Further mathematics for economic analysis:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Harlow ; Munich [u.a.]
Pearson
2008
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xi, 616 Seiten Diagramme |
| ISBN: | 9780273713289 |
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MARC
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| 245 | 1 | 0 | |a Further mathematics for economic analysis |c Knut Sydsaeter ; Peter Hammond ; Atle Seierstad ; Arne Strøm |
| 246 | 1 | 3 | |a Economic analysis |
| 250 | |a Second edition | ||
| 264 | 1 | |a Harlow ; Munich [u.a.] |b Pearson |c 2008 | |
| 300 | |a xi, 616 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804137999030550528 |
|---|---|
| adam_text | NTËNTS
Preface
1
Topics in Linear Algebra
ix 3
Static Optimization
1
LI
Review of Basic Linear Algebra
2
.2
Linear Independence
7
1.3
The Rank of a Matrix
11
1.4
Main Results on Linear Systems
14
1.5
Eigenvalues
19
1.6
Diagonalization
25
.7
Quadratic Forms
28
.8
Quadratic Forms with Linear Constraints
35
.9
Partitioned Matrices and Their Inverses
37
2
Multivariable
Calculus
43
2.1
Gradients and Directional Derivatives
44
2.2
Convex Sets
50
2.3
Concave and Convex Functions I
53
2.4
Concave and Convex Functions
Π
63
2.5
Quasiconcave and Quasiconvex Functions
68
2.6
Taylor s Formula
77
2.7
Implicit and Inverse Function Theorems
80
2.8
Degrees of Freedom and Functional
Dependence
89
2.9
Differentiability
93
2.10
Existence and Uniqueness of Solutions
of Systems of Equations
98
103
3.1
Extreme Points
104
3.2
Local Extreme Points
110
3.3
Equality Constraints:
The
Lagrange
Problem
115
3.4
Local Second-Order Conditions
125
3.5
Inequality Constraints:
Nonlinear Programming
129
3.6
Sufficient Conditions
135
3.7
Comparative Statics
139
3.8
Nonnegativity Constraints
143
3.9
Concave Programming
148
3.10
Precise Comparative Statics Results
150
3.11
Existence of
Lagrange
Multipliers
153
4
Topics in Integration
157
4.1
Review of One-Variable Integration
157
4.2
Leibniz s Formula
159
4.3
The Gamma Function
164
4.4
Multiple Integrals over
Product Domains
166
4.5
Double Integrals over General Domains
171
4.6
The Multiple Riemann Integral
175
4.7
Change of Variables
178
4.8
Generalized Double Integrals
186
VI
CONTENTS
5 Differential
Equations
I:
First-Order Equations in
One Variable
189
5.1
Introduction
190
5.2
The Direction is Given: Find the Path!
193
5.3
Separable Equations
194
5.4
First-Order Linear Equations
200
5.5
Exact Equations and Integrating Factors
206
5.6
Transformation of Variables
208
5.7
Qualitative Theory and Stability
211
5.8
Existence and Uniqueness
217
6
Differential Equations II:
Second-Order Equations
and Systems in the Plane
223
6.1
Introduction
223
6.2
Linear Differential Equations
226
6.3
Constant Coefficients
228
6.4
Stability for Linear Equations
235
6.5
Simultaneous Equations in the Plane
237
6.6
Equilibrium Points for Linear Systems
243
6.7
Phase Plane Analysis
246
6.8
Stability for Nonlinear Systems
251
6.9
Saddle Points
255
7
Differential Equations III:
Higher-Order Equations
259
7.1
Linear Differential Equations
259
7.2
The Constant Coefficients Case
263
7.3
Stability of Linear Differential
Equations
266
7.4
Systems of Differential Equations
269
7.5
Stability for Nonlinear Systems
273
7.6
Qualitative Theory
278
7.7
A Glimpse at Partial Differential
Equations
280
8
Calculus of Variations
287
8.1
The Simplest Problem
288
8.2
The
Euler
Equation
290
8.3
Why the
Euler
Equation is Necessary
293
8.4
Optimal Savings
298
8.5
More General Terminal Conditions
300
9
Control Theory:
Basic Techniques
305
9.1
The Basic Problem
306
9.2
A Simple Case
308
9.3
Regularity Conditions
312
9.4
The Standard Problem
314
9.5
The Maximum Principle and the
Calculus of Variations
322
9.6
