Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations. I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes.
This section attempts to answer some of the questions you might formulate when you turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc.
What Does this Toolbox Do?
The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time. The equations are discretized by the Finite Element Method (FEM). The objectives of the PDE Toolbox are to provide you with tools that:
• Define a PDE problem, i.e.
A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, with particular emphasis on developing an appreciation of underlying mathematical theory. Beginning with basic deﬁnitions, properties and derivations of some fundamental equations of mathematical physics from basic principles, the book studies ﬁrst-order equat
n mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below). The derivatives are ordinary because partial derivatives only apply to functions of many independent variables (see Partial differential equation).
Here follows the continuation of a collection of examples from Calculus 4c-1, Systems of differential
systems. The reader is also referred to Calculus 4b and to Complex Functions.
We focus in particular on the linear differential equations of second order of variable coefficients,
although the amount of examples is far from exhausting.
It should no longer be necessary rigourously to use the ADIC-model, described in Calculus 1c and
Calculus 2c, because we now assume that the reader can do this himself....
We have attempted to write a concise modern treatment of differential equations
emphasizing applications and containing all the core parts of a course in differential
equations.Asemester or quarter course in differential equations is taught to most engineering
students (and many science students) at all universities, usually in the second
year. Some universities have an earlier brief introduction to differential equations and
others do not. Some students will have already seen some differential equations in
their science classes.We do not assume any prior exposure to differential equations.
Nonhomogeneous ordinary differential equations can be solved if the general solution to the homogenous version is known, in which case the undetermined coefficients method or variation of parameters can be used to find the particular solution.
(BQ) Part 1 book "A first course in differential equations" has contents: Introduction to differential equations, first order differential equations, modeling with first order differential equations, higher order differential equations.
(BQ) Part 2 book "A first course in differential equations" has contents: Modeling with higher order differential equations, modeling with higher order differential equations, the laplace transform, systems of linear first order differential equations, numerical solutions of ordinary differential equations.
(BQ) Part 2 book "A first course in differential equations" has contents: Linear systems (matrices and linear systems, the eigenvalue problem, phase plane analysis, nonhomogeneous systems), nonlinear systems, computation of solutions.
(BQ) Part 1 book "Ordinary differential equations and dynamical systems" has contents: Introduction, initial value problems, linear equations, differential equations in the complex domain, boundary value problems.
(BQ) Part 2 book "Ordinary differential equations and dynamical systems" has contents: Dynamical systems, planar dynamical systems, higher dimensional dynamical systems, local behavior near fixed points, discrete dynamical systems, discrete dynamical systems in one dimension, chaos in higher dimensional systems, periodic solutions.
(BQ) Part 1 book "Functional analysis, sobolev spaces and partial differential equations" has contents: The hahn–banach theorems - introduction to the theory of conjugate convex functions; the uniform boundedness principle and the closed graph theorem; compact operators - spectral decomposition of self adjoint compact operators,...and other contents.
(BQ) Part 2 book "Functional analysis, sobolev spaces and partial differential equations" has contents: Sobolev spaces and the variational formulation of boundary value problems in one dimension, miscellaneous complements, evolution problems-the heat equation and the wave equation,...and other contents.