SIGNS 10
LAWS OF EXPONENTS 11
LOGARITHMS 13
Laws of Logarithmic Operations 14
Bases of Logarithms
The Relation between Common and Natural Logarithms 19
ALGEBRAIC EXPRESSIONS 20
EQUATIONS AND IDENTITIES 21
SOLUTION OF EQUATIONS 22
Linear Equations
Quadratic Equations
Solution of Pure Quadratic Equations 25
Solution of Complete Quadratic Equations 26
The Character of the Roots of Quadratic Equations 32
COMPLEX NUMBERS 33
Algebraic Operations with Complex Numbers 34
Graphic Solution of Quadratic Equations 36
SYSTEMS OF EQUATIONS 38
Systems of Linear Equations 38
Determinants of Nth Order 46
Systems of Equations Involving Quadratics 51
THEORY OF EQUATIONS 53
Fundamental Theorem of Algebra 53
Remainder Theorem 56
PARTIAL FRACTIONS 57
PROBLEMS 63
CONTENTS
3 TYPES OF FUNCTIONS 69
LINEAR FUNCTION, STRAIGHT LINE 69
Slope 70
Equations of Straight Lines 74
Distance Between Two Points 78
QUADRATIC EQUATIONS, CONIC SECTIONS 79
The Circle 80
Economic Applications of The Circle 86
The Ellipse 89
Economic Applications of The Ellipse 94
The Parabola 96
Economic Applications of the Parabola 100
The Hyperbola 105
Economic Applications of The Hyperbola 113
OTHER ALGEBRAIC FUNCTIONS 118
PROBLEMS 120
4 TRANSCENDENTAL FUNCTIONS AND THEIR GRAPHS 128
EXPONENTIAL FUNCTIONS 128
Logarithmic Functions 135
TRIGONOMETRIC FUNCTIONS 141
Definitions 141
The Meanings and Uses of Trigonometric Functions 143
Trigonometric Identities 149
ECONOMIC APPLICATIONS
OF TRIGONOMETRIC FUNCTIONS 150
Periodic Functions 150
Averages 152
POLAR EQUATIONS 155
COMPLEX NUMBERS 156
Polar Coordinates of a Complex Number 157
Addition of Complex Numbers 159
Multiplication of Complex Numbers 161
Division of Complex Numbers 162
PROBLEMS 163
5 LIMITS, CONTINUITY, AND DERIVATIVES 169
THE CONCEPT OF LIMITS 169
CONTINUITY 176
The Derivative 179
RULES OF DIFFERENTIATION 181
The Derivative of a Constant 181
The Derivative of a First Degree Term 182
The Differentiation of a Power Function 184
The Differentiation of Sums and Differences 185
Differentiation of the Product of Two Functions 187
CONTENTS
Differentiation of a Quotient 189
Differentiation of a Composite Function 191
Differentiation of an Inverse Function 194
Differentiation of Implicit Functions 195
Successive Differentiation 196
DIFFERENTIALS 199
Definition of a Differential 199
Geometric Interpretation of a Differential 200
Some Numerical Examples of Differentials 202
PROBLEMS 203
6 ECONOMIC APPLICATIONS OF DERIVATIVES 211
THE THEORY OF DEMAND 211
ELASTICITY 214
Price Elasticity 214
Gross Elasticity of Demand 218
Income Elasticity 219
ELASTICITY OF THE TOTAL REVENUE FUNCTION 219
MARGINAL REVENUE 222
MARGINAL COST 224
ELASTICITY OF TOTAL COST 226
LONG RUN AND SHORT RUN COSTS 228
THE NEOCLASSICAL MACROECONOMIC MODEL 234
MARGINAL PROPENSITY TO CONSUME AND TO SAVE 237
AN ANALYSIS OF INCOME TAXATION AND
GOVERNMENT EXPENDITURES 239
PROBLEMS 243
7 DIFFERENTIATION OF TRANSCENDENTAL FUNCTIONS 249
DIFFERENTIATION OF LOGARITHMIC FUNCTIONS 249
DIFFERENTIATION OF EXPONENTIAL FUNCTIONS 255
DIFFERENTIATION OF LOGARITHMIC EXPRESSIONS
TO ANY BASE 257
TRIGONOMETRIC FUNCTIONS 261
ECONOMIC APPLICATIONS OF DIFFERENTIATION
OF TRANSCENDENTAL EXPRESSIONS 269
PROBLEMS 272
8 PARTIAL DIFFERENTIATION 278
PARTIAL DERIVATIVES 278
TOTAL DIFFERENTIAL 282
DIFFERENTIATION OF IMPLICIT FUNCTIONS 283
PARTIAL DERIVATIVES OF HIGHER ORDER 286
HOMOGENEOUS FUNCTIONS 288
Homogeneity of Degree Zero 289
Homogeneity of Degree One 290
Homogeneity of Degrees Higher than One 295
CONTENTS
EULER S THEOREM 297
Economic Applications of Euler s Theorem 299
A Geometric Interpretation of Euler s Theorem and Its Applications 302
RELATIONSHIP OF CONSTANT RETURNS TO SCALE
AND MARGINAL PRODUCTIVITY 304
The Theory of Long Run Total Cost 309
Problems 314
9 MAXIMA AND MINIMA OF FUNCTIONS 322
FUNCTIONS OF ONE VARIABLE 322
THEORY OF THE FIRM 327
Monopoly Output as Half the Competitive Output 330
Sales Maximization 333
POINT OF INFLECTION 336
FUNCTIONS OF SEVERAL VARIABLES 338
