Mathematics for economists: an introductory textbook
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Manchester
Manchester Univ. Press
2016
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| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 757 S. graph. Darst. |
| ISBN: | 9781784991487 |
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| adam_text | Titel: Mathematics for economists
Autor: Pemberton, Malcolm
Jahr: 2016
Contents
Preface xi
Dependence of Chapters xvi
Answers and Solutions xvii
The Greek Alphabet xviii
1 LINEAR EQUATIONS 1
1.1 Straight line graphs............................................................1
1.2 An economic application: supply and demand..............................8
1.3 Simultaneous equations......................................................11
1.4 Input-output analysis..........................................................17
Problems on Chapter 1..............................................................19
2 LINEAR INEQUALITIES 21
2.1 Inequalities....................................................................21
2.2 Economic applications........................................................25
2.3 Linear programming..........................................................29
Problems on Chapter 2..............................................................34
3 SETS AND FUNCTIONS 36
3.1 Sets............................................................................36
3.2 Real numbers..................................................................40
3.3 Functions......................................................................46
3.4 Mappings......................................................................54
Problems on Chapter 3..............................................................56
4 QUADRATICS, INDICES AND LOGARITHMS 58
4.1 Quadratic functions and equations..........................................58
4.2 Maximising and minimising quadratic functions............................65
4.3 Indices..........................................................................67
4.4 Logarithms....................................................................73
Problems on Chapter 4..............................................................76
SEQUENCES, SERIES AND LIMITS 78
5.1 Sequences...................................78
5.2 Series...................................83
5.3 Geometric progressions in economics........... 87
5.4 Limits and continuity...........................92
Problems on Chapter 5.............................98
INTRODUCTION TO DIFFERENTIATION 100
6.1 The derivative.................................101
6.2 Linear approximations and differentiability.................108
6.3 Two useful rules ...............................112
6.4 Derivatives in economics...........................115
Problems on Chapter 6...............................117
METHODS OF DIFFERENTIATION 119
7.1 The product and quotient rules.......................119
7.2 The composite function rule.......................121
7.3 Monotonic functions...........................125
7.4 Inverse functions.............................131
Problems on Chapter 7.............................134
Appendix to Chapter 7.............................136
8 MAXIMA AND MINIMA 137
8.1 Critical points................................137
8.2 The second derivative............................141
8.3 Optimisation.................................145
8.4 Convexity and concavity...........................153
Problems on Chapter 8...............................161
9 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 163
9.1 The exponential function...........................163
9.2 Natural logarithms..............................168
9.3 Time in economics..............................174
Problems on Chapter 9...............................177
Appendix to Chapter 9...............................179
10 APPROXIMATIONS 181
10.1 Linear approximations and Newton s method ...............182
10.2 The mean value theorem...........................185
10.3 Quadratic approximations and Taylor s theorem..............189
10.4 Taylor and Maclaurin series.........................193
Problems on Chapter 10..............................196
Appendix to Chapter 10..............................198
11 MATRIX ALGEBRA 201
11.1 Vectors.....................................201
11.2 Matrices....................................207
11.3 Matrix multiplication.............................213
11.4 Square matrices................................217
Problems on Chapter 11..............................219
12 SYSTEMS OF LINEAR EQUATIONS 221
12.1 Echelon matrices...............................221
12.2 More on Gaussian elimination........................225
12.3 Inverting a matrix ..............................231
12.4 Linear dependence and rank.........................237
Problems on Chapter 12..............................240
13 DETERMINANTS AND QUADRATIC FORMS 242
13.1 Determinants.................................243
13.2 Transposition.................................249
13.3 Inner products ................................252
13.4 Quadratic forms and symmetric matrices..................256
Problems on Chapter 13..............................263
Appendix to Chapter 13..............................266
14 FUNCTIONS OF SEVERAL VARIABLES 267
14.1 Partial derivatives...............................268
14.2 Approximations and the chain rule.....................274
14.3 An economic application: production functions..............280
14.4 Homogeneous functions...........................283
Problems on Chapter 14..............................288
Appendix to Chapter 14..............................290
15 IMPLICIT RELATIONS 293
15.1 Implicit differentiation............................293
15.2 Comparative statics..............................301
15.3 Generalising to higher dimensions .....................306
Problems on Chapter 15..............................311
Appendix to Chapter 15..............................313
16 OPTIMISATION WITH SEVERAL VARIABLES 315
16.1 Critical points and their classification....................315
16.2 Global optima, concavity and convexity...................323
16.3 Non-negativity constraints..........................331
Problems on Chapter 16..............................334
Appendix to Chapter 16..............................336
17 PRINCIPLES OF CONSTRAINED OPTIMISATION 339
17.1 Lagrange multipliers.....................339
17.2 Extensions and warnings.........................346
17.3 Economic applications..........................350
17.4 Quasi-concave functions.........................359
Problems on Chapter 17............................365
18 FURTHER TOPICS IN CONSTRAINED OPTIMISATION 368
18.1 The meaning of the multipliers.......................369
18.2 Envelope theorems..............................372
18.3 Non-negativity constraints again ...................379
18.4 Inequality constraints.............................383
Problems on Chapter 18..............................390
19 INTEGRATION 393
19.1 Areas and integrals..............................393
19.2 Rules of integration..............................400
19.3 Integration in economics...........................406
19.4 Numerical integration............................409
Problems on Chapter 19..............................416
Appendix to Chapter 19..............................418
20 ASPECTS OF INTEGRAL CALCULUS 420
20.1 Methods of integration............................420
20.2 Infinite integrals ...............................426
20.3 Differentiation under the integral sign...................430
20.4 Double integrals ...............................434
Problems on Chapter 20 .............................. 442
21 PROBABILITY 444
21.1 Events and their probabilities........................444
21.2 Conditional probability and independence.................450
21.3 Random variables..........................................................457
21.4 The binomial, Poisson and exponential distributions............464
Problems on Chapter 21..............................................457
Appendix to Chapter 21......................
