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Week of...
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Notes and Links
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Sep 10
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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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Sep 17
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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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Sep 24
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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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Oct 1
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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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Oct 8
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Monday is thanksgiving. Tuesday: Lagrange multiplyers and the isoperimetric inequality. HW4. Friday: More Lagrange multipliers, numerical methods.
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Oct 15
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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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Oct 22
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Monday: Multiple roots, reduction of order, undetermined coefficients. Tuesday: From systems to matrix exponentiation. HW5. Term Test on Friday.
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Oct 29
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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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Nov 5
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Monday: Non-homogeneous systems. Tuesday: The Catalan numbers, power series, and ODEs. Friday: Global existence for linear ODEs, the Wronskian.
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Nov 12
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Monday-Tuesday is UofT November break. HW7. Friday: Series solutions for  .
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Nov 19
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Monday:  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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Nov 26
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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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Dec 3
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Monday: More Sturm comparisons, changing the independent variable. Tuesday: Amplitudes of oscillations. Last class was on Tuesday!
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| F1
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Dec 10
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Dec 17
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The Final Exam (time, place, style, office hours times)
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Add your name / see who's in!
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Complex Variables
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.
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Teaching Assistant: Jordan Bell, jordan.bell@utoronto.ca.
Tutorials: Tuesdays 10-11 at RW 229. No tutorials on the first week of classes.
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Text
TBD.
Further Resources
- Also previously taught by T. Bloom, C. Pugh, D. Remenik.
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Dror's notes above / Student's notes below
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