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==Advanced Ordinary Differential Equations==
===Department of Mathematics, University of Toronto, Fall 2012===

{{12-267/Crucial Information}}

===Text===
Boyce and DiPrima, [http://ca.wiley.com/WileyCDA/WileyTitle/productCd-EHEP002451.html 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).

===Further Resources===

* [http://www.math.toronto.edu/undergrad/ Undergraduate Information] at the [http://www.math.toronto.edu/ UofT Math Department]

* [http://www.artsandscience.utoronto.ca/ofr/calendar/crs_mat.htm Undergraduate Course Descriptions].

* Vitali Kapovitch's 2007 classes: [http://www.math.toronto.edu/vtk/267/ Spring], [http://www.math.toronto.edu/vtk/267fall07/ Fall].

* Also previously taught by T. Bloom, C. Pugh, D. Remenik.

* My {{Pensieve Link|Classes/12-267/|12-267 notebook}}.

{{Template:12-267:Dror/Students Divider}}

[[User:Drorbn|Drorbn]] 06:36, 12 September 2012 (EDT): Material by [[User:Syjytg|Syjytg]] moved to [[12-267/Tuesday September 11 Notes]].

[http://imgur.com/a/OSx1U#0 Summary of techniques to solve differential equations ] [[User:Vsbdthrsh|Vsbdthrsh]]

[http://drorbn.net/index.php?title=12-267/Existence_And_Uniqueness_Theorem Fundamental Theorem and Proof from Lecture] [[User:Twine|Twine]]

[http://drorbn.net/index.php?title=12-267/Derivation_of_Euler-Lagrange Derivation of Euler-Lagrange from Lecture] [[User:Twine|Twine]]

[http://graphics.ethz.ch/teaching/former/vc_master_06/Downloads/viscomp-varcalc_6.pdf Useful PDF: proof of Euler-Lagrange equation, explanation, examples ] [[User:Vsbdthrsh|Vsbdthrsh]]

12-267 [http://math.hunter.cuny.edu/mbenders/cofv.pdf In-depth coverage of Calculus of Variations][[User:Simon1|Simon1]]

12-267 [http://highered.mcgraw-hill.com/sites/dl/free/007063419x/392340/Calculus_of_Variations.pdf A good summary of Calculus of Variations]
[[User:Simon1|Simon1]]

12-267 [http://imgur.com/a/1vy11#0 All class notes from September 10th to October 5th] [[User:Simon1|Simon1]]

12-267 [http://imgur.com/a/uLSlM Summary of Numerical Methods] [[User:Simon1|Simon1]]

[http://drorbn.net/index.php?title=Numerical_Methods Numerical Methods (wiki)] [[User:Twine|Twine]]

12-267 [http://imgur.com/a/tliYg Summary of Chapter 3 from the Textbook on Constant Coefficient Second Order ODEs] [[User:Simon1|Simon1]]

[http://drorbn.net/images/e/e6/Geometric_Interpretation_of_Lagrange_Multiplier.pdf Geometric Interpretation of Lagrange Multiplier] [[User:Mathstudent|Mathstudent]]

Past exams from [http://exams.library.utoronto.ca.myaccess.library.utoronto.ca/handle/exams/4429 December 2009] and [http://exams.library.utoronto.ca.myaccess.library.utoronto.ca/handle/exams/4429 December 2010] [[User:Twine|Twine]]

Handwritten notes by [[User:Ktnd3|Ktnd3]]:

* September: [[Media:Mat267_-_lecture_1(sep.10).PDF|10th]], [[Media:Mat267_-_lecture_2%28sep.11%29.PDF|11th]], [[Media:Mat267_-_lecture_3%28sep.14%29.PDF|14th]], [[Media:Mat267_-_lecture_4%28sep.17%29.PDF|17th]], [[Media:12-267%28lecture5%29.PDF|18th]], [[Media:12-267%28lecture6%29.PDF|21st]], [[Media:12-267%28lecture7%29.PDF|24th]], [[Media:12-267%28lecture8%29.PDF|25th]], [[Media:12-267%28lecture9%29.PDF|28th]]

* October: [[Media:12-267%28lecture10%29.PDF|1st]], [[Media:12-267%28lecture11%29.PDF|2nd]], [[Media:12-267%28lecture12%29.PDF|5th]], [[Media:12-267%28lecture13%29.PDF|9th]] [[Media:12-267%28lecture14%29.PDF|12th]]

[http://i.imgur.com/uTugV.jpg Quick guide: system of 1st order linear equations] [[User:Vsbdthrsh|Vsbdthrsh]]

Help of Inverse Matrix [http://mathworld.wolfram.com/MatrixInverse.html Matrix Inverse] [[User:Dongwoo.kang|Dongwoo.kang]]

12-267 [http://imgur.com/a/50sRR All class notes from October 5th to October 30th] [[User:Simon1|Simon1]]

[http://imgur.com/a/sZSYx#0 Quick guide: Power Series + ODE] [[User:Vsbdthrsh|Vsbdthrsh]]

[https://lh4.googleusercontent.com/-V1WnvvzXRlE/TxTGwl_BBjI/AAAAAAAAE9k/yVuy1zRmnWs/Gatos-cute-cute-32-800x500.jpg Mirrors do actually flip top-to-bottom, depending on how you look at them] [[User:jonathanrlove|jonathanrlove]]

[http://www.guardian.co.uk/notesandqueries/query/0,5753,-19877,00.html Actually, mirrors don't flip top-to-bottom *or* left-to-right] [[User:Twine|Twine]]

[[12-267/Topic_List|Topics covered this semester]] - [[User:Twine|Twine]]

(Summary of ODE) Hope it is Helpful.
[[Media:12-267(ODE-Summary).pdf]] -  [[User:Dongwoo.kang|Dongwoo.kang]]