Mathematical physics: applied mathematics for scientists and engineers
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2007
|
| Edition: | 2. ed., 1. repr. |
| Series: | Physics textbook
|
| Subjects: | |
| Online Access: | Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 671) and index |
| Physical Description: | XI, 678 S. graph. Darst. |
| ISBN: | 3527406727 9783527406722 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematical physics |b applied mathematics for scientists and engineers |c Bruce R. Kusse and Erik A. Westwig |
| 250 | |a 2. ed., 1. repr. | ||
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2007 | |
| 300 | |a XI, 678 S. |b graph. Darst. | ||
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| 650 | 4 | |a Mathematische Physik | |
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Record in the Search Index
| _version_ | 1804137294621310976 |
|---|---|
| adam_text | CONTENTS
1
A
Review
of Vector and Matrix Algebra Using
Subscript/Summation Conventions
1
1.1
Notation,
1
1.2
Vector Operations,
5
2
Differential and Integral Operations on Vector and Scalar Fields
18
2.1
Plotting Scalar and Vector Fields,
18
2.2
Integral Operators,
20
2.3
Differential Operations,
23
2.4
Integral Definitions of the Differential Operators,
34
2.5
The Theorems,
35
3
Curvilinear Coordinate Systems
44
3.1
The Position Vector,
44
3.2
The Cylindrical System,
45
3.3
The Spherical System,
48
3.4
General Curvilinear Systems,
49
3.5
The Gradient, Divergence, and Curl in Cylindrical and Spherical
Systems,
58
viü
CONTENTS
4
Introduction to Tensors
67
4.1
The Conductivity Tensor and Ohm s Law,
67
4.2
General Tensor Notation and Terminology,
71
4.3
Transformations Between Coordinate Systems,
71
4.4
Tensor Diagonalization,
78
4.5
Tensor Transformations in Curvilinear Coordinate Systems,
84
4.6
Pseudo-Objects,
86
5
The Dirac
ô-Function
100
5.1
Examples of Singular Functions in Physics,
100
5.2
Two Definitions of
б(ѓ),
103
5.3
Ő-Functions
with Complicated Arguments,
108
5.4
Integrals and Derivatives of
δ(ί),
Ш
5.5
Singular Density Functions,
114
5.6
The Infinitesimal Electric
Dipole,
121
5.7
Riemann Integration and the Dirac
б
-Function,
125
6
Introduction to Complex Variables
135
6.1
A Complex Number Refresher,
135
6.2
Functions of a Complex Variable,
138
6.3
Derivatives of Complex Functions,
140
6.4
The Cauchy Integral Theorem,
144
6.5
Contour Deformation,
146
6.6
The Cauchy Integral Formula,
147
6.7
Taylor and Laurent Series,
150
6.8
The Complex Taylor Series,
153
6.9
The Complex Laurent Series,
159
6.10
The Residue Theorem,
171
6.11
Definite Integrals and Closure,
175
6.12
Conformai
Mapping,
189
CONTENTS
ІХ
7
Fourier
Series
219
7.1
The Sine-Cosine
Series,
219
7.2
The Exponential Form of Fourier Series,
227
7.3
Convergence of Fourier Series,
231
7.4
The Discrete Fourier Series,
234
8
Fourier Transforms
250
8.1
Fourier Series as To
->
oo,
250
8.2
Orthogonality,
253
8.3
Existence of the Fourier Transform,
254
8.4
The Fourier Transform Circuit,
256
8.5
Properties of the Fourier Transform,
258
8.6
Fourier Transforms
—
Examples,
267
8.7
The Sampling Theorem,
290
9
Laplace Transforms
303
9.1
Limits of the Fourier Transform,
303
9.2
The Modified Fourier Transform,
306
9.3
The Laplace Transform,
313
9.4
Laplace Transform Examples,
314
9.5
Properties of the Laplace Transform,
318
9.6
The Laplace Transform Circuit,
327
9.7
Double-Sided or Bilateral Laplace Transforms,
331
10
Differential Equations
339
10.1
Terminology,
339
10.2
Solutions for First-Order Equations,
342
10.3
Techniques for Second-Order Equations,
347
10.4
The Method of Frobenius,
354
10.5
The Method of Quadrature,
358
10.6
Fourier and Laplace Transform Solutions,
