Fourier series and boundary value problems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
McGraw-Hill
1978
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 271 S. graph. Darst. |
| ISBN: | 0070108439 |
Staff View
MARC
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| 245 | 1 | 0 | |a Fourier series and boundary value problems |c Ruel V. Churchill ; James Ward Brown |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b McGraw-Hill |c 1978 | |
| 300 | |a VIII, 271 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Fourier series | |
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Record in the Search Index
| _version_ | 1804119500508889088 |
|---|---|
| adam_text | CONTENTS
PREFACE Vii
1. PARTIAL DIFFERENTIAL EQUATIONS OF PHYSICS 1
Two Related Problems. Linear Boundary Value Problems. The Vibrating
String. Modifications and End Conditions. Other Examples of Wave Equa¬
tions. Conduction of Heat. Discussion of the Heat Equation. Laplace s
Equation. Cylindrical and Spherical Coordinates. Types of Equations and
Conditions.
2. THE METHOD OF SEPARATION OF VARIABLES 23
Linear Combinations. Examples. Series of Solutions. Uniform Conver¬
gence and Example. Separation of Variables. The Fourier Sine Series. A
Plucked String. Ordinary Differential Equations. General Solutions of
Partial Differential Equations. On Other Methods. Historical Development.
3. ORTHOGONAL SETS OF FUNCTIONS 46
The Inner Product of Two Vectors. Orthonormal Sets of Vectors. Piecewise
Continuous Functions. Orthogonality of Functions. Generalized Fourier
Series. Approximation in the Mean. Closed and Complete Sets. Complex-
valued Functions. Other Types of Orthogonality. Sturm-Liouville Problems.
Orthogonality of the Eigenfunctions. Uniqueness of Eigenfunctions. An¬
other Example.
4. FOURIER SERIES 78
The Basic Series. Example. Fourier Cosine and Sine Series. Further Ex¬
amples. One-sided Derivatives. Preliminary Theory. A Fourier Theorem.
Discussion of the Theorem. Other Forms of Fourier Series. The Ortho-
normal Trigonometric Functions.
5. FURTHER PROPERTIES OF FOURIER SERIES 104
Uniform Convergence. Observations. Differentiation of Fourier Series. In¬
tegration of Fourier Series. More General Conditions.
6. BOUNDARY VALUE PROBLEMS 116
Formal and Rigorous Solutions. The Vibrating String Initially Displaced.
Discussion of the Solution. Prescribed Initial Velocity. Nonhomogeneous
Differential Equations. Elastic Bar. Temperatures in a Bar. Other Boundary
Conditions. Dirichlet Problems. Fourier Series in Two Variables. Obser¬
vations and Further Examples.
v
VI CONTENTS
7. FOURIER INTEGRALS AND APPLICATIONS 149
The Fourier Integral Formula. Preliminary Lemmas. A Fourier Integral
Theorem. The Cosine and Sine Integrals. The Exponential Form. Fourier
Transforms. More on Superposition of Solutions. Temperatures in a Semi-
infinite Solid. Temperatures in an Unlimited Medium.
8. BESSEL FUNCTIONS AND APPLICATIONS 174
Bessel s Equation. Bessel Functions Jn. Some Other Bessel Functions.
Recurrence Relations. Bessel s Integral Form of Jn. Consequences of Bessel s
Integral Form. The Zeros of J0(x)- Zeros of Related Functions. Or¬
thogonal Sets of Bessel Functions. The Orthonormal Functions. Fourier-
Bessel Series. Temperatures in a Long Cylinder. Heat Transfer at the
Surface of the Cylinder. Vibration of a Circular Membrane.
9. LEGENDRE POLYNOMIALS AND APPLICATIONS 218
Solutions of Legendre s Equation. Orthogonality of Legendre Polynomials.
Rodrigues Formula and Norms. Laplace s Integral Form of Pn. Further
Order Properties. Legendre Series. Convergence of the Series. Dirichlet
Problems in Spherical Regions. Steady Temperatures in a Hemisphere.
Other Orthogonal Sets.
10. UNIQUENESS OF SOLUTIONS 248
Cauchy Criterion for Uniform Convergence. Abel s Test for Uniform Conver¬
gence. Uniqueness of Solutions of the Heat Equation. Example. Solutions
of Laplace s or Poisson s Equation. An Application. Solutions of a Wave
Equation.
BIBLIOGRAPHY 263
INDEX 267
|
| any_adam_object | 1 |
| author | Churchill, Ruel Vance 1899-1987 Brown, James Ward 1934- |
| author_GND | (DE-588)115367608 (DE-588)136655386 |
| author_facet | Churchill, Ruel Vance 1899-1987 Brown, James Ward 1934- |
| author_role | aut aut |
| author_sort | Churchill, Ruel Vance 1899-1987 |
| author_variant | r v c rv rvc j w b jw jwb |
| building | Verbundindex |
| bvnumber | BV005297764 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
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| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV005297764 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:27:11Z |
| institution | BVB |
| isbn | 0070108439 |
| language | English |
| lccn | 77012779 |
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| physical | VIII, 271 S. graph. Darst. |
| publishDate | 1978 |
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| publisher | McGraw-Hill |
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| spelling | Churchill, Ruel Vance 1899-1987 Verfasser (DE-588)115367608 aut Fourier series and boundary value problems Ruel V. Churchill ; James Ward Brown 3. ed. New York, NY [u.a.] McGraw-Hill 1978 VIII, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fourier-reeksen gtt Randwaardeproblemen gtt Boundary value problems Fourier Analysis Fourier series Functions, Orthogonal Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Fourier-Reihe (DE-588)4155109-6 s Orthogonale Funktionen (DE-588)4475233-7 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s 1\p DE-604 Differentialgleichung (DE-588)4012249-9 s 2\p DE-604 Brown, James Ward 1934- Verfasser (DE-588)136655386 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003308504&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Churchill, Ruel Vance 1899-1987 Brown, James Ward 1934- Fourier series and boundary value problems Fourier-reeksen gtt Randwaardeproblemen gtt Boundary value problems Fourier Analysis Fourier series Functions, Orthogonal Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Fourier-Reihe (DE-588)4155109-6 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4012249-9 (DE-588)4155109-6 (DE-588)4475233-7 (DE-588)4048395-2 |
| title | Fourier series and boundary value problems |
| title_auth | Fourier series and boundary value problems |
| title_exact_search | Fourier series and boundary value problems |
| title_full | Fourier series and boundary value problems Ruel V. Churchill ; James Ward Brown |
| title_fullStr | Fourier series and boundary value problems Ruel V. Churchill ; James Ward Brown |
| title_full_unstemmed | Fourier series and boundary value problems Ruel V. Churchill ; James Ward Brown |
| title_short | Fourier series and boundary value problems |
| title_sort | fourier series and boundary value problems |
| topic | Fourier-reeksen gtt Randwaardeproblemen gtt Boundary value problems Fourier Analysis Fourier series Functions, Orthogonal Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Fourier-Reihe (DE-588)4155109-6 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Fourier-reeksen Randwaardeproblemen Boundary value problems Fourier Analysis Fourier series Functions, Orthogonal Partielle Differentialgleichung Differentialgleichung Fourier-Reihe Orthogonale Funktionen Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003308504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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