Mathematics for economics:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Cambridge, Mass. [u.a.]
MIT Press
2011
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XIV, 959 S. graph. Darst. |
| ISBN: | 9780262015073 9780262516228 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Preface xiii
Parti Introduction and Fundamentals
Chapter 1
Introduction 3
1 1 What Is an Economic Model? 3
1 2 How to Use This Book 8
1 3 Conclusion 9
Chapter 2
Review of Fundamentals 11
2 1 Setsand Subsets 11
2 2 Numbers 23
2 3 Some Properties of Point SetsinR 31
2 4 Functions 41
Chapter 3
Sequences, Series, and Limits 61
3 1 Definition of aSequence 61
3 2 Limit ofa Sequence 65
3 3 Present-Value Calculations 69
3 4 Properties of Sequences 79
3 5 Series 84
Part If Univariate’Calculus and Optimization
Chapter 4
Continuity of Functions 103
4 1 Continuity of a Function of One Variable 103
4 2 Economic Applications of Continuous and Discontinuous Functions 113
viii
CONTENTS
Chapter 5
The Derivative and Differential for Functions of One Variable 127
5 1 Definition of a Tangent Line 127
5 2 Definition of the Derivative and the Differential 134
5 3 Conditions for Differentiability 141
5 4 Rules of Differentiation 147
5 5 Higher Order Derivatives: Concavity and Convexity of a Function 175
5 6 Taylor Series Formula and the Mean-Value Theorem 185
Chapter 6
Optimization of Functions of One Variable 195
6 1 Necessary Conditions for Unconstrained Maxima and Minima 196
6 2 Second-Order Conditions 211
6 3 Optimization over an Interval 220
Part Ill Linear Algebra
Chapter 7
Systems of Linear Equations 235
7 1 Solving Systems of Linear Equations 236
7 2 Linear Systems inn-Variables 250
Chapter 8
Matrices 267
8 1 General Notation 267
8 2 Basic Matrix Operations 273
8 3 Matrix Transposition 288
8 4 Some Special Matrices 293
Chapter 9
Determinants and the Inverse Matrix 301
9 1 Defining the Inverse 301
9 2 Obtaining the Determinant and Inverse of a3 x 3 Matrix 318
9 3 The Inverse of ann x n Matrix and Its Properties 324
9 4 Cramer’s Rule 329
Chapter 10
Some Advanced Topics in Linear Algebra 347
10 1 Vector Spaces 347
10 2 The Eigenvalue Problem 363
10 3 QuadraticForms 378
CONTENTS ix
Part IV Multivariate Calculus
Chapter 11
Calculus for Functions of n-Variables 393
11 1 Partial Differentiation 393
11 2 Second-Order Partial Derivatives 407
11 3 The First-Order Total Differential 415
11 4 Curvature Properties: Concavity and Convexity 436
11 5 More Properties of Functions with Economic Applications 451
11 6 Taylor Series Expansion* 464
Chapter 12
Optimization of Functions of n-Variables 473
12 1 First-Order Conditions 474
12 2 Second-Order Conditions 484
12 3 Direct Restrictions on Variables 491
Chapter 13
Constrained Optimization 503
13 1 Constrained Problems and Approaches to Solutions 504
13 2 Second-Order Conditions for Constrained Optimization 516
13 3 Existence, Uniqueness, and Characterization of Solutions 520
Chapter 14
Comparative Statics 529
14 1 Introduction to Comparative Statics 529
14 2 General Comparative-Statics Analysis 540
14 3 The Envelope Theorem 554
Chapter 15
Concave Programming and the Kuhn-Tucker Conditions 567
15 1 The Concave-Programming Problem 567
15 2 Many Variables and Constraints 575
PartV Integration and Dynamic Methods
Chapter 16
Integration 585
16 1 The Indefinite Integral 585 -
16 2 The Riemann (Definite) Integral 593
16 3 Properties of Integrals 605
x CONTENTS
16 4 Improper Integrals 613
16 5 Techniques of Integration 623
Chapter 17
An Introduction to Mathematics for Economic Dynamics 633
17 1 Modeling Time 634
Chapter 18
Linear, First-Order Difference Equations 643
18 1 Linear, First-Order, Autonomous Difference Equations 643
18 2 The General, Linear, First-Order Difference Equation 656
Chapter 19
Nonlinear, First-Order Difference Equations 665
19 1 The Phase Diagram and Qualitative Analysis 665
19 2 Cyclesand Chaos 673
Chapter 20
Linear, Second-Order Difference Equations 681
20 1 The Linear, Autonomous, Second-Order Difference Equation 681
20 2 The Linear, Second-Order Difference Equation witha Variable Term 708
Chapter 21
Linear, First-Order Differential Equations 715
21 1 Autonomous Equations 715
21 2 Nonautonomous Equations 731
Chapter 22
Nonlinear, First-Order Differential Equations 739
22 1 Autonomous Equations and Qualitative Analysis 739
22 2 Two Special Forms of Nonlinear, First-Order Differential Equations 748
Chapter 23
Linear, Second-Order Differential Equations 753 3
23 1 The Linear, Autonomous, Second-Order Differential Equation 75 Mm
23 2 TheLinear, Second-Order Differential Equation with a Variable Term
Chapt
pter 24 781
Simultaneous Systems of Differential and Difference Equations
24 1 Linear Differential Equation Systems 781
24 2 Stability Analysis and Linear Phase Diagrams 803
24 3 Systems of Linear Difference Equations 825
Chapter 25
Optimal Control Theory 845
The Maximum Principle 848
Optimization Problems Involving Discounting 860
Alternative Boundary Conditions onx(T) 872
Infinite-Time Horizon Problems 886
Constraints on the Control Variable 899
Free-Terminal-Time Problems (T Free) 909
Answers 921
Index
CONTENTS
xi
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:22:51Z |
| institution | BVB |
| isbn | 9780262015073 9780262516228 |
| language | English |
| lccn | 2010022679 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022524002 |
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| physical | XIV, 959 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | MIT Press |
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| spelling | Mathematics for economics Michael Hoy ... 3. ed. Cambridge, Mass. [u.a.] MIT Press 2011 XIV, 959 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s b DE-188 Hoy, Michael 1953- Sonstige (DE-588)131472968 oth V:DE-601;B:AGI pdf/application https://external.dandelon.com/download/attachments/dandelon/ids/CH001219BB16A6B8FDAFEC12579DD003851CD.pdf Inhaltsverzeichnis HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022524002&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematics for economics Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4123623-3 |
| title | Mathematics for economics |
| title_auth | Mathematics for economics |
| title_exact_search | Mathematics for economics |
| title_full | Mathematics for economics Michael Hoy ... |
| title_fullStr | Mathematics for economics Michael Hoy ... |
| title_full_unstemmed | Mathematics for economics Michael Hoy ... |
| title_short | Mathematics for economics |
| title_sort | mathematics for economics |
| topic | Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Economics, Mathematical Wirtschaftsmathematik Lehrbuch |
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