366
10.7
Green s Function Solutions,
376
x
CONTENTS
11 Solutions
to Laplace s Equation
424
11.1
Cartesian Solutions,
424
11.2
Expansions With Eigenfunctions,
433
11.3
Cylindrical Solutions,
441
11.4
Spherical Solutions,
458
12
Integral Equations
491
12.1
Classification of Linear Integral Equations,
492
12.2
The Connection Between Differential and
Integral Equations,
493
12.3
Methods of Solution,
498
13
Advanced Topics in Complex Analysis
509
13.1
Multivalued Functions,
509
13.2
The Method of Steepest Descent,
542
14
Tensors in Non-Orthogonal Coordinate Systems
562
14.1
A Brief Review of Tensor Transformations,
562
14.2
Non-Orthonormal Coordinate Systems,
564
15
Introduction to Group Theory
597
15.1
The Definition of a Group,
597
15.2
Finite Groups and Their Representations,
598
15.3
Subgroups, Cosets, Class, and Character,
607
15.4
Irreducible Matrix Representations,
612
15.5
Continuous Groups,
630
Appendix A The Levi-Civita Identity
639
Appendix
В
The Curvilinear Curl
641
Appendix
С
The Double Integral Identity
645
Appendix
D
Green s Function Solutions
647
Appendix
E Pseudovectors
and the Mirror Test
653
CONTENTS Xl
Appendix
F
Christoffel Symbols and Covariant Derivatives 655
Appendix
G
Calculus of
Variations
661
Errata List
665
Bibliography
671
Index
673
|
| adam_txt |
CONTENTS
1
A
Review
of Vector and Matrix Algebra Using
Subscript/Summation Conventions
1
1.1
Notation,
1
1.2
Vector Operations,
5
2
Differential and Integral Operations on Vector and Scalar Fields
18
2.1
Plotting Scalar and Vector Fields,
18
2.2
Integral Operators,
20
2.3
Differential Operations,
23
2.4
Integral Definitions of the Differential Operators,
34
2.5
The Theorems,
35
3
Curvilinear Coordinate Systems
44
3.1
The Position Vector,
44
3.2
The Cylindrical System,
45
3.3
The Spherical System,
48
3.4
General Curvilinear Systems,
49
3.5
The Gradient, Divergence, and Curl in Cylindrical and Spherical
Systems,
58
viü
CONTENTS
4
Introduction to Tensors
67
4.1
The Conductivity Tensor and Ohm's Law,
67
4.2
General Tensor Notation and Terminology,
71
4.3
Transformations Between Coordinate Systems,
71
4.4
Tensor Diagonalization,
78
4.5
Tensor Transformations in Curvilinear Coordinate Systems,
84
4.6
Pseudo-Objects,
86
5
The Dirac
ô-Function
100
5.1
Examples of Singular Functions in Physics,
100
5.2
Two Definitions of
б(ѓ),
103
5.3
Ő-Functions
with Complicated Arguments,
108
5.4
Integrals and Derivatives of
δ(ί),
Ш
5.5
Singular Density Functions,
114
5.6
The Infinitesimal Electric
Dipole,
121
5.7
Riemann Integration and the Dirac
б
-Function,
125
6
Introduction to Complex Variables
135
6.1
A Complex Number Refresher,
135
6.2
Functions of a Complex Variable,
138
6.3
Derivatives of Complex Functions,
140
6.4
The Cauchy Integral Theorem,
144
6.5
Contour Deformation,
146
6.6
The Cauchy Integral Formula,
147
6.7
Taylor and Laurent Series,
150
6.8
The Complex Taylor Series,
153
6.9
The Complex Laurent Series,
159
6.10
The Residue Theorem,
171
6.11
Definite Integrals and Closure,
175
6.12
Conformai
Mapping,
189
CONTENTS
ІХ
7
Fourier
Series
219
7.1
The Sine-Cosine
Series,
219
7.2
The Exponential Form of Fourier Series,
227
7.3
Convergence of Fourier Series,
231
7.4
The Discrete Fourier Series,
234
8
Fourier Transforms
250
8.1
Fourier Series as To
->
oo,
250
8.2
Orthogonality,
253
8.3
Existence of the Fourier Transform,
254
8.4
The Fourier Transform Circuit,
256
8.5
Properties of the Fourier Transform,
258
8.6
Fourier Transforms
—
Examples,
267
8.7
The Sampling Theorem,
290
9
Laplace Transforms
303
9.1
Limits of the Fourier Transform,
303
9.2
The Modified Fourier Transform,
306
9.3
The Laplace Transform,
313
9.4
Laplace Transform Examples,
314