Adjoint Variables as Shadow Prices
324
9.7
Sufficient Conditions
330
9.8
Variable Final Time
336
9.9
Current Value Formulations
338
9.10
Scrap Values
341
9.11
Infinite Horizon
348
9.12
Phase Diagrams
353
10
Control Theory with
Many Variables
359
10.1
Several Control and State Variables
360
10.2
Some Examples
366
10.3
Infinite Horizon
370
10.4
Existence Theorems and Sensitivity
373
10.5
A Heuristic Proof of the Maximum
Principle
377
10.6
Mixed Constraints
380
10.7
Pure State Constraints
383
10.8
Generalizations
386
11
Difference Equations
389
11.1
First-Order Difference Equations
390
11.2
Economic Applications
396
11.3
Second-Order Difference Equations
401
11.4
Linear Equations with Constant
Coefficients
404
11.5
Higher-Order Equations
410
11.6
Systems of Difference Equations
415
11.7
Stability of Nonlinear Difference
Equations
419
12
Discrete Time
Optimization
423
12.1
Dynamic Programming
424
12.2
The
Euler
Equation
433
12.3
Infinite Horizon
435
CONTENTS
VII
12.4 The Maximum
Principle
12.5
More Variables
12.6
Stochastic Optimization
12.7
Infinite Horizon Stationary Problems
13
Topology and Separation
13.1
Point Set Topology in
IR
13.2
Topology and Convergence
13.3
Continuous Functions
13.4
Maximum Theorems
13.5
Convex Sets
13.6
Separation Theorems
13.7
Productive Economies and
Frobenius s Theorem
14
Correspondences and
Fixed Points
14.1
Correspondences
14.2
A General Maximum Theorem
14.3
Fixed Points for Contraction Mappings
14.4
Brouwer s and Kakutani s
Fixed Point Theorems
14.5
Equilibrium in a Pure Exchange
Economy
441
Appendix A
444
Sets, Completeness, and
448
Convergence
525
458
A.
1
Sets and Functions
525
ЛГ
A.2 Least Upper Bound Principle
530
65
A.3 Sequences of Real Numbers
533
465
A.4 Infimum and Supremum of Functions
541
471
475
Appendix
В
481
Trigonometric Functions
545
486
B.I Basic Definitions and Results
545
491
B.2 Differentiating Trigonometric Functions
551
495
B.3 Complex Numbers
555
Answers
559
99
500
References
605
509
513
Index
609
516
521
second
edition
Further Mathematics for Economic Analysis
Knut Sydsaeter,
Peter Hammond, Atle Seierstad and
Arne
Strem
Further Mathematics for Economic Analysis, second edition, takes you to the next level beyond the widely-used
companion volume Essential Mathematics for Economic Analysis. You can progressively extend your existing
mathematical knowledge through its systematic and appropriately rigorous treatment of topics like
multivariable
calculus, constrained static optimization, the calculus of variations, optimal control theory,
and dynamic programming.
Further Mathematics for Economic Analysis, second edition, is distinctive because of its emphasis on dynamic
optimization, an important yet often underplayed tool in areas such as resource and environmental economics
and growth theory. It is written in such a way that many chapters can be read in isolation, so you ye free to pick
the topics most relevant to you. In this new edition, several chapters have been extensively rewritA and numerous
other improvements made.
*
New to this Edition:
•
Answers to almost all of the
600
problems in the
bèoTc
for
studen
•
Student s Manual with extended worked answers to selected probl·
•
Instructor s Manual now contains a large range of additiona^Cwe
use in examinations.
u vę
tree
-itAand
о
self check
in the book
ntary problems, simple to advanced, suitable fc
The book is ideal for advanced undergraduate and graduate students of economics who have completed a basic
undergraduate course in calculus and linear algebra. It presents roost of the mathematical tools they will encounter
in their advanced courses in economics. It is also ideaUy suited for self-study because of the extensive answers it
offers to problems throughout the book.
