18.03 Differential Equations, Spring 2006
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18-03-spring-2006/contents/index.htm
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Author(s)
Miller, Haynes
Mattuck, Arthur
Alternative Title
Differential Equations
Date Issued
June 2006
Abstract
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.
Subjects
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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