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Partial Differential Equations

e-books in Partial Differential Equations category

Book cover: Lectures on Periodic Homogenization of Elliptic SystemsLectures on Periodic Homogenization of Elliptic Systems
by - arXiv.org ,
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 ...
(328 views)
Book cover: Symmetry and Separation of VariablesSymmetry and Separation of Variables
by - Addison-Wesley ,
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.
(4861 views)
Book cover: Introduction to the Method of Multiple ScalesIntroduction to the Method of Multiple Scales
by - arXiv ,
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.
(1995 views)
Book cover: Linear Elliptic Equations of Second OrderLinear Elliptic Equations of Second Order
by - Leipzig University ,
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.
(3021 views)

Book cover: Partial Differential EquationsPartial Differential Equations
by - Leipzig University ,
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.
(6044 views)
Book cover: Partial Differential Equations with MaplePartial Differential Equations with Maple
by - Tampere University of Technology ,
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.
(4253 views)
Book cover: Lectures on Partial Differential EquationsLectures on Partial Differential Equations
by - Tata Institute of Fundamental Research ,
The purpose of this course was to introduce students to the applications of Fourier analysis -- by which I mean the study of convolution operators as well as the Fourier transform itself -- to partial differential equations.
(4112 views)
Book cover: Spectral Theory of Partial Differential EquationsSpectral Theory of Partial Differential Equations
by - arXiv ,
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.
(4640 views)
Book cover: An Algorithm for Constructing Lyapunov FunctionsAn Algorithm for Constructing Lyapunov Functions
by ,
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.
(4178 views)
Book cover: Lectures on Cauchy ProblemLectures on Cauchy Problem
by - Tata Institute of Fundamental Research ,
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.
(4665 views)
Book cover: Mathematical Theory of Scattering ResonancesMathematical Theory of Scattering Resonances
by - MIT ,
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.
(4333 views)
Book cover: An Introduction to Microlocal AnalysisAn Introduction to Microlocal Analysis
by - MIT ,
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.
(4950 views)
Book cover: Lectures on Elliptic Partial Differential EquationsLectures on Elliptic Partial Differential Equations
by - Tata Institute of Fundamental Research ,
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.
(4864 views)
Book cover: Nonlinear Partial Differential Equations of Elliptic TypeNonlinear Partial Differential Equations of Elliptic Type
by - arXiv ,
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.
(4812 views)
Book cover: Introduction to Partial Differential EquationsIntroduction to Partial Differential Equations
by - UCSB ,
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.
(7847 views)
Book cover: Pseudodifferential Operators and Nonlinear PDEPseudodifferential Operators and Nonlinear PDE
by - Birkhäuser Boston ,
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.
(6216 views)
Book cover: Introductory Finite Difference Methods for PDEsIntroductory Finite Difference Methods for PDEs
by - BookBoon ,
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.
(6849 views)
Book cover: Introduction to the Numerical Integration of PDEsIntroduction to the Numerical Integration of PDEs
by - University of Durham ,
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.
(7181 views)
Book cover: An Introduction to D-ModulesAn Introduction to D-Modules
by - Universite de Liege ,
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.
(4720 views)
Book cover: Introduction to Partial Differential EquationsIntroduction to Partial Differential Equations
by - University of Oulu ,
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.
(6979 views)
Book cover: Partial Differential Equations: An IntroductionPartial Differential Equations: An Introduction
by - arXiv ,
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.
(8874 views)
Book cover: Entropy and Partial Differential EquationsEntropy and Partial Differential Equations
by - UC Berkeley ,
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.
(8654 views)
Book cover: Exterior Differential Systems and Euler-Lagrange Partial Differential EquationsExterior Differential Systems and Euler-Lagrange Partial Differential Equations
by - University Of Chicago Press ,
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.
(10245 views)
Book cover: Partial Differential Equations of Mathematical PhysicsPartial Differential Equations of Mathematical Physics
by - Rice University ,
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.
(9028 views)
Book cover: Partial Differential Equations for FinancePartial Differential Equations for Finance
by - New York University ,
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.
(14386 views)
Book cover: Hilbert Space Methods for Partial Differential EquationsHilbert Space Methods for Partial Differential Equations
by - Pitman ,
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.
(9918 views)
Book cover: Linear Partial Differential Equations and Fourier TheoryLinear Partial Differential Equations and Fourier Theory
by - Cambridge University Press ,
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.
(21732 views)