Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1974
|
| Schriftenreihe: | Schaum's outline series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Schaum's outline of theory and problems of Fourier analysis |b with applications to boundary value problems |c by Murray R. Spiegel |
| 246 | 1 | 3 | |a Theory and problems of Fourier analysis |
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1974 | |
| 300 | |a 191 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Schaum's outline series | |
| 650 | 4 | |a Fourier, Analyse de | |
| 650 | 7 | |a Fourier-analyse |2 gtt | |
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 7 | |a Randwaardeproblemen |2 gtt | |
| 650 | 7 | |a Series (Matematica) |2 larpcal | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Fourier analysis | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001278232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-001278232 | |
Datensatz im Suchindex
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| _version_ | 1822735052574818304 |
| adam_text | CONTENTS
Page
Chapter / BOUNDARY VALUE PROBLEMS 1
Mathematical Formulation and Solution of Physical Problems. Definitions Per
taining to Partial Differential Equations. Linear Partial Differential Equa
tions. Some Important Partial Differential Equations. The Laplacian in Differ
ent Coordinate Systems. Methods of Solving Boundary Value Problems.
Chapter 2 FOURIER SERIES AND APPLICATIONS 20
The Need for Fourier Series. Periodic Functions. Piecewise Continuous Func
tions. Definition of Fourier Series. Dirichlet Conditions. Odd and Even
Functions. Half Range Fourier Sine or Cosine Series. Parseval s Identity.
Uniform Convergence. Integration and Differentiation of Fourier Series. Com
plex Notation for Fourier Series. Double Fourier Series. Applications of
Fourier Series.
Chapter 3 ORTHOGONAL FUNCTIONS 52
Definitions Involving Orthogonal Functions. Orthonormal Sets. Orthogonality
with Respect to a Weight Function. Expansion of Functions in Orthonormal
Series. Approximations in the Least Squares Sense. Parseval s Identity for
Orthonormal Series. Completeness. Sturm Liouville Systems. Eigenvalues and
Eigenfunctions. The Gram Schmidt Orthonormalization Process. Applications
to Boundary Value Problems.
Chapter 4 GAMMA, BETA AND OTHER SPECIAL FUNCTIONS 67
Special Functions. The Gamma Function. Table of Values and Graph of the
Gamma Function. Asymptotic Formula for V(n). Miscellaneous Results Involv¬
ing the Gamma Function. The Beta Function. Other Special Functions.
Asymptotic Series or Expansions.
Chapter 5 FOURIER INTEGRALS AND APPLICATIONS 80
The Need for Fourier Integrals. The Fourier Integral. Equivalent Forms of
Fourier s Integral Theorem. Fourier Transforms. Fourier Sine and Cosine
Transforms. Parseval s Identities for Fourier Integrals. The Convolution
Theorem for Fourier Transforms. Applications of Fourier Integrals and Trans¬
forms.
Chapter 6 BESSEL FUNCTIONS AND APPLICATIONS 97
Bessel s Differential Equation. The Method of Frobenius. Bessel Functions of
the First Kind. Bessel Functions of the Second Kind. Generating Function for
Jn(x). Recurrence Formulas. Functions Related to Bessel Functions. Equa¬
tions Transformable into Bessel s Equation. Asymptotic Formulas for Bessel
Functions. Zeros of Bessel Functions. Orthogonality of Bessel Functions of the
First Kind. Series of Bessel Functions of the First Kind. Orthogonality and
Series of Bessel Functions of the Second Kind. Solutions to Boundary Value
Problems Using Bessel Functions.
CONTENTS
Page
Chapter 7 LEGENDRE FUNCTIONS AND APPLICATIONS 130
Legendre s Differential Equation. Legendre Polynomials. Generating Function
for Legendre Polynomials. Recurrence Formulas. Legendre Functions of the
Second Kind. Orthogonality of Legendre Polynomials. Series of Legendre
Polynomials. Associated Legendre Functions. Orthogonality of Associated
Legendre Functions. Solutions to Boundary Value Problems Using Legendre
Functions.
Chapter 8 HERMITE, LAGUERRE
AND OTHER ORTHOGONAL POLYNOMIALS 154
Hermite s Differential Equation. Hermite Polynomials. Generating Function
for Hermite Polynomials. Recurrence Formulas for Hermite Polynomials.
Orthogonality of Hermite Polynomials. Series of Hermite Polynomials. La
guerre s Differential Equation. Laguerre Polynomials. Some Important Prop¬
erties of Laguerre Polynomials. Miscellaneous Orthogonal Polynomials and
Their Properties.
Appendix A Uniqueness of Solutions 167
Appendix B Special Fourier Series 169
Appendix j Special Fourier Transforms 173
Appendix D Tables of Values for J0(x) and Ji(x) 176
Appendix Cj Zeros of Bessel Functions 177
ANSWERS TO SUPPLEMENTARY PROBLEMS 179
INDEX 187
|
| any_adam_object | 1 |
| author | Spiegel, Murray R. 1923-1991 |
| author_GND | (DE-588)109314840 |
| author_facet | Spiegel, Murray R. 1923-1991 |
| author_role | aut |
| author_sort | Spiegel, Murray R. 1923-1991 |
| author_variant | m r s mr mrs |
| building | Verbundindex |
| bvnumber | BV001960275 |
| callnumber-first | Q - Science |
| callnumber-label | QA403 |
| callnumber-raw | QA403.5 |
| callnumber-search | QA403.5 |
| callnumber-sort | QA 3403.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)612072949 (DE-599)BVBBV001960275 |
| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV001960275 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T10:26:37Z |
| institution | BVB |
| isbn | 0070602190 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001278232 |
| oclc_num | 612072949 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-384 DE-19 DE-BY-UBM DE-20 DE-1051 DE-188 DE-898 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-384 DE-19 DE-BY-UBM DE-20 DE-1051 DE-188 DE-898 DE-BY-UBR |
| physical | 191 S. graph. Darst. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | Schaum's outline series |
| spellingShingle | Spiegel, Murray R. 1923-1991 Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems Fourier, Analyse de Fourier-analyse gtt Problèmes aux limites Randwaardeproblemen gtt Series (Matematica) larpcal Boundary value problems Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4143389-0 |
| title | Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems |
| title_alt | Theory and problems of Fourier analysis |
| title_auth | Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems |
| title_exact_search | Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems |
| title_full | Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems by Murray R. Spiegel |
| title_fullStr | Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems by Murray R. Spiegel |
| title_full_unstemmed | Schaum's outline of theory and problems of Fourier analysis with applications to boundary value problems by Murray R. Spiegel |
| title_short | Schaum's outline of theory and problems of Fourier analysis |
| title_sort | schaum s outline of theory and problems of fourier analysis with applications to boundary value problems |
| title_sub | with applications to boundary value problems |
| topic | Fourier, Analyse de Fourier-analyse gtt Problèmes aux limites Randwaardeproblemen gtt Series (Matematica) larpcal Boundary value problems Fourier analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fourier, Analyse de Fourier-analyse Problèmes aux limites Randwaardeproblemen Series (Matematica) Boundary value problems Fourier analysis Harmonische Analyse Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001278232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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