This course introduces students to the basic techniques for solving partial differential equations as well as the underlying theories. Classification of partial differential equations.
Boundary-value, initial-value and eigenvalue problems. Separation of variables, Fourier series, linearity and superposition, Duhamel's principle, characteristic method. Fourier Series 9. Maximum Principles Weak Solutions Variational Methods Distributions The Fourier Transform A.
The author gives a balanced presentation that includes modern methods, without requiring prerequisites beyond vector calculus and linear algebra. Concepts and definitions from analysis are introduced only as they are needed in the text. Palagachev, zbMATH Email Address.
- Introduction to Partial Differential Equations!
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Please enter the letters displayed. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout.
The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics.
The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators. Gerald B.
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