| Additions to this web site no longer count towards good deed points.
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| #
| Week of...
| Notes and Links
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| 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.
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| 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.
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| 3
| Sep 24
| Monday: Solving exact equations, integration factors. HW2. Tuesday: Statement of the Fundamental Theorem. Class Photo. Friday: Proof of the Fundamental Theorem.
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| 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.
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| 5
| Oct 8
| Monday is thanksgiving. Tuesday: Lagrange multiplyers and the isoperimetric inequality. HW4. Friday: More Lagrange multipliers, numerical methods.
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| 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.
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| 7
| Oct 22
| Monday: Multiple roots, reduction of order, undetermined coefficients. Tuesday: From systems to matrix exponentiation. HW5. Term Test on Friday.
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| 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
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| 9
| Nov 5
| Monday: Non-homogeneous systems. Tuesday: The Catalan numbers, power series, and ODEs. Friday: Global existence for linear ODEs, the Wronskian.
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| 10
| Nov 12
| Monday-Tuesday is UofT November break. HW7. Friday: Series solutions for y' = f(x,y).
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| 11
| Nov 19
| Monday: π 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..
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| 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.
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| 13
| Dec 3
| Monday: More Sturm comparisons, changing the independent variable. Tuesday: Amplitudes of oscillations. Last class was on Tuesday!
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| F1
| Dec 10
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| F2
| Dec 17
| The Final Exam (time, place, style, office hours times)
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