Peter Hammond is curmotly the Marie Curie Professor of Economics at the University of Warwick, and an Emeritus
Professor at Stanford University. His many publications extend ewer several different fieldsef economics. For many
years he taught courses in mathematics for economists and in mathematical economics at Stanford, as well as eariier
at the University of Essex and the London School of Economics.
Knut
Sydsaeter, Atle Seierstad, and
Ame
Strem
all have extensive experience in teaching mathematics for
economists in the Department of Economics at the University of Oslo. With Peter Berck at Berkeley,
Knut
Sydsaeter
and
Arne Strom
have written a widely used formula book, Economists Mathematical Manual (Springer,
2005).
The
1987
North-Holland book Optimal Control Theory for Economists by Atle Seierstad and
Knut
Sydsaeter is still
a standard reference in the field.
Visit www.pearsoned.co.uk/sydsaeter to access the supplementary
w
Student s Manual with
extended answers broken dow
in the text.
ISBN
978-0-273-71328-9
|
| adam_txt |
NTËNTS
Preface
1
Topics in Linear Algebra
ix 3
Static Optimization
1
LI
Review of Basic Linear Algebra
2
.2
Linear Independence
7
1.3
The Rank of a Matrix
11
1.4
Main Results on Linear Systems
14
1.5
Eigenvalues
19
1.6
Diagonalization
25
.7
Quadratic Forms
28
.8
Quadratic Forms with Linear Constraints
35
.9
Partitioned Matrices and Their Inverses
37
2
Multivariable
Calculus
43
2.1
Gradients and Directional Derivatives
44
2.2
Convex Sets
50
2.3
Concave and Convex Functions I
53
2.4
Concave and Convex Functions
Π
63
2.5
Quasiconcave and Quasiconvex Functions
68
2.6
Taylor's Formula
77
2.7
Implicit and Inverse Function Theorems
80
2.8
Degrees of Freedom and Functional
Dependence
89
2.9
Differentiability
93
2.10
Existence and Uniqueness of Solutions
of Systems of Equations
98
103
3.1
Extreme Points
104
3.2
Local Extreme Points
110
3.3
Equality Constraints:
The
Lagrange
Problem
115
3.4
Local Second-Order Conditions
125
3.5
Inequality Constraints:
Nonlinear Programming
129
3.6
Sufficient Conditions
135
3.7
Comparative Statics
139
3.8
Nonnegativity Constraints
143
3.9
Concave Programming
148
3.10
Precise Comparative Statics Results
150
3.11
Existence of
Lagrange
Multipliers
153
4
Topics in Integration
157
4.1
Review of One-Variable Integration
157
4.2
Leibniz's Formula
159
4.3
The Gamma Function
164
4.4
Multiple Integrals over
Product Domains
166
4.5
Double Integrals over General Domains
171
4.6
The Multiple Riemann Integral
175
4.7
Change of Variables
178
4.8
Generalized Double Integrals
186
VI
CONTENTS
5 Differential
Equations
I:
First-Order Equations in
One Variable
189
5.1
Introduction
190
5.2
The Direction is Given: Find the Path!
