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Author: Martin Schechter
Publisher: Courier Corporation
Published: 2014-01-15
Total Pages: 259
ISBN-13: 0486492966
DOWNLOAD EBOOKWhen first published in 1977, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Now it remains a permanent, much-cited contribution to the ever-expanding literature.
Author: Martin Schechter
Publisher: Courier Corporation
Published: 2013-12-10
Total Pages: 259
ISBN-13: 0486783073
DOWNLOAD EBOOKWhen first published in 1977, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Now it remains a permanent, much-cited contribution to the ever-expanding literature.
Author: Avner Friedman
Publisher: Courier Corporation
Published: 2008-11-24
Total Pages: 276
ISBN-13: 0486469190
DOWNLOAD EBOOKLargely 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.
Author: Mark S. Gockenbach
Publisher: SIAM
Published: 2010-12-02
Total Pages: 665
ISBN-13: 0898719356
DOWNLOAD EBOOKA fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.
Author: Walter A. Strauss
Publisher: John Wiley & Sons
Published: 2007-12-21
Total Pages: 467
ISBN-13: 0470054565
DOWNLOAD EBOOKOur 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.
Author: David Borthwick
Publisher: Springer
Published: 2017-01-12
Total Pages: 293
ISBN-13: 3319489364
DOWNLOAD EBOOKThis modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions: What is the scientific problem we are trying to understand? How do we model that with PDE? What techniques can we use to analyze the PDE? How do those techniques apply to this equation? What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Author: Silvia Bertoluzza
Publisher: Springer Science & Business Media
Published: 2009-03-13
Total Pages: 196
ISBN-13: 3764389400
DOWNLOAD EBOOKThis book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.
Author: G. Evans
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 299
ISBN-13: 1447103777
DOWNLOAD EBOOKThe subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.
Author: Irene Fonseca
Publisher: Springer Science & Business Media
Published: 2007-08-22
Total Pages: 602
ISBN-13: 0387690069
DOWNLOAD EBOOKThis is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
Author: G. Evans
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 308
ISBN-13: 1447103793
DOWNLOAD EBOOKThis is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.