9.5
Properties of the Laplace Transform,
318
9.6
The Laplace Transform Circuit,
327
9.7
Double-Sided or Bilateral Laplace Transforms,
331
10
Differential Equations
339
10.1
Terminology,
339
10.2
Solutions for First-Order Equations,
342
10.3
Techniques for Second-Order Equations,
347
10.4
The Method of Frobenius,
354
10.5
The Method of Quadrature,
358
10.6
Fourier and Laplace Transform Solutions,
366
10.7
Green's Function Solutions,
376
x
CONTENTS
11 Solutions
to Laplace's Equation
424
11.1
Cartesian Solutions,
424
11.2
Expansions With Eigenfunctions,
433
11.3
Cylindrical Solutions,
441
11.4
Spherical Solutions,
458
12
Integral Equations
491
12.1
Classification of Linear Integral Equations,
492
12.2
The Connection Between Differential and
Integral Equations,
493
12.3
Methods of Solution,
498
13
Advanced Topics in Complex Analysis
509
13.1
Multivalued Functions,
509
13.2
The Method of Steepest Descent,
542
14
Tensors in Non-Orthogonal Coordinate Systems
562
14.1
A Brief Review of Tensor Transformations,
562
14.2
Non-Orthonormal Coordinate Systems,
564
15
Introduction to Group Theory
597
15.1
The Definition of a Group,
597
15.2
Finite Groups and Their Representations,
598
15.3
Subgroups, Cosets, Class, and Character,
607
15.4
Irreducible Matrix Representations,
612
15.5
Continuous Groups,
630
Appendix A The Levi-Civita Identity
639
Appendix
В
The Curvilinear Curl
641
Appendix
С
The Double Integral Identity
645
Appendix
D
Green's Function Solutions
647
Appendix
E Pseudovectors
and the Mirror Test
653
CONTENTS Xl
Appendix
F
Christoffel Symbols and Covariant Derivatives 655
Appendix
G
Calculus of
Variations
661
Errata List
665
Bibliography
671
Index
673 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:27:44Z |
| indexdate | 2024-07-09T21:10:01Z |
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| isbn | 3527406727 9783527406722 |
| language | English |
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| spelling | Kusse, Bruce R. 1938- Verfasser (DE-588)130871788 aut Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse and Erik A. Westwig 2. ed., 1. repr. Weinheim Wiley-VCH 2007 XI, 678 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Includes bibliographical references (p. 671) and index Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Westwig, Erik A. Verfasser (DE-588)130871796 aut http://www.loc.gov/catdir/toc/fy0610/2006277389.html Table of contents only Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016261701&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kusse, Bruce R. 1938- Westwig, Erik A. Mathematical physics applied mathematics for scientists and engineers Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4123623-3 |
| title | Mathematical physics applied mathematics for scientists and engineers |
| title_auth | Mathematical physics applied mathematics for scientists and engineers |
| title_exact_search | Mathematical physics applied mathematics for scientists and engineers |
| title_exact_search_txtP | Mathematical physics applied mathematics for scientists and engineers |
| title_full | Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse and Erik A. Westwig |
| title_fullStr | Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse and Erik A. Westwig |
| title_full_unstemmed | Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse and Erik A. Westwig |
| title_short | Mathematical physics |
| title_sort | mathematical physics applied mathematics for scientists and engineers |
| title_sub | applied mathematics for scientists and engineers |
| topic | Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Lehrbuch |
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