This course will be an introduction to ordinary differential equations.

Announcements

• (12/08): Finals are now available for pickup. Thanks for a great quarter!
• (12/01): Office hours next week will be on Tuesday 2:00-4:00pm in 155 Sloan.
• (10/10): My office hours this week will be Thursday 2:00-3:00pm in 155 Sloan, right after recitation.
• (09/29): My office hours this Friday are 3:00-4:00pm in 155 Sloan.
• Please fill out and return the questionnaire to me during office hours.

Lecture Notes

• Lecture 1 (09/29): How to solve differential equations, guessing, existence and uniqueness of solutions to ODES, first order ODEs, integrating factors, separable differential equations, tips for writing up the homework.
• Lecture 2 (10/06): HW remarks, how to solve exact equations, finding integrating factors for exactness, difference equations.
• Lecture 3 (10/13): Linear and nonlinear first-order difference equations, analyzing complex solutions to difference equtaions, Euler's method.
• Lecture 4 (10/20): Midterm information, two problems on solving systems of differential equations, midterm advice.
• Lecture 5 (10/27): Linear independence of solutions, the Wronskian, Abel's identity.
• Lecture 6 (11/03): Nonhomogeneous linear systems of differential equations, the matrix exponential operator.
• Lecture 7 (11/10): Variation of parameters for 2nd order nonhomogeneous linear ODEs, variation of parameters for 3rd order and higher, how not to use the variation of parameters.
• Lecture 8 (11/17): Review of power series, analyticity, radius of convergence, series solution method for ODEs.
• Lecture 9 (12/01): The Laplace transform, inverse Laplace transform, and convolution.

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