193
5.3
Separable Equations
194
5.4
First-Order Linear Equations
200
5.5
Exact Equations and Integrating Factors
206
5.6
Transformation of Variables
208
5.7
Qualitative Theory and Stability
211
5.8
Existence and Uniqueness
217
6
Differential Equations II:
Second-Order Equations
and Systems in the Plane
223
6.1
Introduction
223
6.2
Linear Differential Equations
226
6.3
Constant Coefficients
228
6.4
Stability for Linear Equations
235
6.5
Simultaneous Equations in the Plane
237
6.6
Equilibrium Points for Linear Systems
243
6.7
Phase Plane Analysis
246
6.8
Stability for Nonlinear Systems
251
6.9
Saddle Points
255
7
Differential Equations III:
Higher-Order Equations
259
7.1
Linear Differential Equations
259
7.2
The Constant Coefficients Case
263
7.3
Stability of Linear Differential
Equations
266
7.4
Systems of Differential Equations
269
7.5
Stability for Nonlinear Systems
273
7.6
Qualitative Theory
278
7.7
A Glimpse at Partial Differential
Equations
280
8
Calculus of Variations
287
8.1
The Simplest Problem
288
8.2
The
Euler
Equation
290
8.3
Why the
Euler
Equation is Necessary
293
8.4
Optimal Savings
298
8.5
More General Terminal Conditions
300
9
Control Theory:
Basic Techniques
305
9.1
The Basic Problem
306
9.2
A Simple Case
308
9.3
Regularity Conditions
312
9.4
The Standard Problem
314
9.5
The Maximum Principle and the
Calculus of Variations
322
9.6
Adjoint Variables as Shadow Prices
324
9.7
Sufficient Conditions
330
9.8
Variable Final Time
336
9.9
Current Value Formulations
338
9.10
Scrap Values
341
9.11
Infinite Horizon
348
9.12
Phase Diagrams
353
10
Control Theory with
Many Variables
359
10.1
Several Control and State Variables
360
10.2
Some Examples
366
10.3
Infinite Horizon
370
10.4
Existence Theorems and Sensitivity
373
10.5
A Heuristic Proof of the Maximum
Principle
377
10.6
Mixed Constraints
380
10.7
Pure State Constraints
383
10.8
Generalizations
386
11
Difference Equations
389
11.1
First-Order Difference Equations
390
11.2
Economic Applications
396
11.3
Second-Order Difference Equations
401
11.4
Linear Equations with Constant
Coefficients
404
11.5
Higher-Order Equations
410
11.6
Systems of Difference Equations
415
11.7
Stability of Nonlinear Difference
Equations
419
12
Discrete Time
Optimization
423
12.1
Dynamic Programming
424
12.2
The
Euler
Equation
433
12.3
Infinite Horizon
435
CONTENTS
VII
12.4 The Maximum
Principle
12.5
More Variables
12.6
Stochastic Optimization
12.7
Infinite Horizon Stationary Problems
13
Topology and Separation
13.1
Point Set Topology in
IR"
13.2
Topology and Convergence
13.3
Continuous Functions
13.4
Maximum Theorems
13.5
Convex Sets
13.6
Separation Theorems
13.7
Productive Economies and
Frobenius's Theorem
14
Correspondences and
Fixed Points
14.1
Correspondences
14.2
A General Maximum Theorem
14.3
Fixed Points for Contraction Mappings
14.4
Brouwer's and Kakutani's
Fixed Point Theorems
14.5
Equilibrium in a Pure Exchange
Economy
441
Appendix A
444
Sets, Completeness, and
448
Convergence
525
458
A.
1
Sets and Functions
525
ЛГ
A.2 Least Upper Bound Principle
530
65
A.3 Sequences of Real Numbers
533
465
A.4 Infimum and Supremum of Functions
541
471
475
Appendix
В
481
Trigonometric Functions
545
486
B.I Basic Definitions and Results
545
491
B.2 Differentiating Trigonometric Functions
551
495
B.3 Complex Numbers
555
Answers
559
99
500
References
605
509
513
Index
609
516
521
second
edition
Further Mathematics for Economic Analysis
Knut Sydsaeter,
Peter Hammond, Atle Seierstad and
Arne
Strem
Further Mathematics for Economic Analysis, second edition, takes you to the next level beyond the widely-used
companion volume Essential Mathematics for Economic Analysis. You can progressively extend your existing
mathematical knowledge through its systematic and appropriately rigorous treatment of topics like
multivariable
calculus, constrained static optimization, the calculus of variations, optimal control theory,
and dynamic programming.
