Partial Differential Equations De Gruyter Textbook I Loadzone
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Partial Differential Equations
Author: Vladimir A. Tolstykh
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2020-06-08
This is a clear, rigorous and self-contained introduction to PDEs for a semester-based course on the topic. For the sake of smooth exposition, the book keeps the amount of applications to a minimum, focusing instead on the theoretical essentials and problem solving. The result is an agile compendium of theorems and methods - the ideal companion for any student tackling PDEs for the first time. Vladimir Tolstykh is a professor of mathematics at Istanbul Arel University. He works in group theory and model-theoretic algebra. Dr. Tolstykh received his Ph.D. in Mathematics from the Ural Institute of Mathematics and Mechanics (Ekaterinburg (Russia) in 1992 and his Doctor of Science degree in Mathematics from the Sobolev Institute of Mathematics (Novosibirsk, Russia) in 2007.
Elements of Partial Differential Equations
Author: Pavel Drábek
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2014-08-19
This textbook is an elementary introduction to the basic principles of partial differential equations. With many illustrations it introduces PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.
Three Courses on Partial Differential Equations
Author: Eric Sonnendrücker
language: en
Publisher: Walter de Gruyter
Release Date: 2008-08-22
Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences. Hence its mathematical understanding is an important issue for today's research. This book provides an introduction to three different topics in partial differential equations arising from applications. The subject of the first course by Michel Chipot (Zurich) is equilibrium positions of several disks rolling on a wire. In particular, existence and uniqueness of and the exact position for an equilibrium are discussed. The second course by Josselin Garnier (Toulouse) deals with problems arising from acoustics and geophysics where waves propagate in complicated media, the properties of which can only be described statistically. It turns out that if the different scales presented in the problem can be separated, there exists a deterministic result. The third course by Otared Kavian (Versailles St.-Quentin) is devoted to so-called inverse problems where one or several parameters of a partial differential equation need to be determined by using, for instance, measurements on the boundary of the domain. The question that arises naturally is what information is necessary to determine the unknown parameters. This question is answered in different settings. The text is addressed to students and researchers with a basic background in partial differential equations.