Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.
While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave ...
Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them.
Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables.
This text explores the essentials of partial differential equations as applied to engineering and the physical sciences.
Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
The aim of this text is to aquaint the student with the fundamental classical results of partial differential equations and to guide them into some of the modern theory, enabling them to read more advanced works on the subject.
The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional ...
The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.
Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included.