Mathematics for economists and social scientists:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Macmillan
1971
|
| Schriftenreihe: | University of Southampton economics ser.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 616 S. |
Internformat
MARC
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| 100 | 1 | |a O'Brien, Raymond J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics for economists and social scientists |c R. J. O'Brien ; G. G. Garcia* |
| 264 | 1 | |a London [u.a.] |b Macmillan |c 1971 | |
| 300 | |a XII, 616 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a University of Southampton economics ser. | |
| 650 | 7 | |a Economie |2 gtt | |
| 650 | 4 | |a Mathématiques économiques | |
| 650 | 7 | |a Mathématiques économiques |2 ram | |
| 650 | 4 | |a Sciences sociales - Mathématiques | |
| 650 | 7 | |a Sciences sociales - Mathématiques |2 ram | |
| 650 | 7 | |a Sociale wetenschappen |2 gtt | |
| 650 | 7 | |a Wiskundige methoden |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Economics, Mathematical | |
| 650 | 4 | |a Social sciences |x Mathematics | |
| 700 | 1 | |a Garcia, G. G. |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001895234 | ||
Datensatz im Suchindex
| _version_ | 1804117315169550336 |
|---|---|
| adam_text | Contents
Preface xi
1 Introduction 1
1.1 An A ttempt at a Definition of Mathematics 1
1.2 Problems with Abstraction and Generality 2
1.3 Mathematics Cannot Prove Anything 3
1.4 The Internal Structure of a Mathematical System 4
1.5 Change in Mathematics 7
1.6 The Problem of Examples 8
1.7 Mathematical History and Organisation 11
2 Linear Relations and their Implications 17
2.1 Introduction 17
2.2 Policemen with Precision 17
2.3 More Straight Lines . 19
2.4 Examples: Consumption and Reaction 25
2.5 Convention and Generality 28
2.6 From Straight Line to Function 31
2.7 Summary 36
2.8 Exercises . 37
3 Some Sets, More Numbers 38
3.1 Introduction 38
3.2 The Idea of a Set 38
3.3 Membership 39
3.4 7%e Algebra and Arithmetic of Sets 40
3.5 The Number System 42
3.6 Numbers Used for Counting 43
3.7 Numbers Used for Subtraction 45
3.8 Recapitulation 46
3.9 Numbers Used for Multiplying and Dividing 47
3.10 From Axioms to Theorems 54
3.11 Factorisation and its Reversal 56
v
vi Mathematics for Economists and Social Scientists
3.12 Axioms for Inequalities 59
3.13 Is Q Enough? 60
3.14 Q versus R 63
3.15 Functions, Relations and Cartesian Products 65
3.16 Summary 69
3.17 Exercises 69
4 More Sets, Some Logic 72
4.1 Introduction 72
4.2 Universes and Venn Diagrams 72
4.3 Set functions and Measure 74
4.4 n(J+) = d=n(Q) n(R)(=c) 81
4.5 Axioms for Sets 88
4.6 Logic 93
4.7 Proof and Induction 100
4.8 The Binomial Theorem 102
4.9 Permutations, Combinations, Summations 106
4.10 The Binomial Distribution 108
4.11 Summary 109
4.12 Exercises 111
5 Elementary Functions 114
5.1 Introduction 114
5.2 Quadratic Functions, or Second order Polynomials 114
5.3 77ie Solution of Quadratic Equations 116
5.4 The Uses of Quadratics 119
5.5 Polynomials of Higher Order 122
5.6 Rational Functions and Beyond 128
5.7 Examining the Index Notation 132
5.8 Models with Fractional Powers 135
5.9 Interest Tables, and Money lending Models 137
5.10 Extending our Money lending 139
5.11 Changing the Base, or the Irrelevance of a. 142
5.12 Practical Applications 146
5.13 7%e Logarithmic Function: Geometrically Described 149
5.14 The Algebra of Logarithms 152
5.15 Applications 154
5.16 Surveyors, Architects and Oscillating Functions 158
5.17 7%e Practical Origins of Trigonometry 159
5.18 A Look at Limits 161
Contents vii
5.19 Trigonometric Algebra 162
5.20 Generalising our Definitions 163
5.21 Whither! 167
5.22 Practicality 169
5.23 Summary 169
5.24 Exercises 170
6 Groups, Fields and Complex Numbers 172
6.1 Introduction 172
6.2 Different Arithmetics: Binary Arithmetic 172
6.3 Different Arithmetics: Modular Arithmetic 174
6.4 Different Algebras 177
6.5 Groups 179
6.6 Rotations 180
6.7 184
6.8 .ReWs 186
6.9 Complex or Imaginary Numbers 188
6.10 Uses of Complex Numbers 193
6.11 7%e Fundamental Theorem of Algebra 195
6.12 Summary 196
6.13 Exercises 198
6.14 Postscript: Binary Numbers, Information Content and
Stimulus Complexity 200
7 Calculus 202
7.1 Introduction 202
7.2 An Algebraic Tool: Geometric Series 202
7.3 7%e Qzse o/ the Persistent Fly 203
7.4 The Case of the Victorious Tortoise! 207
7.5 A Warning, and an Example 209
7.6 Another Sort of Limit 211
7.7 Yet Another Sort of Limit 214
7.8 A Digression on Rigour 216
: 7.9 Integrals 217
7.10 Digression on Measure Theory 224
7.11 The Indefinite Integral 226
[ 7.12 Differentiation 237
7.13 Summary 245
7.14 Exercises 248
7.15 More Analysis 249
viii Mathematics for Economists and Social Scientists
7.16 Practical Applications 250
7.17 Maximisation 257
7.18 The Algebra of Limits 269
7.19 The Algebra of Differentiation 211
7.20 Summary of the Algebra of Differentiation 283
7.21 Some Worked Examples 283
7.22 Exercises on Differentiation 285
7.23 The Algebra of Integration ! 285
7.24 Notation, and the Operator D Again 296
7.25 The Algebra of Integration 298