Further Mathematics for Economic Analysis, second edition, is distinctive because of its emphasis on dynamic
optimization, an important yet often underplayed tool in areas such as resource and environmental economics
and growth theory. It is written in such a way that many chapters can be read in isolation, so you ye free to pick
the topics most relevant to you. In this new edition, several chapters have been extensively rewritA and numerous
other improvements made.
*
New to this Edition:
•
Answers to almost all of the
600
problems in the
bèoTc
for
studen
•
Student's Manual with extended worked answers to selected probl·
•
Instructor's Manual now contains a large range of additiona^Cwe
use in examinations.
u vę
tree
-itAand
о
self check
in the book
ntary problems, simple to advanced, suitable fc
The book is ideal for advanced undergraduate and graduate students of economics who have completed a basic
undergraduate course in calculus and linear algebra. It presents roost of the mathematical tools they will encounter
in their advanced courses in economics. It is also ideaUy suited for self-study because of the extensive answers it
offers to problems throughout the book.
Peter Hammond is curmotly the Marie Curie Professor of Economics at the University of Warwick, and an Emeritus
Professor at Stanford University. His many publications extend ewer several different fieldsef economics. For many
years he taught courses in mathematics for economists and in mathematical economics at Stanford, as well as eariier
at the University of Essex and the London School of Economics.
Knut
Sydsaeter, Atle Seierstad, and
Ame
Strem
all have extensive experience in teaching mathematics for
economists in the Department of Economics at the University of Oslo. With Peter Berck at Berkeley,
Knut
Sydsaeter
and
Arne Strom
have written a widely used formula book, Economists' Mathematical Manual (Springer,
2005).
The
1987
North-Holland book Optimal Control Theory for Economists by Atle Seierstad and
Knut
Sydsaeter is still
a standard reference in the field.
Visit www.pearsoned.co.uk/sydsaeter to access the supplementary
w
Student's Manual with
extended answers broken dow
in the text.
ISBN
978-0-273-71328-9 |
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| author_GND | (DE-588)129255114 (DE-588)129255122 (DE-588)170327558 (DE-588)120816253 |
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| ctrlnum | (OCoLC)226974602 (DE-599)BVBBV035056642 |
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| dewey-ones | 330 - Economics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035056642 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:58:48Z |
| indexdate | 2024-07-09T21:21:12Z |
| institution | BVB |
| isbn | 9780273713289 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016725222 |
| oclc_num | 226974602 |
| open_access_boolean | |
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| physical | xi, 616 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Pearson |
| record_format | marc |
| spelling | Further mathematics for economic analysis Knut Sydsaeter ; Peter Hammond ; Atle Seierstad ; Arne Strøm Economic analysis Second edition Harlow ; Munich [u.a.] Pearson 2008 xi, 616 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Economía matemática lemb Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Sydsæter, Knut 1937-2012 Sonstige (DE-588)129255114 oth Hammond, Peter J. 1945- Sonstige (DE-588)129255122 oth Seierstad, Atle 1939- Sonstige (DE-588)170327558 oth Strøm, Arne 1941- Sonstige (DE-588)120816253 oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016725222&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016725222&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Further mathematics for economic analysis Economía matemática lemb Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4123623-3 |
| title | Further mathematics for economic analysis |
| title_alt | Economic analysis |
| title_auth | Further mathematics for economic analysis |
| title_exact_search | Further mathematics for economic analysis |
| title_exact_search_txtP | Further mathematics for economic analysis |
| title_full | Further mathematics for economic analysis Knut Sydsaeter ; Peter Hammond ; Atle Seierstad ; Arne Strøm |
| title_fullStr | Further mathematics for economic analysis Knut Sydsaeter ; Peter Hammond ; Atle Seierstad ; Arne Strøm |
| title_full_unstemmed | Further mathematics for economic analysis Knut Sydsaeter ; Peter Hammond ; Atle Seierstad ; Arne Strøm |
| title_short | Further mathematics for economic analysis |
| title_sort | further mathematics for economic analysis |
| topic | Economía matemática lemb Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Economía matemática Economics, Mathematical Wirtschaftsmathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016725222&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016725222&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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