21-260 Differential Equations

Description

The subject of differential equations can be described as the study of equations involving derivatives. It can also be described as the study of anything that changes. The reason for this goes back to differential calculus, where one learns that the derivative of a function describes the rate of change of the function. Thus any quantity that varies can be described by an equation involving its derivative, whether the quantity is a position, velocity, temperature, population or volume.

There are three main ways to study differential equations. There are analytic methods, wherein a mathematical formula for a solution of a differential equation is obtained. There are Numerical techniques, which provide an approximate solution, generally using a computer or programmable calculator. Differential Equations can also be studied qualitatively, determining general properties of solution without concern for exact behavior.

In this course, we will emphasize analytic methods. Qualitative will also be studied, but numerical techniques will be left to other courses.

Learning Objectives

After completing this course, you should be able to

1. Use analytic techniques to compute solutions to various differential equations.
2. Use analytic and qualitative techniques to understand the behavior of solutions to various differential equations.
3. Understand the mathematical foundations of the techniques we study and why they are valid.

How to use this site...

Home

The description gives a brief overview of the topics we will discuss this semester. The learning objectives give an itemized list of the skills you should be developing. The list of learning objectives may give you some useful direction in terms of studying for exams.

Course Information

Times and rooms for lecture and recitation sections.

Schedule

List of topics to be covered each week, with links to reading assignments and homework.

Policies

Information about the calculation of grades, dates for exams, policies for late assignments and other matters. Familiarize yourself with these policies early in the semester.