# Partial Differential Equations

## e-books in Partial Differential Equations category An Introduction to Partial Differential Equations
by - arXiv.org ,
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.
(954 views) The Place of Partial Differential Equations in Mathematical Physics
by - Patna University ,
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.
(2196 views) Finite Difference Computing with PDEs
by - Springer ,
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.
(1965 views) Solving PDEs in Python
by - Springer ,
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.
(1937 views) Lectures 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 ...
(1537 views) Symmetry 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.
(6486 views) Introduction 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.
(3235 views) Linear 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.
(4269 views) Partial 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.
(7494 views) Partial 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.
(5576 views) Lectures 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.
(5496 views) Spectral 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.
(6059 views) An 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.
(5470 views) Lectures 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.
(5795 views) Mathematical 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.
(5957 views) An 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.
(6575 views) Lectures 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.
(6208 views) Nonlinear 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.
(6107 views) A First Course of Partial Differential Equations in Physical Sciences and Engineering
by - Arkansas Tech University ,
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.
(8657 views) Introduction 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.
(9326 views) Pseudodifferential 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.
(7447 views) Introductory 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.
(8179 views) Introduction 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.
(8645 views) An 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.
(5833 views) Introduction 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.
(8806 views) Partial 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.
(10552 views) Entropy 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.
(10632 views) Exterior 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.
(12580 views) Partial 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.
(10935 views) Partial 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.
(17339 views) Hilbert 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.
(11587 views) Linear 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.
(23846 views)
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