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The book contains selected problems which were offered to the students at the Department of Mechanics and Mathematics at Lomonosov Moscow State University as part of examination test for courses in PDEs and Equations of Mathematical Physics.

The problems are divided into five sections: Auxiliary Facts of Functional Analysis, General Notions of the Theory of Partial Differential Equations, Hyperbolic equations, Parabolic equations, Elliptic equations. At the beginning of each section the necessary theoretical background related to the exercises of the section is briefly given. Some of the problems are accompanied with detailed solutions and answers are provided for all problems except for those that require theoretical arguments.