A Compact Course on Linear PDEs

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Focusing on second order linear partial differential equations, this textbook emphasizes variational formulations within Hilbert spaces. It covers key topics such as elliptic equations, the biharmonic problem, functional analysis, Sobolev spaces, and spectral theory. Additionally, it addresses saddle point problems and various types of equations, including parabolic and hyperbolic equations. With nearly 80 exercises and complete solutions, the text is designed for Mathematics students and those in Engineering with a solid mathematical foundation. The second edition features new sections and exercises, enhancing its comprehensive approach.