skip to content
Partial differential equations / 1 Basic theory. Preview this item
ClosePreview this item
Checking...

Partial differential equations / 1 Basic theory.

Author: Michael Eugene Taylor
Publisher: New York [u.a.] : Springer, 1996.
Series: Applied mathematical sciences, 115.
Edition/Format:   Print bookView all editions and formats
Database:WorldCat
Summary:

Providing an introduction to the theory of partial differential equations (PDEs), this text examines basic examples of linear PDEs arising in continuum mechanics, electromagnetism, complex analysis  Read more...

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michael Eugene Taylor
ISBN: 0387946535 9780387946535 0387946543 9780387946542
OCLC Number: 164817918
Description: XXI, 563 S. : graph. Darst.
Contents: Basic Theory of ODE and Vector Fields.- 1 The derivative.- 2 Fundamental local existence theorem for ODE.- 3 Inverse function and implicit function theorems.- 4 Constant-coefficient linear systems; exponentiation of matrices.- 5 Variable-coefficient linear systems of ODE: Duhamel's principle.- 6 Dependence of solutions on initial data and on other parameters.- 7 Flows and vector fields.- 8 Lie brackets.- 9 Commuting flows; Frobenius's theorem.- 10 Hamiltonian systems.- 11 Geodesies.- 12 Variational problems and the stationary action principle.- 13 Differential forms.- 14 The symplectic form and canonical transformations.- 15 First-order, scalar, nonlinear PDE.- 16 Completely integrable Hamiltonian systems.- 17 Examples of integrable systems; central force problems.- 18 Relativistic motion.- 19 Topological applications of differential forms.- 20 Critical points and index of a vector field.- A Nonsmooth vector fields.- References.- 2 The Laplace Equation and Wave Equation.- 1 Vibrating strings and membranes.- 2 The divergence of a vector field.- 3 The covariant derivative and divergence of tensor fields.- 4 The Laplace operator on a Riemannian manifold.- 5 The wave equation on a product manifold and energy conservation.- 6 Uniqueness and finite propagation speed.- 7 Lorentz manifolds and stress-energy tensors.- 8 More general hyperbolic equations; energy estimates.- 9 The symbol of a differential operator and a general Green-Stokes formula.- 10 The Hodge Laplacian on k-forms.- 11 Maxwell's equations.- References.- 3 Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE.- 1 Fourier series.- 2 Harmonic functions and holomorphic functions in the plane.- 3 The Fourier transform.- 4 Distributions and tempered distributions.- 5 The classical evolution equations.- 6 Radial distributions, polar coordinates, and Bessel functions.- 7 The method of images and Poisson's summation formula.- 8 Homogeneous distributions and principal value distributions.- 9 Elliptic operators.- 10 Local solvability of constant-coefficient PDE.- 11 The discrete Fourier transform.- 12 The fast Fourier transform.- The mighty Gaussian and the sublime gamma function.- References.- 4 Sobolev Spaces.- 1 Sobolev spaces on ?n.- 2 The complex interpolation method.- 3 Sobolev spaces on compact manifolds.- 4 Sobolev spaces on bounded domains.- 5 The Sobolev spaces Hs0(?).- 6 The Schwartz kernel theorem.- References.- 5 Linear Elliptic Equations.- 1 Existence and regularity of solutions to the Dirichlet problem.- 2 The weak and strong maximum principles.- 3 The Dirichlet problem on the ball in ?n.- 4 The Riemann mapping theorem (smooth boundary).- 5 The Dirichlet problem on a domain with a rough boundary.- 6 The Riemann mapping theorem (rough boundary).- 7 The Neumann boundary problem.- 8 The Hodge decomposition and harmonic forms.- 9 Natural boundary problems for the Hodge Laplacian.- 10 Isothermal coordinates and conformal structures on surfaces.- 11 General elliptic boundary problems.- 12 Operator properties of regular boundary problems.- Spaces of generalized functions on manifolds with boundary.- The Mayer-Vietoris sequence in deRham cohomology.- References.- 6 Linear Evolution Equations.- 1 The heat equation and the wave equation on bounded domains.- 2 The heat equation and wave equation on unbounded domains.- 3 Maxwell's equations.- 4 The Cauchy-Kowalewsky theorem.- 5 Hyperbolic systems.- 6 Geometrical optics.- 7 The formation of caustics.- Some Banach spaces of harmonic functions.- The stationary phase method.- References.- A Outline of Functional Analysis.- 1 Banach spaces.- 2 Hilbert spaces.- 3 Frechet spaces; locally convex spaces.- 4 Duality.- 5 Linear operators.- 6 Compact operators.- 7 Fredholm operators.- 8 Unbounded operators.- 9 Semigroups.- References.- B Manifolds, Vector Bundles, and Lie Groups.- 1 Metric spaces and topological spaces.- 2 Manifolds.- 3 Vector bundles.- 4 Sard's theorem.- 5 Lie groups.- 6 The Campbell-Hausdorff formula.- 7 Representations of Lie groups and Lie algebras.- 8 Representations of compact Lie groups.- 9 Representations of SU(2) and related groups.- References.
Series Title: Applied mathematical sciences, 115.
Responsibility: Michael E. Taylor.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/164817918> # Partial differential equations 1 Basic theory.
    a schema:CreativeWork, schema:Book ;
   library:oclcnum "164817918" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/2909612669#Place/new_york_u_a> ; # New York u.a.
   schema:about <http://experiment.worldcat.org/entity/work/data/2909612669#Topic/partielle_differentialgleichung> ; # Partielle Differentialgleichung
   schema:about <http://experiment.worldcat.org/entity/work/data/2909612669#Thing/partielle_differentialgleichung> ; # Partielle Differentialgleichung
   schema:bookFormat bgn:PrintBook ;
   schema:creator <http://experiment.worldcat.org/entity/work/data/2909612669#Person/taylor_michael_eugene> ; # Michael Eugene Taylor
   schema:datePublished "1996" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/2909612669> ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/2909612669#Series/applied_mathematical_sciences> ; # Applied mathematical sciences ;
   schema:name "Partial differential equations 1 Basic theory." ;
   schema:productID "164817918" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/164817918#PublicationEvent/new_york_u_a_springer_1996> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/2909612669#Agent/springer> ; # Springer
   schema:url <http://d-nb.info/948464348/04> ;
   schema:url <http://swbplus.bsz-bw.de/bsz053577647cov.htm> ;
   schema:workExample <http://worldcat.org/isbn/9780387946542> ;
   schema:workExample <http://worldcat.org/isbn/9780387946535> ;
   umbel:isLike <http://d-nb.info/948464348> ;
   umbel:isLike <http://d-nb.info/948303638> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/164817918> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/2909612669#Person/taylor_michael_eugene> # Michael Eugene Taylor
    a schema:Person ;
   schema:familyName "Taylor" ;
   schema:givenName "Michael Eugene" ;
   schema:name "Michael Eugene Taylor" ;
    .

<http://experiment.worldcat.org/entity/work/data/2909612669#Series/applied_mathematical_sciences> # Applied mathematical sciences ;
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/164817918> ; # Partial differential equations 1 Basic theory.
   schema:name "Applied mathematical sciences ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/2909612669#Thing/partielle_differentialgleichung> # Partielle Differentialgleichung
    a schema:Thing ;
   schema:name "Partielle Differentialgleichung" ;
    .

<http://experiment.worldcat.org/entity/work/data/2909612669#Topic/partielle_differentialgleichung> # Partielle Differentialgleichung
    a schema:Intangible ;
   schema:name "Partielle Differentialgleichung" ;
    .

<http://worldcat.org/isbn/9780387946535>
    a schema:ProductModel ;
   schema:isbn "0387946535" ;
   schema:isbn "9780387946535" ;
    .

<http://worldcat.org/isbn/9780387946542>
    a schema:ProductModel ;
   schema:isbn "0387946543" ;
   schema:isbn "9780387946542" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.