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Applications of Symmetry Methods to Partial Differential Equations (Applied Mathematical Sciences)

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Applications of Symmetry Methods to Partial Differential Equations (Applied Mathematical Sciences)

Applications of Symmetry Methods to Partial Differential Equations by George W. Bluman
English | PDF(True) | 2010 | 415 Pages | ISBN : 038798612X | 1.9 MB

This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful.

Principles of Partial Differential Equations

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Principles of Partial Differential Equations

Principles of Partial Differential Equations by Alexander Komech
English | PDF(True) | 2009 | 165 Pages | ISBN : 1441910956 | 3.2 MB

This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques.

Phase Space Analysis of Partial Differential Equations

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Phase Space Analysis of Partial Differential Equations

Phase Space Analysis of Partial Differential Equations by Antonio Bove
English | PDF | 2006 | 356 Pages | ISBN : 081764511X | 3.1 MB

This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory.

Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type

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Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type

Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type by Samuil D. Eidelman
English | PDF | 2004 | 395 Pages | ISBN : 3034895925 | 26.9 MB

The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. A continuing interest in parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in specific applied problems of natural science, technology, and economics.

Differential Quadrature and Its Application in Engineering

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Differential Quadrature and Its Application in Engineering

Differential Quadrature and Its Application in Engineering by Chang Shu
English | PDF | 2000 | 356 Pages | ISBN : 144711132X | 26.1 MB

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration.

Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations

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Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations

Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations by Peter Kotelenez
English | PDF | 2008 | 449 Pages | ISBN : 0387743162 | 3.9 MB

This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation.

Wave Propagation and Time Reversal in Randomly Layered Media

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Wave Propagation and Time Reversal in Randomly Layered Media

Wave Propagation and Time Reversal in Randomly Layered Media by Jean-Pierre Fouque
English | PDF | 2007 | 623 Pages | ISBN : 0387308903 | 16.3 MB

Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments.

Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

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Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming by Hans Petter Langtangen
English | PDF | 2003 | 676 Pages | ISBN : 3540014381 | 56.9 MB

The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems, hence algorithmic and software issues play a central role.

Recent Developments in Domain Decomposition Methods

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Recent Developments in Domain Decomposition Methods

Recent Developments in Domain Decomposition Methods by Luca F. Pavarino
English | PDF | 2002 | 255 Pages | ISBN : 3540434135 | 20.5 MB

This volume collects some of the papers presented at the Workshop on Do- main Decompositionheld at ETH, Zurich,on June 7-8th 2001.The Workshop was organized by Luca F. Pavarino (University of Milan), Christoph Schwab (ETH Zurich), Andrea Toselli (ETH Zurich), and OlofB. Widlund (Courant Institute of Mathematical Sciences). Our sponsors were the University of Milan, Department of Mathematics (MURST projects: "Calcolo Scientifico: modelli e metodi numerici innovativi" and "Simmetrie, forme geometriche, evoluzione e memoria nelle equazioni alle derivate parziali"), the Seminar for Applied Mathematics, ETH Zurich, and the Program on Computational Science and Engineering at ETH Zurich.

Higher Order Partial Differential Equations in Clifford Analysis: Effective Solutions to Problems

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Higher Order Partial Differential Equations in Clifford Analysis: Effective Solutions to Problems

Higher Order Partial Differential Equations in Clifford Analysis: Effective Solutions to Problems by Elena Obolashvili
English | PDF | 2003 | 183 Pages | ISBN : 0817642862 | 9.58 MB

The most important thing is to write equations in a beautiful form and their success in applications is ensured. Paul Dirac The uniqueness and existence theorems for the solutions of boundary and initial value problems for systems of high-order partial differential equations (PDE) are sufficiently well known.

Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods

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Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods

Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods by Philippe Blanchard
English | PDF | 2003 | 469 Pages | ISBN : 1461265894 | 38.8 MB

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work.