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A Compact Course on Linear PDEs

2023-09-30 Mathematics
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Release : 2023-09-30
Genre : Mathematics
Kind : eBook
Book Rating : 763/5 ( reviews)

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Book Synopsis A Compact Course on Linear PDEs by : Alberto Valli

Download or read book A Compact Course on Linear PDEs written by Alberto Valli. This book was released on 2023-09-30. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.

Introduction to Partial Differential Equations

2017-01-12 Mathematics
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Release : 2017-01-12
Genre : Mathematics
Kind : eBook
Book Rating : 364/5 ( reviews)

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Book Synopsis Introduction to Partial Differential Equations by : David Borthwick

Download or read book Introduction to Partial Differential Equations written by David Borthwick. This book was released on 2017-01-12. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Beyond Partial Differential Equations

2007-04-10 Mathematics
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Release : 2007-04-10
Genre : Mathematics
Kind : eBook
Book Rating : 295/5 ( reviews)

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Book Synopsis Beyond Partial Differential Equations by : Horst Reinhard Beyer

Download or read book Beyond Partial Differential Equations written by Horst Reinhard Beyer. This book was released on 2007-04-10. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

The Analysis of Linear Partial Differential Operators I

1990-08-10 Mathematics
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Release : 1990-08-10
Genre : Mathematics
Kind : eBook
Book Rating : 437/5 ( reviews)

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Book Synopsis The Analysis of Linear Partial Differential Operators I by : Lars Hörmander

Download or read book The Analysis of Linear Partial Differential Operators I written by Lars Hörmander. This book was released on 1990-08-10. Available in PDF, EPUB and Kindle. Book excerpt: The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

An Introduction to Partial Differential Equations

2006-04-18 Mathematics
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Release : 2006-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 871/5 ( reviews)

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Book Synopsis An Introduction to Partial Differential Equations by : Michael Renardy

Download or read book An Introduction to Partial Differential Equations written by Michael Renardy. This book was released on 2006-04-18. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

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