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Advanced Ordinary Differential Equations

Department of Mathematics, University of Toronto, Fall 2012

Agenda: If calculus is about change, differential equations are the equations governing change. We'll learn much about these, and nothing's more important!

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes: Mondays, Tuesdays, and Fridays 9-10 in RW 229.

Teaching Assistant
Teaching Assistant: Jordan Bell, jordan.bell@utoronto.ca.

Tutorials: Tuesdays 10-11 at RW 229. No tutorials on the first week of classes.


Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (current edition is 9th and 10th will be coming out shortly. Hopefully any late enough edition will do).

Further Resources

  • Also previously taught by T. Bloom, C. Pugh, D. Remenik.
Dror's notes above / Student's notes below

Drorbn 06:36, 12 September 2012 (EDT): Material by Syjytg moved to 12-267/Tuesday September 11 Notes.

Summary of techniques to solve differential equations Vsbdthrsh

Fundamental Theorem and Proof from Lecture Twine

Derivation of Euler-Lagrange from Lecture Twine

Useful PDF: proof of Euler-Lagrange equation, explanation, examples Vsbdthrsh

12-267 In-depth coverage of Calculus of VariationsSimon1

12-267 A good summary of Calculus of Variations Simon1

12-267 All class notes from September 10th to October 5th Simon1

12-267 Summary of Numerical Methods Simon1

Numerical Methods (wiki) Twine

12-267 Summary of Chapter 3 from the Textbook on Constant Coefficient Second Order ODEs Simon1

Past exams from December 2009 and December 2010 Twine

Handwritten notes by Ktnd3:

Quick guide: system of 1st order linear equations Vsbdthrsh

Help of Inverse Matrix Matrix Inverse Dongwoo.kang

12-267 All class notes from October 5th to October 30th Simon1

Quick guide: Power Series + ODE Vsbdthrsh

Mirrors do actually flip top-to-bottom, depending on how you look at them jonathanrlove

Actually, mirrors don't flip top-to-bottom *or* left-to-right Twine

Topics covered this semester - Twine

(Summary of ODE) Hope it is Helpful. Media:12-267(ODE-Summary).pdf - Dongwoo.kang

A full exposition on most of the topics covered Samer