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Eigenvalue Problem For A P Laplacian Equation With Trapping Potentials
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Book Synopsis Minimax Methods in Critical Point Theory with Applications to Differential Equations by : Paul H. Rabinowitz
Download or read book Minimax Methods in Critical Point Theory with Applications to Differential Equations written by Paul H. Rabinowitz and published by American Mathematical Soc.. This book was released on 1986-07-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
Book Synopsis Mathematical Theory of Scattering Resonances by : Semyon Dyatlov
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Book Synopsis Partial Differential Equations in Action by : Sandro Salsa
Download or read book Partial Differential Equations in Action written by Sandro Salsa and published by Springer. This book was released on 2015-04-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.
Book Synopsis Mathematics for Physics by : Michael Stone
Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
Book Synopsis Perturbation theory for linear operators by : Tosio Kato
Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fast Direct Solvers for Elliptic PDEs by : Per-Gunnar Martinsson
Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
Book Synopsis The Principles of Quantum Mechanics by : Paul Adrien Maurice Dirac
Download or read book The Principles of Quantum Mechanics written by Paul Adrien Maurice Dirac and published by Oxford University Press. This book was released on 1981 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this work appeared in 1930, and its originality won it immediate recognition as a classic of modern physical theory. The fourth edition has been bought out to meet a continued demand. Some improvements have been made, the main one being the complete rewriting of the chapter on quantum electrodymanics, to bring in electron-pair creation. This makes it suitable as an introduction to recent works on quantum field theories.
Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Book Synopsis I do like CFD, VOL.1, Second Edition by : Katate Masatsuka
Download or read book I do like CFD, VOL.1, Second Edition written by Katate Masatsuka and published by Lulu.com. This book was released on 2009-02-11 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 2.9 (May. 2024): This is a unique and highly technical book on Computational Fluid Dynamics (CFD). The first half talks about mathematical foundations and governing equations ranging from simple model equations (advection/diffusion, Euler-Tricomi, Cauchy-Riemann, Burgers, etc.) used for algorithm development to the incompressible/compressible Euler and Navier-Stokes equations in various forms with complete Jacobians and eigen-structures in 1, 2, and 3 dimensions. The other half talks about general methods for deriving exact solutions (separation of variables, transformation, superposition, etc.) and numerous exact solutions that can be readily used for accuracy verification of a CFD code (Ringleb's flow, Fraenkel's flow, boundary layer, viscous shock structure, etc.). This book can be a very useful resource for students studying basics of CFD as well as researchers/practitioners in CFD. - PDF version is available at cfdbooks.com. [Note: PDF does not contain some contents of the Printed version.]
Book Synopsis Exploring ODEs by : Lloyd N. Trefethen
Download or read book Exploring ODEs written by Lloyd N. Trefethen and published by SIAM. This book was released on 2017-12-21 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.?
Book Synopsis Spectral Methods in MATLAB by : Lloyd N. Trefethen
Download or read book Spectral Methods in MATLAB written by Lloyd N. Trefethen and published by SIAM. This book was released on 2000-07-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth
Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Book Synopsis The Physics of Quantum Mechanics by : James Binney
Download or read book The Physics of Quantum Mechanics written by James Binney and published by Oxford University Press, USA. This book was released on 2013-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.
Book Synopsis Nonlinear Waves by : Lokenath Debnath
Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Book Synopsis Process Dynamics and Control by : Dale E. Seborg
Download or read book Process Dynamics and Control written by Dale E. Seborg and published by John Wiley & Sons. This book was released on 2016-09-13 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new 4th edition of Seborg’s Process Dynamics Control provides full topical coverage for process control courses in the chemical engineering curriculum, emphasizing how process control and its related fields of process modeling and optimization are essential to the development of high-value products. A principal objective of this new edition is to describe modern techniques for control processes, with an emphasis on complex systems necessary to the development, design, and operation of modern processing plants. Control process instructors can cover the basic material while also having the flexibility to include advanced topics.
Book Synopsis Stochastic Differential Equations by : Bernt Oksendal
Download or read book Stochastic Differential Equations written by Bernt Oksendal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.
Book Synopsis Optimal Transport by : Cédric Villani
Download or read book Optimal Transport written by Cédric Villani and published by Springer Science & Business Media. This book was released on 2008-10-26 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
