18.03 Differential Equations, Spring 2006
Author(s)Miller, Haynes; Mattuck, Arthur
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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.
Ordinary Differential Equations, ODE, modeling physical systems, first-order ODE's, Linear ODE's, second order ODE's, second order ODE's with constant coefficients, Undetermined coefficients, variation of parameters, Sinusoidal signals, exponential signals, oscillations, damping, resonance, Complex numbers and exponentials, Fourier series, periodic solutions, Delta functions, convolution, Laplace transform methods Matrix systems, first order linear systems, eigenvalues and eigenvectors, Non-linear autonomous systems, critical point analysis, phase plane diagrams