7.26 Exercises on Integration 299
7.27 Infinite Series are Awkward 300
7.28 Tests for Convergence 301
7.29 Summary and Exercises 316
7.30 Uses for Series: e* 317
7.31 Lo£e(jt) 320
7.32 z* in General 326
7.33 More Generalisation: The Trigonometric Functions 328
7.34 Curiouser and Curiouser 330
7.35 The Standard Formi 336
7.36 Does iY Exist! or Problems with Improper Integrals 337
7.37 Can it be Simplified into a Standard FormV 342
7.38 Wfetf to do if there is no Standard Form 342
7.39 Taylor Series, an Infinite Sausage Machine 345
7.40 Exercises on Sections 7.30 7.39 353
7.41 Summary 354
8 Difference (and Differential) Equations 356
8.1 Introductory 356
8.2 Continuous Versus Discrete 356
8.3 A First Attempt 358
8.4 Differential Equivalent 361
8.5 Comparative Behaviour 364
8.6 WfcYfer? 369
8.7 An Example: The Accelerator Multiplier Model 370
8.8 Simple Second order Systems 371
8.9 Coincident and Imaginary Roots ¦ 374
8.10 Second order Differential Equations 384
8.11 Non homogeneous Equations 386
Contents ix
8.12 In terest Models and the A ccelerator Multiplier Model
Again 390
8.13 Summary 393
8.14 Exercises 394
9 Matrix Algebra 396
9.1 Introduction 396
9.2 Definitions, Arithmetic 396
9.3 Notation, Algebra 401
9.4 Codes 412
9.5 Inverses for 2 x 2s 414
9.6 Commutation 418
9.7 Recapitulation 420
9.8 Rotations and Transformations 420
9.9 Rotations in General 426
9.10 Circles and Ellipses 431
9.11 Component Analysis 449
9.12 Vectors and Vector Spaces 444
9.13 I%e Geometry of Vector Spaces 449
9.14 The Algebra of Linear Dependence 452
9.15 The Solution of Simultaneous Equations 456
9.16 Matrix Inversion, Elementary Operations, and Rank 461
9.17 The General Algorithm 466
9.18 Theorems on Rank, Inverses and Linear Dependence 469
9.19 Determinants Ml
9.20 Latent Roots and Latent Vectors 488
9.21 Some Applications of Matrices 491
9.22 Summary 498
9.23 Postscript: Some Proofs 499
; 9.24 Exercises 504
1
10 Multivariate Calculus 508
10.1 Introductory 508
10.2 Functions of Several Variables 509
10.3 Partial Derivatives 514
10.4 More Partial Derivatives 517
10.5 Differentials 519
10.6 Turning points 525
10.7 Turning points in General 534
10.8 Constrained Maxima and Minima 542
x Mathematics for Economists and Social Scientists
10.9 Constrained Maxima or Minima in Three or more
Dimensions 552
10.10 Linear Programming 554
10.11 Multiple Integration 562
10.12 Change of Variable in Multiple Integration 568
10.13 Some Loose Ends: Homogeneous Functions 584
10.14 Summary 589
10.15 Exercises 591
Bibliography 593
Index of Symbols and Abbreviations 597
Index 601
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| language | English |
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| physical | XII, 616 S. |
| publishDate | 1971 |
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| series2 | University of Southampton economics ser. |
| spelling | O'Brien, Raymond J. Verfasser aut Mathematics for economists and social scientists R. J. O'Brien ; G. G. Garcia* London [u.a.] Macmillan 1971 XII, 616 S. txt rdacontent n rdamedia nc rdacarrier University of Southampton economics ser. Economie gtt Mathématiques économiques Mathématiques économiques ram Sciences sociales - Mathématiques Sciences sociales - Mathématiques ram Sociale wetenschappen gtt Wiskundige methoden gtt Mathematik Sozialwissenschaften Wirtschaft Economics, Mathematical Social sciences Mathematics Garcia, G. G. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001895234&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Brien, Raymond J. Garcia, G. G. Mathematics for economists and social scientists Economie gtt Mathématiques économiques Mathématiques économiques ram Sciences sociales - Mathématiques Sciences sociales - Mathématiques ram Sociale wetenschappen gtt Wiskundige methoden gtt Mathematik Sozialwissenschaften Wirtschaft Economics, Mathematical Social sciences Mathematics |
| title | Mathematics for economists and social scientists |
| title_auth | Mathematics for economists and social scientists |
| title_exact_search | Mathematics for economists and social scientists |
| title_full | Mathematics for economists and social scientists R. J. O'Brien ; G. G. Garcia* |
| title_fullStr | Mathematics for economists and social scientists R. J. O'Brien ; G. G. Garcia* |
| title_full_unstemmed | Mathematics for economists and social scientists R. J. O'Brien ; G. G. Garcia* |
| title_short | Mathematics for economists and social scientists |
| title_sort | mathematics for economists and social scientists |
| topic | Economie gtt Mathématiques économiques Mathématiques économiques ram Sciences sociales - Mathématiques Sciences sociales - Mathématiques ram Sociale wetenschappen gtt Wiskundige methoden gtt Mathematik Sozialwissenschaften Wirtschaft Economics, Mathematical Social sciences Mathematics |
| topic_facet | Economie Mathématiques économiques Sciences sociales - Mathématiques Sociale wetenschappen Wiskundige methoden Mathematik Sozialwissenschaften Wirtschaft Economics, Mathematical Social sciences Mathematics |
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