Pde Examples
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Partial Differential Equations through Examples and Exercises
Author: E. Pap
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The book Partial Differential Equations through Examples and Exercises has evolved from the lectures and exercises that the authors have given for more than fifteen years, mostly for mathematics, computer science, physics and chemistry students. By our best knowledge, the book is a first attempt to present the rather complex subject of partial differential equations (PDEs for short) through active reader-participation. Thus this book is a combination of theory and examples. In the theory of PDEs, on one hand, one has an interplay of several mathematical disciplines, including the theories of analytical functions, harmonic analysis, ODEs, topology and last, but not least, functional analysis, while on the other hand there are various methods, tools and approaches. In view of that, the exposition of new notions and methods in our book is "step by step". A minimal amount of expository theory is included at the beginning of each section Preliminaries with maximum emphasis placed on well selected examples and exercises capturing the essence of the material. Actually, we have divided the problems into two classes termed Examples and Exercises (often containing proofs of the statements from Preliminaries). The examples contain complete solutions, and also serve as a model for solving similar problems, given in the exercises. The readers are left to find the solution in the exercises; the answers, and occasionally, some hints, are still given. The book is implicitly divided in two parts, classical and abstract.
Basic Partial Differential Equations
Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.
Introductory Guide to Partial Differential Equations
"Introductory Guide to Partial Differential Equations" is an accessible and comprehensive introduction to Partial Differential Equations (PDEs) for undergraduate students. We provide a solid foundation in the theory and applications of PDEs, catering to students in mathematics, engineering, physics, and related fields. We present fundamental concepts of PDEs in a clear and engaging manner, emphasizing both theoretical understanding and practical problem-solving skills. Starting with basic concepts such as classification of PDEs, boundary and initial conditions, and solution techniques, we gradually progress to advanced topics including Fourier series, separation of variables, and the method of characteristics. Real-world applications of PDEs are woven throughout the book, demonstrating the relevance of this mathematical theory in fields such as heat conduction, fluid dynamics, quantum mechanics, and finance. Numerous examples, exercises, and applications are included to reinforce learning and encourage active engagement with the material. Whether you're preparing for further study in mathematics or seeking to apply PDEs in your chosen field, this book equips you with the knowledge and skills necessary to tackle a wide range of problems involving partial differential equations. We hope this text will inspire curiosity and confidence in approaching the rich and diverse world of PDEs.