## e-books in Partial Differential Equations category

**Lectures on Periodic Homogenization of Elliptic Systems**

by

**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 ...

(

**328**views)

**Symmetry and Separation of Variables**

by

**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.

(

**4861**views)

**Introduction to the Method of Multiple Scales**

by

**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.

(

**1995**views)

**Linear Elliptic Equations of Second Order**

by

**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.

(

**3021**views)

**Partial Differential Equations**

by

**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.

(

**6044**views)

**Partial Differential Equations with Maple**

by

**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.

(

**4253**views)

**Lectures on Partial Differential Equations**

by

**G.B. Folland**-

**Tata Institute of Fundamental Research**,

**1983**

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)

**Spectral Theory of Partial Differential Equations**

by

**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.

(

**4640**views)

**An Algorithm for Constructing Lyapunov Functions**

by

**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.

(

**4178**views)

**Lectures on Cauchy Problem**

by

**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.

(

**4665**views)

**Mathematical Theory of Scattering Resonances**

by

**Semyon Dyatlov, Maciej Zworski**-

**MIT**,

**2017**

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)

**Existence, multiplicity, perturbation, and concentration results for a class of quasi-linear elliptic problems**

by

**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.

(

**4251**views)

**An Introduction to Microlocal Analysis**

by

**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.

(

**4950**views)

**Lectures on Elliptic Partial Differential Equations**

by

**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.

(

**4864**views)

**Lectures on Semi-group Theory and its Application to Cauchy's Problem in Partial Differential Equations**

by

**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.

(

**6408**views)

**Nonlinear Partial Differential Equations of Elliptic Type**

by

**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.

(

**4812**views)

**A First Course of Partial Differential Equations in Physical Sciences and Engineering**

by

**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.

(

**7146**views)

**Introduction to Partial Differential Equations**

by

**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.

(

**7847**views)

**Pseudodifferential Operators and Nonlinear PDE**

by

**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.

(

**6216**views)

**Introductory Finite Difference Methods for PDEs**

by

**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.

(

**6849**views)

**Introduction to the Numerical Integration of PDEs**

by

**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.

(

**7181**views)

**An Introduction to D-Modules**

by

**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.

(

**4720**views)

**Introduction to Partial Differential Equations**

by

**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.

(

**6979**views)

**Partial Differential Equations: An Introduction**

by

**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.

(

**8874**views)

**Entropy and Partial Differential Equations**

by

**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.

(

**8654**views)

**Exterior Differential Systems and Euler-Lagrange Partial Differential Equations**

by

**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.

(

**10245**views)

**Partial Differential Equations of Mathematical Physics**

by

**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.

(

**9028**views)

**Partial Differential Equations for Finance**

by

**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.

(

**14386**views)

**Hilbert Space Methods for Partial Differential Equations**

by

**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.

(

**9918**views)

**Linear Partial Differential Equations and Fourier Theory**

by

**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.

(

**21732**views)