|Additions to this web site no longer count towards good deed points.
||Notes and Links
||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.
|| Monday: Separated equations, escape velocities. HW1. Tuesday: Escape velocities, changing source and target coordinates, homogeneous equations. Friday: Reverse engineering separated and exact equations.
|| Monday: Solving exact equations, integration factors. HW2. Tuesday: Statement of the Fundamental Theorem. Class Photo. Friday: Proof of the Fundamental Theorem.
|| 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.
||Monday is thanksgiving. Tuesday: Lagrange multiplyers and the isoperimetric inequality. HW4. Friday: More Lagrange multipliers, numerical methods.
|| 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.
|| Monday: Multiple roots, reduction of order, undetermined coefficients. Tuesday: From systems to matrix exponentiation. HW5. Term Test on Friday.
|| 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
|| Monday: Non-homogeneous systems. Tuesday: The Catalan numbers, power series, and ODEs. Friday: Global existence for linear ODEs, the Wronskian.
||Monday-Tuesday is UofT November break. HW7. Friday: Series solutions for .
|| 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..
|| 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.
|| Monday: More Sturm comparisons, changing the independent variable. Tuesday: Amplitudes of oscillations. Last class was on Tuesday!
||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 Bar-Natan, firstname.lastname@example.org, Bahen 6178, 416-946-5438. Office hours: by appointment.
Classes: Mondays, Tuesdays, and Fridays 9-10 in RW 229.
||Teaching Assistant: Jordan Bell, email@example.com.
Tutorials: Tuesdays 10-11 at RW 229. No tutorials on the first week of classes.
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).
- 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 12-267/Tuesday September 11 Notes.
Summary of techniques to solve differential equations Vsbdthrsh
Fundamental Theorem and Proof from Lecture Twine
Derivation of Euler-Lagrange from Lecture Twine
Useful PDF: proof of Euler-Lagrange equation, explanation, examples Vsbdthrsh
12-267 In-depth coverage of Calculus of VariationsSimon1
12-267 A good summary of Calculus of Variations
12-267 All class notes from September 10th to October 5th Simon1
12-267 Summary of Numerical Methods Simon1
Numerical Methods (wiki) Twine
12-267 Summary of Chapter 3 from the Textbook on Constant Coefficient Second Order ODEs Simon1
Geometric Interpretation of Lagrange Multiplier Mathstudent
Past exams from December 2009 and December 2010 Twine
Handwritten notes by Ktnd3: