e-books in Partial Differential Equations category
An Introduction to Partial Differential Equationsby Per Kristen Jakobsen - arXiv.org , 2019
These lecture notes view the subject through the lens of applied mathematics. The physical context for basic equations like the heat equation, the wave equation and the Laplace equation are introduced early on, and the focus is on methods.
(5253 views)
The Place of Partial Differential Equations in Mathematical Physicsby Ganesh Prasad - Patna University , 1924
The reason for my choosing the partial differential equations as the subject for these lectures is my wish to inspire in my audience a love for Mathematics. I give a brief historical account of the application of Mathematics to natural phenomena.
(7098 views)
Finite Difference Computing with PDEsby Hans Petter Langtangen, Svein Linge - Springer , 2017
This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners.
(6640 views)
Solving PDEs in Pythonby Hans Petter Langtangen, Anders Logg - Springer , 2017
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, it guides readers through the essential steps to quickly solving a PDE in FEniCS.
(7103 views)
Lectures on Periodic Homogenization of Elliptic Systemsby Zhongwei Shen - arXiv.org , 2017
In recent years considerable advances have been made in quantitative homogenization of PDEs in the periodic and non-periodic settings. This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems ...
(5499 views)
Symmetry and Separation of Variablesby Willard Miller - Addison-Wesley , 1977
This volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics and the coordinate systems in which the equation admits solutions via separation of variables.
(10657 views)
Introduction to the Method of Multiple Scalesby Per Jakobsen - arXiv , 2014
These lecture notes give an introduction to perturbation method with main focus on the method of multiple scales as it applies to pulse propagation in nonlinear optics. Aimed at students that have little or no background in perturbation methods.
(7034 views)
Linear Elliptic Equations of Second Orderby Erich Miersemann - Leipzig University , 2012
These lecture notes are intended as an introduction to linear second order elliptic partial differential equations. From the table of contents: Potential theory; Perron's method; Maximum principles; A discrete maximum principle.
(9064 views)
Partial Differential Equationsby Erich Miersemann - Leipzig University , 2012
These lecture notes are intended as a straightforward introduction to partial differential equations which can serve as a textbook for undergraduate and beginning graduate students. Some material of the lecture notes was taken from some other books.
(11834 views)
Partial Differential Equations with Mapleby Robert Piche, Keijo Ruohonen - Tampere University of Technology , 1997
The course presents the basic theory and solution techniques for the partial differential equation problems most commonly encountered in science. The student is assumed to know something about linear algebra and ordinary differential equations.
(9513 views)
Spectral Theory of Partial Differential Equationsby Richard S. Laugesen - arXiv , 2012
This text aims at highlights of spectral theory for self-adjoint partial differential operators, with an emphasis on problems with discrete spectrum. The course aims to develop your mental map of spectral theory in partial differential equations.
(10354 views)
An Algorithm for Constructing Lyapunov Functionsby Sigurdur Freyr Hafstein , 2007
In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems, possessing a uniformly asymptotically stable equilibrium. We give examples of Lyapunov functions constructed by our method.
(9420 views)
Lectures on Cauchy Problemby Sigeru Mizohata - Tata Institute of Fundamental Research , 1965
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions which are given on a hypersurface in the domain. Cauchy problems are an extension of initial value problems.
(10231 views)
Mathematical Theory of Scattering Resonancesby Semyon Dyatlov, Maciej Zworski - MIT , 2018
Contents: Scattering resonances in dimension one; Resonances for potentials in odd dimensions; Black box scattering in Rn; The method of complex scaling; Perturbation theory for resonances; Resolvent estimates in semiclassical scattering; etc.
(10834 views)
Existence, multiplicity, perturbation, and concentration results for a class of quasi-linear elliptic problemsby Marco Squassina - Electronic Journal of Differential Equations , 2006
A survey of results about existence, multiplicity, perturbation from symmetry and concentration phenomena for a class of quasi-linear elliptic equations coming from functionals of the calculus of variations which turn out to be merely continuous.
(9519 views)
An Introduction to Microlocal Analysisby Richard B. Melrose, Gunther Uhlmann - MIT , 2008
The origin of scattering theory is the study of quantum mechanical systems. The scattering theory for perturbations of the flat Laplacian is discussed with the approach via the solution of the Cauchy problem for the corresponding perturbed equation.
(11462 views)
Lectures on Elliptic Partial Differential Equationsby J.L. Lions - Tata Institute of Fundamental Research , 1957
In these lectures we study the boundary value problems associated with elliptic equation by using essentially L2 estimates (or abstract analogues of such estimates). We consider only linear problem, and we do not study the Schauder estimates.
