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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 Euler-Lagrange.  Friday: Reductions of Euler-Lagrange.
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, Runge-Kutta, 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: Non-homogeneous systems.  Tuesday: The Catalan numbers, power series, and ODEs.  Friday: Global existence for linear ODEs, the Wronskian.
10	Nov 12	Monday-Tuesday 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: Non-oscillation, Sturm comparison.
13	Dec 3	Monday: More Sturm comparisons, changing the independent variable. UofT Fall Semester ends Wednesday; Wednesday is UofT Monday, we'll hold class!
F1	Dec 10
F2	Dec 17	The Final Exam (time, place, style, office hours times)
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