22 EXPECTATION 471
22.1 Expected value..............................471
22.2 The variance and higher moments ......................476
22.3 Two or more random variables ..................482
22.4 Random samples and limit theorems....... .............492
Problems on Chapter 22..............498
Appendix to Chapter 22.......................500
23 INTRODUCTION TO DYNAMICS 502
23.1 Differential equations ............................502
23.2 Linear equations with constant coefficients.................507
23.3 Harder first-order equations.........................513
23.4 Difference equations.............................519
Problems on Chapter 23 .............................. 526
24 THE CIRCULAR FUNCTIONS 529
24.1 Cycles, circles and trigonometry.......................529
24.2 Extending the definitions...........................535
24.3 Calculus with circular functions.......................542
24.4 Polar coordinates...............................548
Problems on Chapter 24 .............................. 551
25 COMPLEX NUMBERS 553
25.1 The complex number system.........................553
25.2 The trigonometric form ...........................558
25.3 Complex exponentials and polynomials...................562
Problems on Chapter 25 ............................................................568
26 FURTHER DYNAMICS 569
26.1 Second-order differential equations.....................569
26.2 Qualitative behaviour ............................578
26.3 Second-order difference equations .....................585
Problems on Chapter 26 .............................. 593
Appendix to Chapter 26 .............................. 595
27 EIGENVALUES AND EIGENVECTORS 597
27.1 Diagonalisable matrices...........................597
27.2 The characteristic polynomial........................603
27.3 Eigenvalues of symmetric matrices.....................610
Problems on Chapter 27..............................614
28 DYNAMIC SYSTEMS 616
28.1 Systems of difference equations.......................616
28.2 Systems of differential equations......................624
28.3 Qualitative behaviour ............................629
28.4 Non-linear systems..............................641
Problems on Chapter 28 .............................. 648
Appendix to Chapter 28 .............................. 650
29 DYNAMIC OPTIMISATION IN DISCRETE TIME 651
29.1 The basic problem..............................651
29.2 Variants of the basic problem........................657
29.3 Dynamic programming............................660
Problems on Chapter 29...............667
Appendix to Chapter 29...............669
30 DYNAMIC OPTIMISATION IN CONTINUOUS TIME 671
30.1 The basic problem and its variants .....................671
30.2 The maximum principle...........................676
30.3 Two applications to resource economics ..................681
30.4 Problems with an infinite horizon......................688
Problems on Chapter 30 ............................................................691
Appendix to Chapter 30 ............................................................695
31 INTRODUCTION TO ANALYSIS 700
31.1 Rigour.....................................700
31.2 More on the real number system ......................704
31.3 Sequences of real numbers..........................708
31.4 More on limits and continuity........................713
Problems on Chapter 31..............................716
32 METRIC SPACES AND EXISTENCE THEOREMS 719
32.1 Metric spaces.................................720
32.2 Open, closed and compact sets .......................725
32.3 Continuous mappings ............................730
32.4 Fixed point theorems..............................................734
Problems on Chapter 32................................................739
Appendix to Chapter 32............................................741
Notes on Further Reading 745
Index 747
|
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| spelling | Pemberton, Malcolm Verfasser (DE-588)170225984 aut Mathematics for economists an introductory textbook Malcolm Pemberton and Nicholas Rau 4. ed. Manchester Manchester Univ. Press 2016 XVIII, 757 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Rau, Nicholas Verfasser (DE-588)170468445 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028242897&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Mathematics for economists an introductory textbook |
| title_auth | Mathematics for economists an introductory textbook |
| title_exact_search | Mathematics for economists an introductory textbook |
| title_full | Mathematics for economists an introductory textbook Malcolm Pemberton and Nicholas Rau |
| title_fullStr | Mathematics for economists an introductory textbook Malcolm Pemberton and Nicholas Rau |
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| title_short | Mathematics for economists |
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