This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.
Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables.
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 ...
... 111231 dy t5 = a21x + a22y where all, a12, a21, and a22 are real constants, show that the transformation to the new independent variable defined by w = In t (t = e”) transforms Eq. (25) to a new system with constant coefficients.
Largely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.
The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
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.
This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years.
Secondly, numerous case histories are given of how researchers have used differential equations to solve real life problems. This book is the outgrowth of this course.
The book can be used to teach a variety of different courses. This new edition features new problems throughout, and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added.