(10329 views)
Lectures on Semi-group Theory and its Application to Cauchy's Problem in Partial Differential Equationsby K. Yosida - Tata Institute of Fundamental Research , 1957
In these lectures, we shall be concerned with the differentiability and the representation of one-parameter semi-groups of bounded linear operators on a Banach space and their applications to the initial value problem for differential equations.
(12773 views)
Nonlinear Partial Differential Equations of Elliptic Typeby Vicentiu Radulescu - arXiv , 2005
This textbook provides the background which is necessary to initiate work on a Ph.D. thesis in Applied Nonlinear Analysis. The purpose is to provide a broad perspective in the subject. The level is aimed at beginning graduate students.
(10209 views)
A First Course of Partial Differential Equations in Physical Sciences and Engineeringby Marcel B. Finan - Arkansas Tech University , 2009
Partial differential equations are often used to construct models of the most basic theories underlying physics and engineering. This book develops the basic ideas from the theory of partial differential equations, and applies them to simple models.
(13316 views)
Introduction to Partial Differential Equationsby John Douglas Moore - UCSB , 2003
The author develops the most basic ideas from the theory of partial differential equations, and apply them to the simplest models arising from physics. He presents some of the mathematics that can be used to describe the vibrating circular membrane.
(14111 views)
Pseudodifferential Operators and Nonlinear PDEby Michael E. Taylor - Birkhäuser Boston , 1991
Since the 1980s, the theory of pseudodifferential operators has yielded many significant results in nonlinear PDE. This monograph is devoted to a summary and reconsideration of some uses of this important tool in nonlinear PDE.
(11194 views)
Introductory Finite Difference Methods for PDEsby D. M. Causon, C. G. Mingham - BookBoon , 2010
This book presents finite difference methods for solving partial differential equations (PDEs) and also general concepts like stability, boundary conditions etc. The book is intended for undergraduates who know Calculus and introductory programming.
(12652 views)
Introduction to the Numerical Integration of PDEsby B. Piette - University of Durham , 2004
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.
(13262 views)
An Introduction to D-Modulesby Jean-Pierre Schneiders - Universite de Liege , 1991
These notes introduce the reader to the algebraic theory of systems of partial differential equations on a complex analytic manifold. We start by explaining how to switch from the classical point of view to the point of view of algebraic analysis.
(9918 views)
Introduction to Partial Differential Equationsby Valeriy Serov - University of Oulu , 2011
Contents: Preliminaries; Local Existence Theory; Fourier Series; One-dimensional Heat Equation; One-dimensional Wave Equation; Laplace Equation; Laplace Operator; Dirichlet and Neumann Problems; Layer Potentials; The Heat Operator; The Wave Operator.
(14212 views)
Partial Differential Equations: An Introductionby A.D.R. Choudary, Saima Parveen, Constantin Varsan - arXiv , 2010
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects.
(14638 views)
Entropy and Partial Differential Equationsby Lawrence C. Evans - UC Berkeley , 2003
This course surveys various uses of 'entropy' concepts in the study of PDE, both linear and nonlinear. This is a mathematics course, the main concern is PDE and how various notions involving entropy have influenced our understanding of PDE.
(15833 views)
Exterior Differential Systems and Euler-Lagrange Partial Differential Equationsby R. Bryant, P. Griffiths, D. Grossman - University Of Chicago Press , 2008
The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.
(18029 views)
Partial Differential Equations of Mathematical Physicsby William W. Symes - Rice University , 2006
This course aims to make students aware of the physical origins of the main partial differential equations of classical mathematical physics, including the equations of fluid and solid mechanics, thermodynamics, and classical electrodynamics.
(16332 views)
Partial Differential Equations for Financeby Robert V. Kohn - New York University , 2003
An introduction to those aspects of partial differential equations and optimal control most relevant to finance: PDE’s naturally associated to diffusion processes, Kolmogorov equations and their applications, linear parabolic equations, etc.
(23208 views)
Hilbert Space Methods for Partial Differential Equationsby R. E. Showalter - Pitman , 1994
Written for beginning graduate students of mathematics, engineering, and the physical sciences. It covers elements of Hilbert space, distributions and Sobolev spaces, boundary value problems, first order evolution equations, etc.
(16631 views)
Linear Partial Differential Equations and Fourier Theoryby Marcus Pivato - Cambridge University Press , 2005
Textbook for an introductory course on linear partial differential equations and boundary value problems. It also provides introduction to basic Fourier analysis and functional analysis. Written for third-year undergraduates in mathematical sciences.
(29260 views)