© | Dror Bar-Natan: Classes: 2012-13: Math 267 ODEs:  < > 

121130 Video

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Notes on 12-267-121130:    [edit, refresh]

Non-oscillation, Sturm comparison.


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# Week of... Notes and Links
1 Sep 10 About This Class. dbnvp Monday: Introduction and the Brachistochrone. dbnvp Tuesday: More on the Brachistochrone, administrative issues. Tuesday Notes. dbnvp Friday: Some basic techniques: first order linear equations.
2 Sep 17 dbnvp Monday: Separated equations, escape velocities. HW1. dbnvp Tuesday: Escape velocities, changing source and target coordinates, homogeneous equations. dbnvp Friday: Reverse engineering separated and exact equations.
3 Sep 24 dbnvp Monday: Solving exact equations, integration factors. HW2. dbnvp Tuesday: Statement of the Fundamental Theorem. Class Photo. dbnvp Friday: Proof of the Fundamental Theorem.
4 Oct 1 dbnvp Monday: Last notes on the fundamental theorem. HW3. dbnvp Tuesday Hour 1: The chain law, examples of variational problems. dbnvp Tuesday Hour 2: Deriving Euler-Lagrange. dbnvp Friday: Reductions of Euler-Lagrange.
5 Oct 8 Monday is thanksgiving. dbnvp Tuesday: Lagrange multiplyers and the isoperimetric inequality. HW4. dbnvp Friday: More Lagrange multipliers, numerical methods.
6 Oct 15 dbnvp Monday: Euler and improved Euler. dbnvp Tuesday: Evaluating the local error, Runge-Kutta, and a comparison of methods. dbnvp Friday: Numerical integration, high order constant coefficient homogeneous linear ODEs.
7 Oct 22 dbnvp Monday: Multiple roots, reduction of order, undetermined coefficients. dbnvp Tuesday: From systems to matrix exponentiation. HW5. Term Test on Friday.
8 Oct 29 dbnvp Monday: The basic properties of matrix exponentiation. dbnvp Tuesday: Matrix exponentiation: examples. dbnvp Friday: Phase Portraits. HW6. Nov 4 was the last day to drop this class
9 Nov 5 dbnvp Monday: Non-homogeneous systems. dbnvp Tuesday: The Catalan numbers, power series, and ODEs. dbnvp Friday: Global existence for linear ODEs, the Wronskian.
10 Nov 12 Monday-Tuesday is UofT November break. HW7. dbnvp Friday: Series solutions for y'=f(x,y).
11 Nov 19 dbnvp Monday: \pi is irrational, more on the radius of convergence. dbnvp Tuesday (class): Airy's equation, Fuchs' theorem. dbnvp Tuesday (tutorial): Regular singular points. HW8. dbnvp Friday: Discussion of regular singular points..
12 Nov 26 dbnvp Monday: Frobenius series by computer. Qualitative Analysis Handout (PDF). dbnvp Tuesday: The basic oscillation theorem. Handout on the Frobenius Method. HW9. dbnvp Friday: Non-oscillation, Sturm comparison.
13 Dec 3 dbnvp Monday: More Sturm comparisons, changing the independent variable. dbnvp 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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0:00:00 [edit] Handwritten lecture notes by Ktnd3: 12-267(lecture32).PDF
0:00:02 [add] Today's Catalan.
0:04:18 [add] Reminders
0:09:16 [add] The non-oscillation theorem.
0:13:51 [add] The non-oscillation theorem (2).
0:21:07 [add] The non-oscillation theorem (3).
0:27:15 [add] The non-oscillation theorem (4).
0:31:07 [add] The non-oscillation theorem (5).
0:35:19 [add] $y''+x^\alpha y=0$.
0:40:35 [add] The Sturm Comparison Theorem.
0:43:36 [add] The Sturm Comparison Theorem (2).
0:47:19 [add] The Sturm Comparison Theorem (3).
0:53:24 [add] More on $y''+x^\alpha y=0$.