## subcategories

**Ordinary** (24)

## e-books in Differential Equations category

**Differential Equations From The Algebraic Standpoint**

by

**Joseph Fels Ritt**-

**The American Mathematical Society**,

**1932**

We shall be concerned, in this monograph, with systems of differential equations, ordinary or partial, which are algebraic in the unknowns and their derivatives. The algebraic side of the theory of such systems seems is developed in this book.

(

**2706**views)

**Differential and Integral Equations: Boundary Value Problems and Adjoints**

by

**S. Schwabik, M. Tvrdy, O. Vejvoda**-

**Academia Praha**,

**1979**

The book is devoted to certain problems which belong to the domain of integral equations and boundary value problems for differential equations. Its essential part is concerned with linear systems of integral and generalized differential equations...

(

**1047**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.

(

**4649**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.

(

**1767**views)

**Elementary Differential Equations with Boundary Value Problems**

by

**William F. Trench**-

**Brooks Cole**,

**2001**

Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L ...

(

**5482**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.

(

**2792**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.

(

**5793**views)

**Differential Equations**

by

**William Woolsey Johnson**-

**J. Wiley**,

**1906**

The differential equation must necessarily at first be viewed in connection with a 'primitive', from which it might have been obtained by the direct process, and the solution consists in the discovery of such a primitive, when it exists...

(

**5809**views)

**An Elementary Treatise On Differential Equations And Their Applications**

by

**H.T.H. Piaggio**-

**G. Bell**,

**1920**

The object of this book is to give an account of the central parts of the subject in as simple a form as possible, suitable for those with no previous knowledge of it, and to point out the different directions in which it may be developed.

(

**4251**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.

(

**4050**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.

(

**3846**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.

(

**4375**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.

(

**3918**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.

(

**4466**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.

(

**3980**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.

(

**4022**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.

(

**4642**views)

**Mathematical Physics II**

by

**Boris Dubrovin**-

**SISSA**,

**2008**

These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.

(

**9502**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.

(

**4621**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.

(

**6125**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.

(

**4577**views)

**Lectures on Exterior Differential Systems**

by

**M. Kuranishi**-

**Tata Institute of Fundamental Research**,

**1962**

Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.

(

**6055**views)

**Beyond partial differential equations: A course on linear and quasi-linear abstract hyperbolic evolution equations**

by

**Horst R. Beyer**-

**arXiv**,

**2011**

This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems.

(

**6843**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.

(

**6916**views)

**Techniques of Applied Mathematics**

by

**Andrew Fowler**-

**University of Oxford**,

**2005**

This course develops mathematical techniques which are useful in solving 'real-world' problems involving differential equations. The course embraces the ethos of mathematical modelling, and aims to show in a practical way how equations 'work'.

(

**5668**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.

(

**7584**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.

(

**6011**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.

(

**6616**views)

**Introduction to Differential Equations**

by

**Jeffrey R. Chasnov**-

**The Hong Kong University of Science &Technology**,

**2010**

Contents: A short mathematical review; Introduction to odes; First-order odes; Second-order odes, constant coefficients; The Laplace transform; Series solutions; Systems of equations; Bifurcation theory; Partial differential equations.

(

**12027**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.

(

**6963**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.

(

**4547**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.

(

**6702**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.

(

**8568**views)

**Computational Mathematics for Differential Equations**

by

**N. V. Kopchenova, I. A. Maron**,

**1975**

This is a manual on solving problems in computational mathematics. The book is intended primarily for engineering students, but may also prove useful for economics students, graduate engineers, and postgraduate students in the applied sciences.

(

**10583**views)

**Analysis Tools with Applications**

by

**Bruce K. Driver**-

**Springer**,

**2003**

These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.

(

**8083**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.

(

**8360**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.

(

**9982**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.

(

**8693**views)

**Why the Boundary of a Round Drop Becomes a Curve of Order Four**

by

**A. N. Varchenko, P. I. Etingof**-

**American Mathematical Society**,

**1992**

This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution.

(

**10788**views)

**Notes on Diffy Qs: Differential Equations for Engineers**

by

**Jiří Lebl**-

**Lulu.com**,

**2009**

One semester introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, and the Laplace transform.

(

**13437**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.

(

**14030**views)

**Traveling Wave Solutions of Parabolic Systems**

by

**A. Volpert, V. Volpert, V. Volpert**-

**American Mathematical Society**,

**2000**

The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems and their stability.

(

**9318**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.

(

**9657**views)

**Differential Equations**

by

**Paul Dawkins**-

**Lamar University**,

**2011**

Contents: Basic Concepts; First Order Differential Equations; Second Order DE; Laplace Transforms; Systems of Differential Equations; Series Solutions; Higher Order DE; Boundary Value Problems and Fourier Series; Partial Differential Equations.

(

**10002**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.

(

**11429**views)

**Topics in dynamics I: Flows**

by

**Edward Nelson**-

**Princeton University Press**,

**1969**

Lecture notes for a course on differential equations covering differential calculus, Picard's method, local structure of vector fields, sums and Lie products, self-adjoint operators on Hilbert space, commutative multiplicity theory, and more.

(

**13228**views)

**Notes on Differential Equations**

by

**Bob Terrell**,

**2005**

Introductory notes on ordinary and partial differential equations for engineers. The text covers only the most important ideas. Assumed background is calculus and a little physics. Linear algebra is introduced in four of the lectures.

(

**11654**views)

**Difference Equations to Differential Equations - An introduction to calculus**

by

**Dan Sloughter**,

**2000**

The book is on sequences, limits, difference equations, functions and their properties, affine approximations, integration, polynomial approximations and Taylor series, transcendental functions, complex plane and differential equations.

(

**17646**views)