Presenting a rich collection of exercises on partial differential equations, this textbooknow in its second editionequips readers with over 600 examples, exercises, and problems, complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus. New in this edition is the examination of models in physics that can be described by partial differential equations, including those in diffusion, acoustics, quantum mechanics, electromagnetism, and more. A new section is devoted to the use of distributions, or generalized functions, with a focus on the highly useful delta function. Additional problems and examples have been included, along with an expanded bibliography.

Thoughtfully organized into eight chapters, plus two additional chapters with solutions, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first- and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically rigorous format, ensuring that concepts are introduced with clarity and structure.

Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solving skills will also find this exercise collection both challenging and beneficial.

Offers a rich assortment of exercises, with detailed solutions or hints Provides insights into the practical application of PDEs, empowering students to tackle challenges with confidence New edition introduces physics models described by partial differential equations

Autorentext
Svetlin G. Georgiev (born 1974, Bulgaria) has worked in various areas of mathematics. His current focus lies on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He has authored or co-authored several books, including "Real Quaternionic Calculus Handbook" (2014), "Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales" (2018), "Functional Dynamic Equations on Time Scales" (2019), "Theory of Distributions" (2021, now in its second edition), and "Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales" (2021), all published with Springer.

Inhalt

General introduction.- The physical origins of partial differential equations.- First-order partial differential equations.- Classifications of second-order partial differential equations.- Classifications and canonical forms for linear second-order partial differential equations.- The Laplace equation.- The heat equation.- The wave equation.- Solutions, hints, and answers to the exercises.- Solutions, hints, and answers to the problems.- Bibliography.- Index.