PRICE DISCRIMINATION BY A MONOPOLIST 339
CONSTRAINED MAXIMUM, LaGRANGE MULTIPLIER 343
MINIMA 348
MAXIMA OR MINIMA INVOLVING MORE
THAN TWO VARIABLES 349
Maximum 349
Minimum 350
A STUDY OF SEVERAL DUOPOLY MODELS 352
A Generalization of the Cournot Model 352
Hotelling s Stable Duopoly Model 354
Some Duopoly Reaction Models, Including Frisch s 356
Conjectural Variation
Numerical Examples of Conjectural Variation 361
MAXIMIZATION OF A TAX ON OUTPUT 363
PROBLEMS 367
10 ELEMENTS OF INTEGRAL CALCULUS 372
SOME TECHNIQUES OF INTEGRATION 372
INTEGRATION OF TRIGONOMETRIC FORMS 386
CONSTANT OF INTEGRATION 392
THE DEFINITE INTEGRAL 395
Differential of the Area Under a Curve 395
The Definite Integral 396
APPROXIMATE INTEGRATION 406
Trapezoidal Rule 406
Simpson s Rule (Parabolic Rule) 409
PROBLEMS 414
11 DIFFERENCE EQUATIONS 422
DEFINITIONS 423
THE GROWTH RATE 424
CONTENTS
THE HARROD GROWTH MODEL 425
Time Path of a Solution 426
Time Path of the Harrod Model 429
NONHOMOGENEOUS FIRST ORDER LINEAR
DIFFERENCE EQUATIONS 429
THE COBWEB MODEL 435
SECOND ORDER LINEAR DIFFERENCE EQUATIONS 440
MULTIPLIER ACCELERATOR MODEL 443
NONHOMOGENEOUS SECOND ORDER DIFFERENCE
EQUATIONS 445
PROBLEMS 448
12 DIFFERENTIAL EQUATIONS 450
ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS 450
THE ORDER AND DEGREE OF A DIFFERENTIAL
EQUATION 451
SOLVING A DIFFERENTIAL EQUATION 451
DIFFERENTIAL EQUATIONS OF THE FIRST
ORDER AND OF THE FIRST DEGREE 454
Separation of Variables 454
Homogeneous Equations 456
Linear Differential Equations 459
Exact Differential Equations 463
ECONOMIC APPLICATIONS OF DIFFERENTIAL
EQUATIONS 468
The Domar Growth Model 468
The Harrod Growth Model 469
Price Level Adjustment Over Time 470
Derivation of the Cost Function by Separation of Variables 472
Analysis of a Consumer Indifference Curve by the
Homogeneous Differential Equation 474
Exact Differential Equation 476
DIFFERENTIAL EQUATIONS OF HIGHER ORDER 477
Second Order, Linear, Homogeneous Differential Equations
with Constant Coefficients 477
Complete (Nonhomogeneous) Second Order Differential Equations
with Constant Coefficients 484
Method of Undetermined Coefficients 484
Two Special Types of Second Order Differential Equations 487
DIFFERENTIAL EQUATIONS OF ORDER N 489
ECONOMIC APPLICATIONS OF HIGHER ORDER
DIFFERENTIAL EQUATIONS 491
National Debt Related to National Income 491
Domar s Burden of Debt Model 496
PROBLEMS 497
INDEX 499
|
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| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T16:42:46Z |
| institution | BVB |
| language | English |
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| physical | 502 S. graph. Darst. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
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| spelling | KIM, THOMAS K. Verfasser aut Introductory mathematics for economic analysis Thomas K. Kim Glenview, Ill. [u.a.] Scott, Foresman 1971 502 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003958592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | KIM, THOMAS K. Introductory mathematics for economic analysis Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical |
| title | Introductory mathematics for economic analysis |
| title_auth | Introductory mathematics for economic analysis |
| title_exact_search | Introductory mathematics for economic analysis |
| title_full | Introductory mathematics for economic analysis Thomas K. Kim |
| title_fullStr | Introductory mathematics for economic analysis Thomas K. Kim |
| title_full_unstemmed | Introductory mathematics for economic analysis Thomas K. Kim |
| title_short | Introductory mathematics for economic analysis |
| title_sort | introductory mathematics for economic analysis |
| topic | Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical |
| topic_facet | Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003958592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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