A Short Introduction To Partial Differential Equations
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A Short Introduction To Partial Differential Equations
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Author : Arian Novruzi
language : en
Publisher: Springer Nature
Release Date : 2023-12-30
A Short Introduction To Partial Differential Equations written by Arian Novruzi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-30 with Mathematics categories.
This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods. The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces. The book ends with an appendix chapter, which complements the previous chapters with proofs, examples and remarks. This book can be used for an intense one-semester, or normal two-semester, PDE course. The reader isexpected to have knowledge of linear algebra and of differential equations, a good background in real and complex calculus and a modest background in analysis and topology. The book has many examples, which help to better understand the concepts, highlight the key ideas and emphasize the sharpness of results, as well as a section of problems at the end of each chapter.
Introduction To Partial Differential Equations And Hilbert Space Methods
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Author : Karl E. Gustafson
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Introduction To Partial Differential Equations And Hilbert Space Methods written by Karl E. Gustafson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Register Of The University Of California
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Author : University of California, Berkeley
language : en
Publisher:
Release Date : 1891
Register Of The University Of California written by University of California, Berkeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1891 with categories.
Register
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Author : University of California, Berkeley
language : en
Publisher:
Release Date : 1899
Register written by University of California, Berkeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1899 with categories.
Numerical Analysis Of Partial Differential Equations
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Author : S. H, Lui
language : en
Publisher: John Wiley & Sons
Release Date : 2012-01-10
Numerical Analysis Of Partial Differential Equations written by S. H, Lui and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-10 with Mathematics categories.
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
Annual Announcement Of Courses Of Instruction
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Author : University of California (1868-1952)
language : en
Publisher:
Release Date : 1896
Annual Announcement Of Courses Of Instruction written by University of California (1868-1952) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with categories.
Partial Differential Equations
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Author : Jeffrey Rauch
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-12-23
Partial Differential Equations written by Jeffrey Rauch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-12-23 with Mathematics categories.
This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differenƯ tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "essentials" can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions
Analytic Methods For Partial Differential Equations
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Author : G. Evans
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analytic Methods For Partial Differential Equations written by G. Evans and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The 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. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal 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 forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.
Analytical Methods For Heat Transfer And Fluid Flow Problems
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Author : Bernhard Weigand
language : en
Publisher: Springer
Release Date : 2015-05-05
Analytical Methods For Heat Transfer And Fluid Flow Problems written by Bernhard Weigand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-05 with Technology & Engineering categories.
This book describes useful analytical methods by applying them to real-world problems rather than solving the usual over-simplified classroom problems. The book demonstrates the applicability of analytical methods even for complex problems and guides the reader to a more intuitive understanding of approaches and solutions. Although the solution of Partial Differential Equations by numerical methods is the standard practice in industries, analytical methods are still important for the critical assessment of results derived from advanced computer simulations and the improvement of the underlying numerical techniques. Literature devoted to analytical methods, however, often focuses on theoretical and mathematical aspects and is therefore useless to most engineers. Analytical Methods for Heat Transfer and Fluid Flow Problems addresses engineers and engineering students. The second edition has been updated, the chapters on non-linear problems and on axial heat conduction problems were extended. And worked out examples were included.
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications
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Author : Yves Achdou
language : en
Publisher: Springer
Release Date : 2013-05-24
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications written by Yves Achdou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).