MATH235 - Differential Equations (w/ Honors) : Spring2015

This course is offered as a traditional lecture series at the Colorado School of Mines. The goal of this University of Reddit course is to leverage its features to facilitate student interaction in an open and easy way. In return for this functionality, I will make available any academic materials created through the course.

** Course Description **

(I, II, S) Classical techniques for first and higher order equations and systems of equations. Laplace transforms. Phase-plane and stability analysis of non-linear equations and systems. Applications from physics, mechanics, electrical engineering, and environmental sciences. Prerequisite: Consent of Department. 3 hours lecture; 3 semester hours.

Lectures
1. Lecture 0 - Functionality Tests

In r/math there are standard tools to do a little bit of math. There are also a lot of tools to do math, e.g. MathJax etc. I haven't tested how they work here... until NOW!

Prerequisites

It is expected that at the start of the course you are familiar with the concepts and calculations from:

• single variable differential and integral calculus
• Taylor series

As time goes on, our prerequisite needs will grow and at roughly the midway point it is expected that the student will have also seen:

• vector fields
• partial differentiation
• multivariate differential operators on scalar and vector fields
• the fundamental theorem of calculus (specifically the divergence theorem)
Syllabus

A syllabus is, literally, a list of topics to be covered within a course. In most academic settings, a syllabus is devoted to policy and procedure and here(pdf) you will find one for the traditional lecture sequence. The following is a syllabus or content list for what will appear in the lectures.

** Syllabus **

• First--order models: existence and uniqueness, separation of variables, autonomous dynamics, phase--line analysis, introduction to bifurcations, linearization, linear problems.
• Higher--order linear problems: theory, constant coefficients, inhomogeneous/forced systems, variable coefficients and power--series, Laplace transforms and distributional forcing.
• Linear systems: eigenvalues and eigenvectors/eigenfunctions, phase--space and the trace--determinant plane.
• Nonlinear systems: linearization, nullclines, conservation and dissipation.
• Introduction to continuum dynamics