7/27/2019 Video Lectures _ Differential Equations _ Mathematics _ MIT OpenCourseWare

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8/15/13 Video Lectures | Differential Equations | Mathematics | MIT OpenCourseWare

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Lecture 1: The Geometrical View of y'= f(x,y)

Lecture 2: Euler's Num erical Method for y'=f(x,y)

Lecture 3: Solving First-order Linear ODEs

Lecture 4: First-order Substitution Methods

Lecture 5: First-order Autonomous ODEs

Lecture 6: Complex Numbers and Com plex Exponentials

Lecture 7: First-order Linear with Constant Coefficients

Lecture 8: Continuation

Lecture 9: Solving Second-order Linear ODE's with Constant

Coefficients

These video lectures of Profess or Arthur Mattuck teaching 18.03 were recorded live in the Spring of 

2003 and do not correspond precise ly to the lectures taught in the Spring of 2010. This table (PDF)

provides a correlation between the video and the lectures in the 2010 version of the course.

The videotaping was made poss ible by The d'Arbeloff Fund for Excellence in MIT Education.

Note: Lecture 18, 34, and 35 are not available.

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7/27/2019 Video Lectures _ Differential Equations _ Mathematics _ MIT OpenCourseWare

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8/15/13 Video Lectures | Differential Equations | Mathematics | MIT OpenCourseWare

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Lecture 10: Continuation: Com plex Characteristic Roots

Lecture 11: Theory of General Second-order Linear 

Homogeneous ODEs

Lecture 12: Continuation: General Theory for Inhomogeneous

ODEs

Lecture 13: Finding Particular Solutions to Inhom ogeneous

ODEs

Lecture 14: Interpretation of the Exceptional Cas e: Resonance

Lecture 15: Introduction to Fourier Series

Lecture 16: Continuation: More General Periods

Lecture 17: Finding Particular Solutions via Fourier Series

Lecture 19: Introduction to the Laplace Transform

Lecture 20: Derivative Formu las

Lecture 21: Convolution Formula

Lecture 22: Using Laplace Transform to Solve ODEs with

Discontinuous Inputs

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7/27/2019 Video Lectures _ Differential Equations _ Mathematics _ MIT OpenCourseWare

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8/15/13 Video Lectures | Differential Equations | Mathematics | MIT OpenCourseWare

ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ 3/4

Lecture 24: Introduction to First-order Systems o f ODEs

Lecture 25: Homogeneous Linear Systems with Constant

Coefficients

Lecture 26: Continuation: Repeated Real Eigenvalues

Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear 

System with Cons tant Coefficients

Lecture 28: Matrix Methods for Inhomogeneous Systems

Lecture 29: Matrix Exponentials

Lecture 30: Decoupling Linear Systems with Constant

Coefficients

Lecture 31: Non-linear Autonomous Systems

Lecture 32: Limi t Cycles

Lecture 33: Relation Between Non-linear Systems and First-

order ODEs

Lecture 23: Use with Impulse Inputs

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7/27/2019 Video Lectures _ Differential Equations _ Mathematics _ MIT OpenCourseWare

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8/15/13 Video Lectures | Differential Equations | Mathematics | MIT OpenCourseWare

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