Convolution Formula

MIT Math Lecture: Differential Equations - 21 - Convolution Formula

Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. 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.

These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring 2003 and do not correspond precisely to the lectures taught in the Spring of 2006. Professor Mattuck has inspired and informed generations of MIT students with his engaging lectures. The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education. Note: Lecture 18, 34, and 35 are not available. This material was created or adapted from material created by MIT faculty member Arthur Mattuck, Professor. Copyright © 2003 Arthur Mattuck. For more videos from MIT, please visit: ocw.mit.edu. For more education videos, please visit: www.CosmoLearning.com