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Week of...

Notes and Links

1

Sep 10

About This Class. Monday: Introduction and the Brachistochrone. Tuesday: More on the Brachistochrone, administrative issues. Tuesday Notes. Friday: Some basic techniques: first order linear equations.

2

Sep 17

Monday: Separated equations, escape velocities. HW1. Tuesday: Escape velocities, changing source and target coordinates, homogeneous equations. Friday: Reverse engineering separated and exact equations.

3

Sep 24

Monday: Solving exact equations, integration factors. HW2. Tuesday: Statement of the Fundamental Theorem. Class Photo. Friday: Proof of the Fundamental Theorem.

4

Oct 1

Monday: Last notes on the fundamental theorem. HW3. Tuesday Hour 1: The chain law, examples of variational problems. Tuesday Hour 2: Deriving EulerLagrange. Friday: Reductions of EulerLagrange.

5

Oct 8

Monday is thanksgiving. Tuesday: Lagrange multiplyers and the isoperimetric inequality. HW4. Friday: More Lagrange multipliers, numerical methods.

6

Oct 15

Monday: Euler and improved Euler. Tuesday: Evaluating the local error, RungeKutta, and a comparison of methods. Friday: Numerical integration, high order constant coefficient homogeneous linear ODEs.

7

Oct 22

Monday: Multiple roots, reduction of order, undetermined coefficients. Tuesday: From systems to matrix exponentiation. HW5. Term Test on Friday.

8

Oct 29

Monday: The basic properties of matrix exponentiation. Tuesday: Matrix exponentiation: examples. Friday: Phase Portraits. HW6. Nov 4 was the last day to drop this class

9

Nov 5

Monday: Nonhomogeneous systems. Tuesday: The Catalan numbers, power series, and ODEs. Friday: Global existence for linear ODEs, the Wronskian.

10

Nov 12

MondayTuesday is UofT November break. HW7. Friday: Series solutions for $y'=f(x,y)$.

11

Nov 19

Monday: $\pi$ is irrational, more on the radius of convergence. Tuesday (class): Airy's equation, Fuchs' theorem. Tuesday (tutorial): Regular singular points. HW8. Friday: Discussion of regular singular points..

12

Nov 26

Monday: Frobenius series by computer. Qualitative Analysis Handout (PDF). Tuesday: The basic oscillation theorem. Handout on the Frobenius Method. HW9. Friday: Nonoscillation, Sturm comparison.

13

Dec 3

Monday: More Sturm comparisons, changing the independent variable. Tuesday: Amplitudes of oscillations. Last class was on Tuesday!

F1

Dec 10


F2

Dec 17

The Final Exam (time, place, style, office hours times)

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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 BarNatan, drorbn@math.toronto.edu, Bahen 6178, 4169465438. Office hours: by appointment.
Classes: Mondays, Tuesdays, and Fridays 910 in RW 229.

Teaching Assistant: Jordan Bell, jordan.bell@utoronto.ca.
Tutorials: Tuesdays 1011 at RW 229. No tutorials on the first week of classes.

Text
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 12267/Tuesday September 11 Notes.
Summary of techniques to solve differential equations Vsbdthrsh
Fundamental Theorem and Proof from Lecture Twine
Derivation of EulerLagrange from Lecture Twine
Useful PDF: proof of EulerLagrange equation, explanation, examples Vsbdthrsh
12267 Indepth coverage of Calculus of VariationsSimon1
12267 A good summary of Calculus of Variations
Simon1
12267 All class notes from September 10th to October 5th Simon1
12267 Summary of Numerical Methods Simon1
Numerical Methods (wiki) Twine
12267 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
12267 All class notes from October 5th to October 30th Simon1
Quick guide: Power Series + ODE Vsbdthrsh
Mirrors do actually flip toptobottom, depending on how you look at them jonathanrlove
Actually, mirrors don't flip toptobottom *or* lefttoright Twine
Topics covered this semester  Twine
(Summary of ODE) Hope it is Helpful.
Media:12267(ODESummary).pdf  Dongwoo.kang
A full exposition on most of the topics covered Samer