Mathematics for physics: a guided tour for graduate students
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 806 S. Ill., graph. Darst. |
| ISBN: | 9780521854030 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematics for physics |b a guided tour for graduate students |c Michael Stone, University of Illinois at Urbana-Champaign ; Paul Goldbart, University of Illinois at Urbana-Champaign |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XIII, 806 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Mathematische Physik | |
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| 650 | 4 | |a Mathematical physics / Problems, exercises, etc | |
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Record in the Search Index
| _version_ | 1805075387766538240 |
|---|---|
| adam_text |
Contents
Preface
page
xi
Acknowledgments
xiii
1
Calculus of variations
1
1.1
What is it good for?
1
1.2
Functionals
1
1.3
Lagrangian mechanics
10
1.4
Variable endpoints
27
1.5 Lagrange
multipliers
32
1.6
Maximum or minimum?
36
1.7
Further exercises and problems
38
2
Function spaces
50
2.1
Motivation
50
2.2
Norms and inner products
51
2.3
Linear operators and distributions
66
2.4
Further exercises and problems
76
3
Linear ordinary differential equations
86
3.1
Existence and uniqueness of solutions
86
3.2
Normalform
93
3.3
Inhomogeneous equations
94
3.4
Singular points
97
3.5
Further exercises and problems
98
4
Linear differential operators
101
4.1
Formal vs. concrete operators
101
4.2
The adjoint operator
104
4.3
Completeness of eigenfonctions
117
4.4
Further exercises and problems
132
5
Green functions
140
5.1
Inhomogeneous linear equations
140
5.2
Constructing Green functions
141
vii
viii Contents
5.3
Applications of
Lagrange's
identity
150
5.4
Eigenfunction expansions
153
5.5
Analytic properties of Green functions
155
5.6
Locality and the Gelfand-Dikii equation
165
5.7
Further exercises and problems
167
6
Partial differential equations
174
6.1
Classification of PDEs
174
6.2
Cauchydata
176
6.3
Wave equation
181
6.4
Heat equation
196
6.5
Potential theory
201
6.6
Further exercises and problems
224
7
The mathematics of real waves
231
7.1
Dispersive waves
231
7.2
Making waves
242
7.3
Nonlinear waves
246
7.4 Solitons 255
7.5
Further exercises and problems
260
8
Special functions
264
8.1
Curvilinear coordinates
264
8.2
Spherical harmonics
270
8.3
Bessel functions
278
8.4
Singular endpoints
298
8.5
Further exercises and problems
305
9
Integral equations
311
9.1
Illustrations
311
9.2
Classification of integral equations
312
9.3
Integral transforms
313
9.4
Separable kernels
321
9.5
Singular integral equations
323
9.6 Wiener-Hopf
equations I
327
9.7
Some functional analysis
332
9.8
Series solutions
338
9.9
Further exercises and problems
342
10
Vectors and tensors
347
10.1
Covariant and
contravariant
vectors
347
10.2
Tensors
350
10.3
Cartesian tensors
362
10.4
Further exercises and problems
372
Contents ix
11 Differential
calculus on manifolds
376
11.1
Vector and covector fields
376
11.2
Differentiating tensors
381
11.3
Exterior calculus
389
11.4
Physical applications
395
11.5
Co variant derivatives
403
11.6
Further exercises and problems
409
12
Integration on manifolds
414
12.1
Basic notions
414
12.2
Integrating p-forms
417
12.3
Stokes'theorem
422
12.4
Applications
424
12.5
Further exercises and problems
440
13
An introduction to differential topology
449
13.1
Homeomorphism and diffeomorphism
449
13.2
Cohomology
450
13.3
Homology
455
13.4 De
Rham's theorem
469
13.5
Poincaré
duality
473
13.6
Characteristic classes
477
13.7
Hodge theory and the Morse index
483
13.8
Further exercises and problems
496
14
Groups and group representations
498
14.1
Basic ideas
498
14.2
Representations
505
14.3
Physics applications
517
14.4
Further exercises and problems
525
15
Lie groups
530
15.1
Matrix groups
530
15.2
Geometry of SU(2)
535
15.3
Lie algebras
555
15.4
Further exercises and problems
572
16
The geometry of fibre bundles
576
16.1
Fibre bundles
576
16.2
Physics examples
577
16.3
Working in the total space
591
17
Complex analysis
606
17.1
Cauchy-Riemann equations
606
x
Contents
17.2
Complex
integration: Cauchy and Stokes
616
17.3
Applications
624
17.4
Applications of Cauchy's theorem
630
17.5
Meromorphic functions and the winding number
644
17.6
Analytic functions and topology
647
17.7
Further exercises and problems
661
18
Applications of complex variables
666
18.1
Contour integration technology 6M»
18.2
The
Schwarz
reflection principle
676
18.3
Partial-fraction and product expansions
687
18.4 Wiener-Hopf
equations II
692
18.5
Further exercises and problems
701
19
Special functions and complex variables
706
19.1
The Gamma function
706
19.2
Linear differential equations
711
19.3
Solving ODEs via contour integrals
718
19.4
Asymptotic expansions
725
19.5
Elliptic functions
735
19.6
Further exercises and problems
741
A Linear algebra review
744
A.I Vector space
744
A.2 Linear maps
746
A.3 Inner-product spaces
749
A.4 Sums and differences of vector spaces
754
A.5 Inhomogeneous linear equations
757
A.6 Determinants
759
A.7 Diagonalization and canonical forms
766
В
Fourier series and integrals
779
B.I Fourier series
779
B.2 Fourier integral transforms
783
B.3 Convolution
786
B.4 The
Poisson
summation formula
792
References
797
Index
799 |
| any_adam_object | 1 |
| author | Stone, Michael Goldbart, Paul M. |
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| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)268793775 (DE-599)BSZ305984829 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| spelling | Stone, Michael Verfasser aut Mathematics for physics a guided tour for graduate students Michael Stone, University of Illinois at Urbana-Champaign ; Paul Goldbart, University of Illinois at Urbana-Champaign 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XIII, 806 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik Mathematical physics Mathematical physics / Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s DE-604 Goldbart, Paul M. Verfasser (DE-588)17374267X aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017394577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stone, Michael Goldbart, Paul M. Mathematics for physics a guided tour for graduate students Mathematische Physik Mathematical physics Mathematical physics / Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 |
| title | Mathematics for physics a guided tour for graduate students |
| title_auth | Mathematics for physics a guided tour for graduate students |
| title_exact_search | Mathematics for physics a guided tour for graduate students |
| title_full | Mathematics for physics a guided tour for graduate students Michael Stone, University of Illinois at Urbana-Champaign ; Paul Goldbart, University of Illinois at Urbana-Champaign |
| title_fullStr | Mathematics for physics a guided tour for graduate students Michael Stone, University of Illinois at Urbana-Champaign ; Paul Goldbart, University of Illinois at Urbana-Champaign |
| title_full_unstemmed | Mathematics for physics a guided tour for graduate students Michael Stone, University of Illinois at Urbana-Champaign ; Paul Goldbart, University of Illinois at Urbana-Champaign |
| title_short | Mathematics for physics |
| title_sort | mathematics for physics a guided tour for graduate students |
| title_sub | a guided tour for graduate students |
| topic | Mathematische Physik Mathematical physics Mathematical physics / Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Mathematical physics Mathematical physics / Problems, exercises, etc |
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