Differential Equations

e-books in this category

An Introduction to Stochastic Differential Equations
by Lawrence C. Evans - UC Berkeley , 2006
These notes cover the basic theory of probability, random differential equations and some applications. The author designed these lectures so that starting graduate students can follow them, at the cost of some omission of detail and precision.
(4543 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.
(5030 views)

Differential Equations
by H. B. Phillips - John Wiley & Sons , 1922
With the formal exercise in solving the usual types of ordinary differential equations it is the object of this text to combine a thorough drill in the solution of problems in which the student sets up and integrates his own differential equation.
(1210 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.
(3238 views)

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
by Robert L. Bryant, Phillip A. Griffiths, Daniel A. 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.
(3234 views)

Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
by Lloyd N. Trefethen - Cornell University , 1996
An advanced textbook focused on basic principles, it presents a set of ideas rather than a sequence of theorems. The book should be accessible to mathematically inclined graduate students and practitioners in various fields of science and engineering.
(2061 views)

Further Mathematical Methods
by Niels Walet , 2002
Boundary and Initial Conditions; Fourier Series; Separation of variables on rectangular domains; D'Alembert's solution to the wave equation; Polar and spherical coordinate systems; Series solutions of ODE; Bessel functions; and more.
(1733 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.
(2248 views)

Introduction to Methods of Applied Mathematics
by Sean Mauch , 2004
Advanced mathematical methods for scientists and engineers, it contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations.
(6396 views)

Introduction to the Galois Theory of Linear Differential Equations
by Michael F. Singer - arXiv , 2008
The author's goal was to give the audience an introduction to the algebraic, analytic and algorithmic aspects of the Galois theory of linear differential equations by focusing on some of the main ideas and philosophies and on examples.
(226 views)

Lectures on Analytic Differential Equations
by Yulij Ilyashenko, Sergei Yakovenko - American Mathematical Society , 2007
A graduate-level textbook and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. The book includes self-contained demonstrations of several fundamental results.
(2399 views)

Linear Methods of Applied Mathematics
by Evans M. Harrell II, James V. Herod , 2000
This textbook is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. The text concentrates on mathematical concepts rather than on details of calculations.
(3500 views)

Linear Partial Differential Equations and Fourier Theory
by Marcus Pivato - Dover Publications, Inc. , 2007
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.
(2798 views)

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
by R. E. Showalter - American Mathematical Society , 1997
This monograph presents some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations.
(3176 views)

Nonlinear Analysis and Differential Equations
by Klaus Schmitt, Russell C. Thompson - University of Utah , 2004
The intent of this set of notes is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions of solutions.
(2130 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.
(2654 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.
(3648 views)

Numerical Methods for Partial Differential Equations
by Jaime Peraire, at al. - MIT OpenCourseWare , 2003
A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications.
(1723 views)

Ordinary Differential Equations and Dynamical Systems
by Gerald Teschl - Universitaet Wien , 2009
This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem.
(2491 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.
(4430 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.
(3883 views)

Partial Differential Equations of Physics
by Arnold Sommerfeld
From the table of contents: Fourier Series and Integrals; About partial differential equations; Boundary Value Problems in Heat Conduction; Cylinder and Sphere Problems; Eigen-functions and Eigen-values; Problems of wireless telegraphy.
(2938 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.
(820 views)

Real Functions in One Variable: Simple Differential Equations I
by Leif Mejlbro - BookBoon , 2007
Some examples of simple differential equations. The book covers separation of variables, linear differential equation of first order, the existence and uniqueness theorem, the Bernoulli differential equation, and the setup of model equations.
(1772 views)

The Hopf Bifurcation and Its Applications
by J. E. Marsden, M. McCracken - Springer , 1976
The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, including stability calculations.
(1983 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.
(4788 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.
(4246 views)