Differential Equations


Ordinary (24)

e-books in Differential Equations category

Differential Equations From The Algebraic StandpointDifferential 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.
Differential and Integral Equations: Boundary Value Problems and AdjointsDifferential 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...
Symmetry and Separation of VariablesSymmetry 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.
Introduction to the Method of Multiple ScalesIntroduction 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.

Elementary Differential Equations with Boundary Value ProblemsElementary 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 ...
Linear Elliptic Equations of Second OrderLinear 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.
Partial Differential EquationsPartial 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.
Differential EquationsDifferential 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...
An Elementary Treatise On Differential Equations And Their ApplicationsAn 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.
Partial Differential Equations with MaplePartial 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.
Lectures on Partial Differential EquationsLectures 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.
Spectral Theory of Partial Differential EquationsSpectral 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.
An Algorithm for Constructing Lyapunov FunctionsAn 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.
Lectures on Cauchy ProblemLectures 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.
Mathematical Theory of Scattering ResonancesMathematical 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.
An Introduction to Microlocal AnalysisAn 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.
Mathematical Physics IIMathematical 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.
Lectures on Elliptic Partial Differential EquationsLectures 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.
Nonlinear Partial Differential Equations of Elliptic TypeNonlinear 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.
Lectures on Exterior Differential SystemsLectures 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.
Techniques of Applied MathematicsTechniques 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'.
Introduction to Partial Differential EquationsIntroduction 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.
Pseudodifferential Operators and Nonlinear PDEPseudodifferential 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.
Introductory Finite Difference Methods for PDEsIntroductory 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.
Introduction to Differential EquationsIntroduction to Differential Equations
by Jeff rey 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.
Introduction to the Numerical Integration of PDEsIntroduction 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.
An Introduction to D-ModulesAn 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.
Introduction to Partial Differential EquationsIntroduction 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.
Partial Differential Equations: An IntroductionPartial 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.
Computational Mathematics for Differential EquationsComputational 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.
Analysis Tools with ApplicationsAnalysis 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.
Entropy and Partial Differential EquationsEntropy 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.
Exterior Differential Systems and Euler-Lagrange Partial Differential EquationsExterior 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.
Partial Differential Equations of Mathematical PhysicsPartial 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.
Why the Boundary of a Round Drop Becomes a Curve of Order FourWhy 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.
Notes on Diffy Qs: Differential Equations for EngineersNotes 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.
Partial Differential Equations for FinancePartial 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.
Traveling Wave Solutions of Parabolic SystemsTraveling 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.
Hilbert Space Methods for Partial Differential EquationsHilbert 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.
Differential EquationsDifferential 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.
Linear Partial Differential Equations and Fourier TheoryLinear 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.
Topics in dynamics I: FlowsTopics 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.
Notes on Differential EquationsNotes 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.