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Analytic methods for partial differential equations

Author: Gwynne Evans; Jonathan M Blackledge; Peter D Yardley
Publisher: London ; New York ; Heidelberg : Springer, ©2001.
Series: Springer undergraduate mathematics series.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Gwynne Evans; Jonathan M Blackledge; Peter D Yardley
ISBN: 3540761241 9783540761242
OCLC Number: 491119298
Description: 1 v. (xii-299 p.) : illustrations ; 24 cm.
Contents: 1. Mathematical Preliminaries.- 1.1 Introduction.- 1.2 Characteristics and Classification.- 1.3 Orthogonal Functions.- 1.4 Sturm-Liouville Boundary Value Problems.- 1.5 Legendre Polynomials.- 1.6 Bessel Functions.- 1.7 Results from Complex Analysis.- 1.8 Generalised Functions and the Delta Function.- 1.8.1 Definition and Properties of a Generalised Function.- 1.8.2 Differentiation Across Discontinuities.- 1.8.3 The Fourier Transform of Generalised Functions.- 1.8.4 Convolution of Generalised Functions.- 1.8.5 The Discrete Representation of the Delta Function.- 2. Separation of the Variables.- 2.1 Introduction.- 2.2 The Wave Equation.- 2.3 The Heat Equation.- 2.4 Laplace's Equation.- 2.5 Homogeneous and Non-homogeneous Boundary Conditions.- 2.6 Separation of variables in other coordinate systems.- 3. First-order Equations and Hyperbolic Second-order Equations.- 3.1 Introduction.- 3.2 First-order equations.- 3.3 Introduction to d'Alembert's Method.- 3.4 d'Alembert's General Solution.- 3.5 Characteristics.- 3.6 Semi-infinite Strings.- 4. Integral Transforms.- 4.1 Introduction.- 4.2 Fourier Integrals.- 4.3 Application to the Heat Equation.- 4.4 Fourier Sine and Cosine Transforms.- 4.5 General Fourier Transforms.- 4.6 Laplace transform.- 4.7 Inverting Laplace Transforms.- 4.8 Standard Transforms.- 4.9 Use of Laplace Transforms to Solve Partial Differential Equations.- 5. Green's Functions.- 5.1 Introduction.- 5.2 Green's Functions for the Time-independent Wave Equation.- 5.3 Green's Function Solution to the Three-dimensional Inhomogeneous Wave Equation.- 5.4 Green's Function Solutions to the Inhomogeneous Helmholtz and Schroedinger Equations: An Introduction to Scattering Theory.- 5.5 Green's Function Solution to Maxwell's Equations and Time-dependent Problems.- 5.6 Green's Functions and Optics: Kirchhoff Diffraction Theory.- 5.7 Approximation Methods and the Born Series.- 5.8 Green's Function Solution to the Diffusion Equation.- 5.9 Green's Function Solution to the Laplace and Poisson Equations.- 5.10 Discussion.- A. Solutions of Exercises.
Series Title: Springer undergraduate mathematics series.
Responsibility: G. Evans, J. Blackledge, and P. Yardley.

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Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/491119298<\/a>> # Analytic methods for partial differential equations<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Book<\/a>, schema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"491119298<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/enk<\/a>> ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> ; # New York<\/span>\n\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/dbpedia.org\/resource\/London<\/a>> ; # London<\/span>\n\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Place\/heidelberg<\/a>> ; # Heidelberg<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/transformation_integrale<\/a>> ; # transformation int\u00E9grale<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/equations_aux_derivees_partielles_solutions_numeriques<\/a>> ; # \u00E9quations aux d\u00E9riv\u00E9es partielles--solutions num\u00E9riques<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.loc.gov\/authorities\/subjects\/sh85037915<\/a>> ; # Differential equations, Partial--Numerical solutions<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/515.35\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/analytische_losung<\/a>> ; # Analytische L\u00F6sung<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/equation_1er_ordre<\/a>> ; # \u00E9quation 1er ordre<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/partielle_differentialgleichung<\/a>> ; # Partielle Differentialgleichung<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/fonction_green<\/a>> ; # fonction Green<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/equation_differentielle<\/a>> ; # \u00E9quation diff\u00E9rentielle<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.worldcat.org\/fast\/893488<\/a>> ; # Differential equations, Partial--Numerical solutions<\/span>\n\u00A0\u00A0\u00A0\nschema:bookFormat<\/a> bgn:PrintBook<\/a> ;\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/viaf.org\/viaf\/116819962<\/a>> ; # Peter D. Yardley<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/viaf.org\/viaf\/73933797<\/a>> ; # Jonathan M. Blackledge<\/span>\n\u00A0\u00A0\u00A0\nschema:copyrightYear<\/a> \"2001<\/span>\" ;\u00A0\u00A0\u00A0\nschema:copyrightYear<\/a> \"1999<\/span>\" ;\u00A0\u00A0\u00A0\nschema:creator<\/a> <http:\/\/viaf.org\/viaf\/113233114<\/a>> ; # Gwynne Evans<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2001<\/span>\" ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/115580095<\/a>> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Series\/springer_undergraduate_mathematics_series<\/a>> ; # Springer undergraduate mathematics series.<\/span>\n\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/worldcat.org\/issn\/1615-2085<\/a>> ; # Springer undergraduate mathematics series,<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Analytic methods for partial differential equations<\/span>\" ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"491119298<\/span>\" ;\u00A0\u00A0\u00A0\nschema:publication<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/491119298#PublicationEvent\/london_new_york_heidelberg_springer_2001<\/a>> ;\u00A0\u00A0\u00A0\nschema:publisher<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Agent\/springer<\/a>> ; # Springer<\/span>\n\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/bvbr.bib-bvb.de:8991\/F?func=service&doc_library=BVB01&doc_number=014564573&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/bvbr.bib-bvb.de:8991\/F?func=serviceetdoc_library=BVB01etdoc_number=014564573etline_number=0001etfunc_code=DB_RECORDSetservice_type=MEDIA<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9783540761242<\/a>> ;\u00A0\u00A0\u00A0\numbel:isLike<\/a> <http:\/\/bnb.data.bl.uk\/id\/resource\/GB99X1152<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/491119298<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Related Entities<\/h3>\n
