Partial Differential Equations
by Thomas Hillen, I. E. Leonard, and Henry Van Roessel
Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on lin...
Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by P�lya in the 1930's and rediscovered in part several times since, it was not un
Introduction to Partial Differential Equations and Hilbert Space Methods (Dover Books on Mathematics)
by Karl E. Gustafson
This text covers all the major concepts and techniques in an elementary and clear style and explores some fields usually dealt with only in the advanced literature, also in a simplified manner. This edition includes new discussions on the three basic numerical methods, an introduction to computational fluid dynamics, and an introduction to Lie group methods for partial differential equations. All topics are treated as brief descriptions of needed results, not as condensed short courses. The text...
Non-Standard and Improperly Posed Problems. Mathematics in Science and Engineering, Volume 194.
by Karen A Ames and Brian Straughan
Non-Linear Partial Differential Equations (North-Holland Mathematics Studies)
by Elemer E Rosinger and E.E. Rosinger
A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations hav...
Nonlinear Methods in Riemannian & Kahlerian Geometry (DMV Seminar, #10) (Seminare der deutschen Mathematiker Vereinigung)
by J. Jost
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Dusseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximatio...
Two-Point Boundary Value Problems (Mathematics in Science and Engineering, #205)
by De Coster Colette, C De Coster, and P Habets
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications...
Hyperbolic Problems, Part 1; Plenary and Invited Talks (Proceedings of Symposia in Applied Mathematics)
The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. This book, the first in a two-part volume, contains nineteen papers base...
Nonlinear Variational Problems (Pitman Research Notes in Mathematics, #193)
Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of s...
Differential Equations and Dynamical Systems (Texts in Applied Mathematics, #7)
by Lawrence Perko
This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behaviour of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated at the end of the 19th century. It is also intended as a reference book for mathematicians doing re...
This is an up-to-date survey of current research with partial differential equations. Topics discussed include the evolution of hypersurfaces by mean curvature flow, nonlinear wave equations including harmonic maps, and blow-up mechanisms for semilinear parabolic equations. Much of the material presented consists of very recent results and in many cases, no surveys of the topics under consideration are available in the scientific journals.
Theory and Applications of Partial Functional Differential Equations
by Abrar a Khan
This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.
Fully Nonlinear Elliptic Equations (Colloquium Publications)
by Luis A. Caffarelli and Xavier Cabre
This book provides a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and Cabre offer a detailed presentation of all techniques needed to extend the classical Schauder and Calderon-Zygmund regularity theories for linear elliptic equations to the fully nonlinear context. The authors present the key ideas and prove all the results needed for the regularity theory of viscosity solutions of fully nonlinear equations. The book contain...
Partial Differential Equations (Mathematical Engineering, Manufacturing, and Management Sciences)
by Nita H. Shah and udul Y. Jani
Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. They permit us to model changing forms in both mathematical and physical problems. These equations are precisely used when a deterministic relation containing some continuously varying quantities and their rates of change in space and/or time is recognized or postulated. This book is intended to provide a straightforward introduction to the concept of partial differential equations. It provi...
Differential Equations And Their Applications: Analysis From A Physicist's Viewpoint
by Noboru Nakanishi and Kenji Seto
This book is written for students and researchers who are fond of mathematics and the natural sciences. It consists of two parts. Part I presents the theory of analysis in which the mathematical theory is described not as an accomplished palace, but as a building under construction. It uncovers how a theory has been or is being constructed. In Part II, the theory of differential equations is applied to interesting practical problems, such as pursuit-line and tractrix, attack on an object from an...
Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis (Interdisciplinary Mathematical Sciences)
Applications of Lie's Theory of Ordinary and Partial Differential Equations
by Lawrence Dresner
Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emph...
Generalized Inverse Operators (Inverse and Ill-Posed Problems)
by Alexander Andreevych Boichuk and Anatolii M. Samoilenko
The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these prob...
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to abstraction - the most powerful tool for solving problems - rather than simply drilled in the practice of imitating solutions to given examples. The book is therefore id...