Fundamentals of Partial Differential Equations

ISBN-13: 9789811698644 / Angielski / Twarda / 2022 / 568 str.

Atul Kumar Razdan;V. Ravichandran

Opis

The book serves as a primary textbook of partial differential equations (PDEs), with due attention to their importance to various physical and engineering phenomena. The book focuses on maintaining a balance between the mathematical expressions used and the significance they hold in the context of some physical problem. The book has wider outreach as it covers topics relevant to many different applications of ordinary differential equations (ODEs), PDEs, Fourier series, integral transforms, and applications. It also discusses applications of analytical and geometric methods to solve some fundamental PDE models of physical phenomena such as transport of mass, momentum, and energy.As far as possible, historical notes are added for most important developments in science and engineering. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.

Recenzje

"This is a textbook for undergraduate engineering students. ... Many topics of the book are supplemented by historical remarks ... ." (Lutz Recke, zbMATH 1497.35001, 2022)

"This new book on partial differential equations (PDEs) is primarily directed at upper-level undergraduate students in physics and engineering. It would also be appropriate for mathematics students either at that stage or in early graduate studies. ... the text is clear and well written." (Bill Satzer, MAA Reviews, October 31, 2022)

Spis treści

Classical Vector Analysis.- Ordinary Differential Equations.- Partial Differential Equation Models.- Partial Differential Equations.- General Solution and Complete Integral.- Method of Characteristics.- Separation of Variables.- Method of Eigenfunctions Expansion.- Fourier Transforms.-  Laplace Transform.

O autorze

ATUL RAZDAN served at the Department of Mathematics, University of Delhi, India, 2004–2008. He started his career as Lecturer in 1995 at Indira Gandhi National Open University (IGNOU), New Delhi, India, until 2004. His area of research is algebra on which he has published several papers in journals of international repute.

V. RAVICHANDRAN is Professor of Mathematics at the National Institute of Technology, Tiruchirappalli, India. He held positions at Universiti Sains Malaysia (from 2004–2007 and from 2011–2012) and at the University of Delhi, India (from 2007–2018). He specializes in geometric function theory and published more than 150 research papers. Since 2004, he has served as Editor of the Bulletin of the Malaysian Mathematical Sciences Society.