Partial Differential Equations I
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This is the first of three volumes on partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Volume I prepares the way for studies ...
This is the first of three volumes on partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Volume I prepares the way for studies of more advanced topics in linear PDE, in Volume 2, and for studies of nonlinear PDE, in Volume 3. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Table of contents:
Contents: Contents of Volumes II and III.- Introduction.- Basic Theory of ODE and Vector Fields.- The Laplace Equation and Wave Equation.- Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE.- Sobolev Spaces.- Linear Elliptic Equations.- Linear Evolution Equations.- Appendix A: Outline of Functional Analysis.- Appendix B: Manifolds, Vector Bundles, and Lie Groups.- Index.
Table of contents:
Contents: Contents of Volumes II and III.- Introduction.- Basic Theory of ODE and Vector Fields.- The Laplace Equation and Wave Equation.- Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE.- Sobolev Spaces.- Linear Elliptic Equations.- Linear Evolution Equations.- Appendix A: Outline of Functional Analysis.- Appendix B: Manifolds, Vector Bundles, and Lie Groups.- Index.