## MIT 18.03 Differential Equations - Spring 2006

recorded by: Massachusetts Institute of Technology, MIT

released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

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.

**Course Homepage** 18.03 Differential Equations Spring 2006

**Course features at MIT OpenCourseWare page**:

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**Complete MIT OCW video collection at MIT OpenCourseWare - VideoLectures.NET**

## Unit I: First Order Differential Equations | ||||

## Unit II: Second Order Constant Coefficient Linear Equations | ||||

## Unit III: Fourier Series and Laplace Transform | ||||

## IV: First-order Systems | ||||

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