<http:\/\/dbpedia.org\/resource\/London<\/a>> # London<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"London<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> # New York<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"New York<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/dewey.info\/class\/515.35\/<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Agent\/springer<\/a>> # Springer<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:Agent<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Springer<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Place\/heidelberg<\/a>> # Heidelberg<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Heidelberg<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Series\/springer_undergraduate_mathematics_series<\/a>> # Springer undergraduate mathematics series.<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:PublicationSeries<\/a> ;\u00A0\u00A0\u00A0\nschema:hasPart<\/a> <http:\/\/www.worldcat.org\/oclc\/491119298<\/a>> ; # Analytic methods for partial differential equations<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Springer undergraduate mathematics series.<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/analytische_losung<\/a>> # Analytische L\u00F6sung<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Analytische L\u00F6sung<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/equation_1er_ordre<\/a>> # \u00E9quation 1er ordre<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00E9quation 1er ordre<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/equation_differentielle<\/a>> # \u00E9quation diff\u00E9rentielle<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00E9quation diff\u00E9rentielle<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/equations_aux_derivees_partielles_solutions_numeriques<\/a>> # \u00E9quations aux d\u00E9riv\u00E9es partielles--solutions num\u00E9riques<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00E9quations aux d\u00E9riv\u00E9es partielles--solutions num\u00E9riques<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00C9quations aux d\u00E9riv\u00E9es partielles--Solutions num\u00E9riques<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00E9quations aux d\u00E9riv\u00E9es partielles--Solutions num\u00E9riques<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/fonction_green<\/a>> # fonction Green<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"fonction Green<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/partielle_differentialgleichung<\/a>> # Partielle Differentialgleichung<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Partielle Differentialgleichung<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Topic\/transformation_integrale<\/a>> # transformation int\u00E9grale<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"transformation int\u00E9grale<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/authorities\/subjects\/sh85037915<\/a>> # Differential equations, Partial--Numerical solutions<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Differential equations, Partial--Numerical solutions<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/enk<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"enk<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.worldcat.org\/fast\/893488<\/a>> # Differential equations, Partial--Numerical solutions<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Differential equations, Partial--Numerical solutions<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/113233114<\/a>> # Gwynne Evans<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Evans<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Gwynne<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Gwynne Evans<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/116819962<\/a>> # Peter D. Yardley<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1948<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Yardley<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Peter D.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Peter D. Yardley<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/73933797<\/a>> # Jonathan M. Blackledge<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Blackledge<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Jonathan M.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Jonathan M. Blackledge<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9783540761242<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"3540761241<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9783540761242<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/issn\/1615-2085<\/a>> # Springer undergraduate mathematics series,<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:PublicationSeries<\/a> ;\u00A0\u00A0\u00A0\nschema:hasPart<\/a> <http:\/\/www.worldcat.org\/oclc\/491119298<\/a>> ; # Analytic methods for partial differential equations<\/span>\n\u00A0\u00A0\u00A0\nschema:issn<\/a> \"1615-2085<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Springer undergraduate mathematics series,<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/491119298<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/491119298<\/a>> ; # Analytic methods for partial differential equations<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2019-12-21<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/491119298#PublicationEvent\/london_new_york_heidelberg_springer_2001<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:PublicationEvent<\/a> ;\u00A0\u00A0\u00A0\nschema:location<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Place\/heidelberg<\/a>> ; # Heidelberg<\/span>\n\u00A0\u00A0\u00A0\nschema:location<\/a> <http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> ; # New York<\/span>\n\u00A0\u00A0\u00A0\nschema:location<\/a> <http:\/\/dbpedia.org\/resource\/London<\/a>> ; # London<\/span>\n\u00A0\u00A0\u00A0\nschema:organizer<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/115580095#Agent\/springer<\/a>> ; # Springer<\/span>\n\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Content-negotiable representations<\/p>\n