Differential Equations

e-books in this category

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.
(4181 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.
(2707 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.
(3048 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'.
(5302 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.
(6545 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.
(6472 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.
(7261 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.
(5597 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.
(7672 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.
(8648 views)

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.
(9818 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.
(4175 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.
(8706 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.
(9391 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.
(6525 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.
(12587 views)