Mathematical methods in physics: partial differential equations, Fourier series, and special functions
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, Mass.
Peters
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 841 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9781568813356 |
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MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
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| 010 | |a 2008022076 | ||
| 020 | |a 9781568813356 |c alk. paper |9 978-1-56881-335-6 | ||
| 035 | |a (OCoLC)228632672 | ||
| 035 | |a (DE-599)OBVAC07533911 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 044 | |a xxu |c US | ||
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| 100 | 1 | |a Henner, Victor |e Verfasser |0 (DE-588)140492038 |4 aut | |
| 245 | 1 | 0 | |a Mathematical methods in physics |b partial differential equations, Fourier series, and special functions |c Victor Henner ; Tatyana Belozerova ; Kyle Forinash |
| 264 | 1 | |a Wellesley, Mass. |b Peters |c 2009 | |
| 300 | |a XVIII, 841 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics |v Textbooks | |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Belozerova, Tatyana |e Verfasser |0 (DE-588)144048620 |4 aut | |
| 700 | 1 | |a Forinash, Kyle |e Verfasser |0 (DE-588)143920421 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018665337&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018665337 | ||
Record in the Search Index
| _version_ | 1804140754804670464 |
|---|---|
| adam_text | Contents
Introduction
xi
1
Fourier
Series
1
1.1
Periodic
Processes
and
Periodic
Functions
........ 1
1.2
Fourier Formulas
..................... 3
1.3
Orthogonal Systems of Functions
............. 7
1.4
Convergence of Fourier Series
.............. 9
1.5
Fourier Series for Nonperiodic Functions
........ 16
1.6
Fourier Expansions on Intervals of Arbitrary Length
. . . 16
1.7
Fourier Series in Cosine or Sine Functions
........ 18
1.8
The Complex Form of the Fourier Series
......... 30
1.9
Complex Generalized Fourier Series
........... 33
1.10
Fourier Series for Functions of Several Variables
.... 35
1.11
Uniform Convergence of Fourier Series
......... 36
1.12
The Gibbs Phenomenon
.................. 41
1.13
Completeness of a System of Trigonometric Functions
. 42
1.14
General Systems of Functions: Parseval s Equality and
Completeness
....................... 44
1.15
Approximation of Functions in the Mean
......... 45
1.16
Fourier Series of Functions Given at Discrete Points
. . . 49
1.17
Solution of Differential Equations by Using Fourier Series
51
1.18
Fourier Transforms
.................... 55
1.19
The Fourier Integral
.................... 60
Problems
........................... . 68
vii
vin
_______________________________________________________________________
Contents
2
Sturm-Liouville
Theory
79
2.1
The Sturm-Liouville Problem
............... 79
2.2
Mixed Boundary Conditions...............
90
2.3
Examples of Sturm-Liouville Problems
......... 95
Problems
............................ 107
3
One-Dimensional Hyperbolic Equations
113
3.1
Derivation of the Basic Equations
............ 113
3.2
Boundary and Initial Conditions
............. 116
3.3
Other Boundary Value Problems: Longitudinal Vibra¬
tions of a Thin Rod
.................... 121
3.4
Torsionai
Oscillations of an Elastic Cylinder
....... 124
3.5
Acoustic Waves
...................... 127
3.6
Waves in a Shallow Channel
............... 132
3.7
Electrical Oscillations in a Circuit
............ 135
3.8
Traveling Waves: D Alembert Method
.......... 138
3.9
Semi-infinite String Oscillations and the Use of Sym¬
metry Properties
...................... 157
3.10
Finite Intervals: The Fourier Method for One-Dimensional
Wave Equations
...................... 180
3.11
Generalized Fourier Solutions
.............. 211
3.12
Energy of the String
.................... 213
Problems
............................ 222
4
Two-Dimensional Hyperbolic Equations
241
4.1
Derivation of the Equations of Motion
.......... 242
4.2
Oscillations of a Rectangular Membrane
......... 247
4.3
The Fourier Method Applied to Small Transverse Oscil¬
lations of a Circular Membrane
.............. 277
Problems
............................ 317
5
One-Dimensional Parabolic Equations
327
5.1
Physical Problems Described by Parabolic Equations:
Boundary Value Problems
................ 327
5.2
The Principle of the Maximum, Correctness, and the
Generalized Solution
................... 340
Contents
¡χ
5.3
The Fourier Method of Separation of Variables for the
Heat Conduction Equation
................ 344
5.4
Heat Conduction in an Infinite Bar
............ 383
5.5
Heat Equation for a Semi-infinite Bar
.......... 394
Problems
............................ 409
6
Parabolic Equations for Higher-Dimensional Problems
419
6.1
Heat Conduction in More than One Dimension
..... 419
6.2
Heat Conduction within a Finite Rectangular Domain
. . 430
6.3
Heat Conduction within a Circular Domain
....... 460
Problems
............................ 482
7
Elliptic Equations
489
7.1
Elliptic Partial Differential Equations and Related Phys¬
ical Problems
....................... 489
7.2
The Dirichlet Boundary Value Problem for Laplace s
Equation in a Rectangular Domain
............ 508
7.3
Laplace s and Poisson s Equations for Two-Dimensional
