Fourier series and boundary value problems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Tokyo [u.a.]
McGraw-Hill Kogakusha
1978
|
| Edition: | 3. ed., int. student ed. |
| Series: | International student edition
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 271 S. graph. Darst. |
| ISBN: | 007085100X 0070108439 |
Staff View
MARC
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| 100 | 1 | |a Churchill, Ruel Vance |d 1899-1987 |e Verfasser |0 (DE-588)115367608 |4 aut | |
| 245 | 1 | 0 | |a Fourier series and boundary value problems |c Ruel V. Churchill ; James W. Brown |
| 250 | |a 3. ed., int. student ed. | ||
| 264 | 1 | |a Tokyo [u.a.] |b McGraw-Hill Kogakusha |c 1978 | |
| 300 | |a VIII, 271 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804117968508944384 |
|---|---|
| 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 | BV003618082 |
| classification_rvk | SK 420 SK 450 SK 470 SK 540 |
| ctrlnum | (OCoLC)630945990 (DE-599)BVBBV003618082 |
| discipline | Mathematik |
| edition | 3. ed., int. student ed. |
| format | Book |
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| id | DE-604.BV003618082 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:02:50Z |
| institution | BVB |
| isbn | 007085100X 0070108439 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002304442 |
| oclc_num | 630945990 |
| open_access_boolean | |
| owner | DE-384 DE-83 DE-19 DE-BY-UBM DE-188 |
| owner_facet | DE-384 DE-83 DE-19 DE-BY-UBM DE-188 |
| physical | VIII, 271 S. graph. Darst. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | McGraw-Hill Kogakusha |
| record_format | marc |
| series2 | International student edition |
| spelling | Churchill, Ruel Vance 1899-1987 Verfasser (DE-588)115367608 aut Fourier series and boundary value problems Ruel V. Churchill ; James W. Brown 3. ed., int. student ed. Tokyo [u.a.] McGraw-Hill Kogakusha 1978 VIII, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International student edition Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s Fourier-Reihe (DE-588)4155109-6 s DE-604 Orthogonale Funktionen (DE-588)4475233-7 s Differentialgleichung (DE-588)4012249-9 s 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=002304442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Churchill, Ruel Vance 1899-1987 Brown, James Ward 1934- Fourier series and boundary value problems Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd Fourier-Reihe (DE-588)4155109-6 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4012249-9 (DE-588)4475233-7 (DE-588)4155109-6 (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 W. Brown |
| title_fullStr | Fourier series and boundary value problems Ruel V. Churchill ; James W. Brown |
| title_full_unstemmed | Fourier series and boundary value problems Ruel V. Churchill ; James W. Brown |
| title_short | Fourier series and boundary value problems |
| title_sort | fourier series and boundary value problems |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd Fourier-Reihe (DE-588)4155109-6 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Partielle Differentialgleichung Differentialgleichung Orthogonale Funktionen Fourier-Reihe Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002304442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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