Ordinary Differential Equations (ODE)

e-books in this category

Second-order Ordinary Differential Equations
by R.S. Johnson - Bookboon , 2012
This text provides an introduction to all the relevant material normally encountered at university level: series solution, special functions, Sturm-Liouville theory and the definition, properties and use of various integral transforms.
(565 views)

Integration and Differential Equations
by R.S. Johnson - BookBoon , 2012
Part I introduces the standard techniques of elementary integration and, in some cases, takes the ideas a little further. In Part II, ordinary differential equation are explored, and the solution methods for some standard types are explained.
(2175 views)

Linearization via the Lie Derivative
by Carmen Chicone, Richard Swanson - American Mathematical Society , 2000
The proof of the Grobman-Hartman linearization theorem for a flow at a hyperbolic rest point proceeds by establishing the analogous result for hyperbolic fixed points of local diffeomorphisms. We present a proof that avoids the discrete case.
(1150 views)

Periodic Solutions for Evolution Equations
by Mihai Bostan - American Mathematical Society , 2002
We study the existence and uniqueness of periodic solutions for evolution equations. We analyze the one-dimensional case, then for arbitrary dimensions. We consider linear symmetric operators. We prove the same results for non-linear operators.
(1157 views)

The Contraction Mapping Principle and Some Applications
by Robert M. Brooks, Klaus Schmitt - American Mathematical Society , 2009
These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric.
(1225 views)

Lectures on Differential Equations
by Craig A. Tracy - University of California , 2011
From the table of contents: Pendulum and MatLab; First Order Equations; Second Order Linear Equations; Difference Equations; Matrix Differential Equations; Weighted String; Quantum Harmonic Oscillator; Laplace Transform, etc.
(2171 views)

A Second Course in Elementary Ordinary Differential Equations
by Marcel B. Finan - Arkansas Tech University , 2006
Calculus of Matrix-Valued Functions of a Real Variable; nth Order Linear Differential Equations; General Solution of nth Order Linear Homogeneous Equations; Fundamental Sets and Linear Independence; Higher Order Homogeneous Linear Equations; etc.
(3624 views)

A First Course in Elementary Differential Equations
by Marcel B. Finan - Arkansas Tech University , 2006
Contents: Basic Terminology; Qualitative Analysis: Direction Field of y'=f(t,y); Existence and Uniqueness of Solutions to First Order Linear IVP; Solving First Order Linear Homogeneous DE; Solving First Order Linear Non Homogeneous DE; etc.
(6219 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.
(2475 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.
(6119 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.
(4543 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.
(4337 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.
(6608 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.
(4574 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.
(5191 views)