Introduction to partial differential equations and Hilbert space methods

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Bibliographic Information

Introduction to partial differential equations and Hilbert space methods

Karl E. Gustafson

Wiley, c1987

2nd ed

Other Title

Partial differential equations and Hilbert space methods

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Includes indexes

Description and Table of Contents

Description

This text covers all the major concepts and techniques in an elementary and clear style and explores some fields usually dealt with only in the advanced literature, also in a simplified manner. This edition includes new discussions on the three basic numerical methods, an introduction to computational fluid dynamics, and an introduction to Lie group methods for partial differential equations. All topics are treated as brief descriptions of needed results, not as condensed short courses. The text's practical approach will motivate students to pursue many areas of study, such as Fourier series, complex analysis, Lebesgue integration and functional analysis.

Table of Contents

  • THE USUAL TRINITIES
  • The Usual Three Operators and Classes of Equations
  • The Usual Three Types of Problems
  • The Usual Three Questions (and the Other Three)
  • The Usual Three Types of Boundary Conditions.'' The Usual Three Solution Methods (with Historical Remarks)
  • Three Important Mathematical Tools
  • Some Physical Considerations (and Examples)
  • Elements of Bifurcation Theory
  • Supplementary Discussions and Problems
  • FOURIER SERIES AND HILBERT SPACE
  • Lots of Separation of Variables
  • Mathematical Justifications of the Method
  • Fourier Series and Hilbert Space
  • Fourier Series and Sturm-Liouville Equations
  • Fourier Series and Green's Functions
  • Fourier Series and Variational and Numerical Methods
  • Some Unbounded Domain Considerations (and Continuous Spectra)
  • Elements of Scattering Theory
  • Supplementary Discussions and Problems
  • Appendices: First-Order Equations
  • Computational Methods
  • Advanced Fluid Dynamics
  • Selected Answers, Hints and Solutions
  • Author Index
  • Subject Index.

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