Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
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 ...
Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations.
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.
The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.
Modeling, Analysis, Computation R. M. M. Mattheij, S. W. Rienstra, J. H. M. ten Thije Boonkkamp. Bibliography [1] M ... Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Classics in Appl. Math. 13, SIAM ...
1.7 Show that if φ satisfies the heat equation then the change of dependent variable u(x,t) = −2∂∂x logφ (x,t) (commonly referred to as the Cole–Hopf transformation) satisfies the nonlinear PDE ut + uu x = uxx (also known as the ...
This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging.
This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, ...