Applied mathematical methods in theoretical physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
WILEY-VCH
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 377 S. graph. Darst. |
| ISBN: | 3527405348 9783527405343 |
Staff View
MARC
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| 100 | 1 | |a Masujima, Michio |d 1949- |e Verfasser |0 (DE-588)121811212 |4 aut | |
| 245 | 1 | 0 | |a Applied mathematical methods in theoretical physics |c Michio Masujima |
| 264 | 1 | |a Weinheim |b WILEY-VCH |c 2005 | |
| 300 | |a XI, 377 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Physique mathématique | |
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Record in the Search Index
| _version_ | 1804133255699496960 |
|---|---|
| adam_text | Contents
Preface
IX
Introduction
1
1
Function Spaces, Linear Operators and Green s Functions
5
1.1
Function Spaces
................................ 5
1.2
Orthonormal
System of Functions
....................... 7
1.3
Linear Operators
................................ 8
1.4
Eigenvalues and Eigenfiinctions
........................ 11
1.5
The
Fredholm
Alternative
........................... 12
1.6
Self-adjoint Operators
............................. 15
1.7
Green s Functions for Differential Equations
................. 16
1.8
Review of Complex Analysis
......................... 21
1.9
Review of Fourier Transform
......................... 28
2
Integral Equations and Green s Functions
33
2.1
Introduction to Integral Equations
....................... 33
2.2
Relationship of Integral Equations with Differential Equations and Green s
Functions
.................................... 39
2.3
Sturm-Liouville System
............................ 44
2.4
Green s Function for Time-Dependent Scattering Problem
.......... 48
2.5
Lippmann-Schwinger Equation
........................ 52
2.6
Problems for Chapter
2............................ 57
3
Integral Equations of Volterra Type
63
3.1
Iterative Solution to
Volteira
Integral Equation of the Second Kind
..... 63
3.2
Solvable cases of Volterra Integral Equation
................. 66
3.3
Problems for Chapter
3............................ 71
4
Integral Equations of the
Fredholm
Type
75
4.1
Iterative Solution to the
Fredholm
Integral Equation of the Second Kind
.. 75
4.2
Resolvent Kernel
................................ 78
4.3
Pincherle-Goursat Kernel
........................... 81
4.4
Fredholm
Theory for a Bounded Kernel
.................... 86
4.5
Solvable Example
............................... 93
Yj Contenu
4.6
Fredholm Integral
Equation
with a Translation Kernel
............ 95
4.7
System of
Fredholm
Integral Equations of the Second Kind
......... 100
4.8
Problems for Chapter
4............................ 101
5
Hilbert-Schmidt Theory of Symmetric Kernel
109
5.1
Real and Symmetric Matrix
.......................... 109
5.2
Real and Symmetric Kernel
..........................
Ill
5.3
Bounds on the Eigenvalues
.......................... 122
5.4
Rayleigh Quotient
............................... 126
5.5
Completeness of Sturm-Liouville Eigenfunctions
.............. 129
5.6
Generalization of Hilbert-Schmidt Theory
.................. 131
5.7
Generalization of Sturm-Liouville System
.................. 138
5.8
Problems for Chapter
5............................ 144
6
Singular Integral Equations of Cauchy Type
149
6.1
Hubert Problem
................................ 149
6.2
Cauchy Integral Equation of the First Kind
.................. 153
6.3
Cauchy Integral Equation of the Second Kind
................ 157
6.4
Carleman
Integral Equation
.......................... 161
6.5
Dispersion Relations
.............................. 166
6.6
Problems for Chapter
6............................ 173
7 Wiener-Hopf
Method and
Wiener-Hopf
Integral Equation
177
7.1
The
Wiener-Hopf
Method for Partial Differential Equations
......... 177
7.2
Homogeneous
Wiener-Hopf
Integral Equation of the Second Kind
..... 191
7.3
General Decomposition Problem
....................... 207
7.4
Inhomogeneous
Wiener-Hopf
Integral Equation of the Second Kind
.... 216
7.5
Toeplitz Matrix and
Wiener-Hopf
Sum Equation
............... 227
7.6 Wiener-Hopf
Integral Equation of the First Kind and Dual Integral Equations
235
7.7
Problems for Chapter
7............................ 239
8
Nonlinear Integral Equations
249
8.1
Nonlinear Integral Equation of
Volteira
type
................. 249
8.2
Nonlinear Integral Equation of
Fredholm
Type
................ 253
8.3
Nonlinear Integral Equation of
Hammerstein
type
.............. 257
8.4
Problems for Chapter
8............................ 259
9
Calculus of Variations: Fundamentals
263
9.1
Historical Background
............................. 263
9.2
Examples
.................................... 267
9.3
Euler
Equation
................................. 267
9.4
Generalization of the Basic Problems
..................... 272
9.5
More Examples
................................ 276
9.6
Differential Equations, Integral Equations, and Extremization of Integrals
. . 278
9.7
The Second Variation
............................. 283
Contents
VII
9.8 Weierstrass-Erdmann Corner Relation.................... 297
9.9 Problems
for Chapter
9............................ 300
10
Calculus of Variations: Applications
303
10.1
Feynman s Action Principle in Quantum Mechanics
............. 303
10.2
Feynman s Variational Principle in Quantum Statistical Mechanics
..... 308
10.3
Schwinger-Dyson Equation in Quantum Field Theory
............ 312
10.4
Schwinger-Dyson Equation in Quantum Statistical Mechanics
....... 329
10.5
Weyľs
Gauge Principle
............................ 339
10.6
Problems for Chapter
10............................ 356
Bibliography
365
Index
373
|
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| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| discipline | Chemie / Pharmazie Physik Mathematik |
| format | Book |
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| id | DE-604.BV019774392 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:05:49Z |
| institution | BVB |
| isbn | 3527405348 9783527405343 |
| language | English |
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| physical | XI, 377 S. graph. Darst. |
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| spelling | Masujima, Michio 1949- Verfasser (DE-588)121811212 aut Applied mathematical methods in theoretical physics Michio Masujima Weinheim WILEY-VCH 2005 XI, 377 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013100482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Masujima, Michio 1949- Applied mathematical methods in theoretical physics Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4123623-3 |
| title | Applied mathematical methods in theoretical physics |
| title_auth | Applied mathematical methods in theoretical physics |
| title_exact_search | Applied mathematical methods in theoretical physics |
| title_full | Applied mathematical methods in theoretical physics Michio Masujima |
| title_fullStr | Applied mathematical methods in theoretical physics Michio Masujima |
| title_full_unstemmed | Applied mathematical methods in theoretical physics Michio Masujima |
| title_short | Applied mathematical methods in theoretical physics |
| title_sort | applied mathematical methods in theoretical physics |
| topic | Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Physique mathématique Mathematische Physik Mathematical physics Lehrbuch |
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