Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIl as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sci ences (AMS) series, which will focus on advanced textbooks and research level monographs.
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 serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.
This is the second edition of the now definitive text on partial differential equations (PDE).
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 ...
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.
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.