An Excursion Through Partial Differential Equations

Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 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.

Organized thoughtfully into seven chapters, 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 solid format, ensuring concepts are introduced with clarity and organization.

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-solvingskills will also find this exercise collection both challenging and beneficial.

Preface.- General Introduction.- 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.- Index.

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.