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The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs. Part I gives an overview of classical PDEs, that is, equations which admit strong solutions, verifying the equations pointwise. Classical solutions of the Laplace, heat, and wave equations are provided. Part II deals with variational PDEs, where weak (variational) solutions are considered. They are defined by variational formulations of the equations, based on Sobolev spaces. A comprehensive and detailed presentation of these spaces is given. Examples of variational elliptic, parabolic, and hyperbolic problems with different boundary conditions are discussed.
Doug DeWitt is going to Hell. Actually, he's just visiting, because he needs to ask for a favor from his former nemesis, Al Bloom. Unfortunately, Doug has no idea how to find him, and the demons and damned souls aren't helping at all. Doug's only ally is Mallory Gordon, a trigger-happy mercenary with a murky past and questionable motivation. While Mallory and Doug search for Al, they face obnoxious torture, including endless traffic jams, spontaneous fistfights, perpetual nightmares, and a crooked game of Go Fish. As they delve deeper into Hell, Doug recounts the story of how he and Al established a revolutionary charity, only for Al to abandon him and eventually commit suicide. If Doug can't figure out what went wrong on Earth, he'll never be able to obtain Al's help. Even worse, there's a distinct possibility he might become trapped in Hell forever.
* Offers comprehensive coverage of all major modeling viewpoints
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