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.
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Below are the lecture notes for every lecture session. Some lecture sessions also have supplementary files called "Muddy Card Responses." Students pick up half pages of scrap paper when they come into the classroom, jot down on them what they found to be the most confusing point in the day's lecture or the question they would have liked to ask. Responses are then made available to all students on the class Web site.
I. First-order Differential Equations
Simple Models and Separable Equations
Direction Fields, Existence and Uniqueness of Solutions (PDF)
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.