Domains with Circular Symmetry
............ 527
7.4
Laplace s Equation in Cylindrical Coordinates
...... 561
Problems
............................ 590
8
Bessel Functions
613
8.1
Boundary Value Problems Leading to Bessel Functions
. 613
8.2
Bessel Functions of the First Kind
............ 620
8.3
Properties of Bessel Functions of the First Kind: Jn{x)
. 622
8.4
Bessel Functions of the Second Kind
........... 627
8.5
Bessel Functions of the Third Kind
............ 629
8.6
Modified Bessel Functions
........._....... 630
8.7
The Effect of Boundaries on Bessel Functions
...... 632
8.8
Orthogonality and Normalization of Bessel Functions
. . 634
8.9
The Fourier-Bessel Series
................. 638
8.10
Further Examples of Fourier-Bessel Series Expansions
. 655
8.11
Spherical Bessel Functions
................ 663
8.12
The Gamma Function
................... 667
Problems
............................ 670
Contents
9 Legendre
Functions
ó77
9.1
Boundary Value Problems Leading to Legendre Polyno¬
mials
............................ 677
9.2
Generating Function for Legendre Polynomials
..... 686
9.3
Recurrence Relations
................... 687
9.4
Orthogonality of Legendre Polynomials
......... 689
9.5
The Multipole Expansion in Electrostatics
........ 692
9.6
Associated Legendre Functions P™ (x)
.......... 696
9.7
Orthogonality and the Norm of Associated Legendre Func¬
tions
............................ 701
9.8
Fourier-Legendre Series in Legendre Polynomials
.... 702
9.9
Fourier-Legendre Series in Associated Legendre Func¬
tions
............................ 709
9.10
Laplace s Equation in Spherical Coordinates and Spher¬
ical Functions
....................... 713
Problems
............................ 731
A Eigenvalues and Eigenfunctions of the Sturm-Liouville Prob¬
lem
743
В
Auxiliary Functions for Different Types of Boundary Con¬
ditions
747
С
The Sturm-Liouville Problem and the Laplace Equation
751
D
Vector Calculus
757
E
How to Use the Software Associated with this Book
769
E.I Program Overview
.................... 770
E.2 Examples Using the Program TrigSeries
......... 773
E.3 Examples Using the Program Waves
........... 781
E.4 Examples Using the Program Heat
............ 797
E.5 Examples Using the Program Laplace
.......... 811
E.6 Examples Using the Program FourierSeries
....... 822
Bibliography
331
Index
333
|
| any_adam_object | 1 |
| author | Henner, Victor Belozerova, Tatyana Forinash, Kyle |
| author_GND | (DE-588)140492038 (DE-588)144048620 (DE-588)143920421 |
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| dewey-ones | 530 - Physics |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV035806320 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:00Z |
| institution | BVB |
| isbn | 9781568813356 |
| language | English |
| lccn | 2008022076 |
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| owner | DE-703 DE-92 |
| owner_facet | DE-703 DE-92 |
| physical | XVIII, 841 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Peters |
| record_format | marc |
| spelling | Henner, Victor Verfasser (DE-588)140492038 aut Mathematical methods in physics partial differential equations, Fourier series, and special functions Victor Henner ; Tatyana Belozerova ; Kyle Forinash Wellesley, Mass. Peters 2009 XVIII, 841 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematische Physik Mathematical physics Textbooks Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s DE-604 Belozerova, Tatyana Verfasser (DE-588)144048620 aut Forinash, Kyle Verfasser (DE-588)143920421 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018665337&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Henner, Victor Belozerova, Tatyana Forinash, Kyle Mathematical methods in physics partial differential equations, Fourier series, and special functions Mathematische Physik Mathematical physics Textbooks Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 |
| title | Mathematical methods in physics partial differential equations, Fourier series, and special functions |
| title_auth | Mathematical methods in physics partial differential equations, Fourier series, and special functions |
| title_exact_search | Mathematical methods in physics partial differential equations, Fourier series, and special functions |
| title_full | Mathematical methods in physics partial differential equations, Fourier series, and special functions Victor Henner ; Tatyana Belozerova ; Kyle Forinash |
| title_fullStr | Mathematical methods in physics partial differential equations, Fourier series, and special functions Victor Henner ; Tatyana Belozerova ; Kyle Forinash |
| title_full_unstemmed | Mathematical methods in physics partial differential equations, Fourier series, and special functions Victor Henner ; Tatyana Belozerova ; Kyle Forinash |
| title_short | Mathematical methods in physics |
| title_sort | mathematical methods in physics partial differential equations fourier series and special functions |
| title_sub | partial differential equations, Fourier series, and special functions |
| topic | Mathematische Physik Mathematical physics Textbooks Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Mathematical physics Textbooks |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018665337&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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