Notes, Problems and Solutions in Differential Equations - Datti, P. S.

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Résumé :
The proposed book consists of problems and solutions with relevant notes (or brief concepts) provided at the beginning of each chapter. The problems and solutions in the book will be from both ordinary differential equations and partial differential equations. The notes will mainly have the definitions, relevant concepts, statement of results and formulas. A student can therefore straightaway begin to solve the problems, turning to other textbooks only to learn proofs and additional material, if required. The book is also based on the authors' online courses on the popular e-learning platform NPTEL (National Programme on Technology Enhanced Learning). The book will be useful for the graduate and senior undergraduate students of mathematics, physics, and engineering. It will also be used by the researchers and professionals in these disciplines and in biology--...

Biographie:
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Sommaire:
This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm-Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway....