18.03 Differential Equations

Spring 2006

Screenshot of Mathlet from the d'Arbeloff Interactive Math Project.
Linear Phase Portraits Mathlet from the d'Arbeloff Interactive Math Project. (Image courtesy of Hu Hohn and Prof. Haynes Miller.)

Course Highlights

This course includes lecture notes, assignments, and a full set of video lectures.

Course Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

Special Features

Technical Requirements

Special software is required to use some of the files in this course: .jar, .mp4, .rm.

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Staff

Instructors:
Prof. Arthur Mattuck
Prof. Haynes Miller

Course Meeting Times

Lectures:
Three sessions / week
1 hour / session

Recitations:
Two sessions / week
1 hour / session

Level

Undergraduate

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