Class Diary for M531, Fall 2016, Jochen Denzler
Wed Aug 17:
Intro: Def and key examples for ODEs.
Fri Aug 19:
Autonomous ODEs; conversion to 1st order systems (autonomous if desired).
Local existence and uniqueness; examples, and examples where uniqueness fails.
Results and def of Lipschitz satted; proofs follow later.
Mon Aug 22:
Algebraic methods for specific first order ODEs. Qualitative analysis
sketched.
Wed Aug 24:
Banach's Fixed Point Theorem
Fri Aug 26:
Local Existence and Uniqueness Proof; Variant with weighted norm sketched.
Hwk 1-5 due Sep 07.
Mon Aug 29:
variant of BFPT. Compactness in C^0 and Arzela-Ascoli. Proof of Peano by
explicit Euler method (sketched).
Wed Aug 31:
Schauders FPT stated and explained; proof of Peano by using Schauder
Fri Sep 02:
maximum existence interval and extension; if ifnite existence time; soln must
leave every compact set. Continuous dependence on initial data by `uniqueness
implies continuous dependence' argument.
Mon Sep 05:
LABOR DAY
Wed Sep 07:
Cont dependence on parameter finished. Semicontinuity of maximal existence
time. Intro to Gronwall's inequality, towards Lip dependence on initial data.
Fri Sep 09:
Proof of Gronwall and Lipschitz dependence on data; preliminary
comments on differentiable dependence; example.
Mon Sep 12:
Differentiable dependence on initial data
Wed Sep 14:
Linear hom ODE systems. Case of const coeff's. Matrix exponential introduced.
Fri Sep 16:
Practical calculation of matrix exps; Jordan normal form. Phase space.
Mon Sep 19:
Wed Sep 21:
Fri Sep 23:
Mon Sep 26:
Wed Sep 28:
Fri Sep 30:
Mon Oct 03:
Wed Oct 05:
Fri Oct 07:
FALL BREAK
Mon Oct 10:
Wed Oct 12:
Fri Oct 14:
Mon Oct 17:
Wed Oct 19:
Fri Oct 21:
Mon Oct 24:
Wed Oct 26:
Fri Oct 28:
Mon Oct 31:
Wed Nov 02:
Fri Nov 04:
Mon Nov 07:
Wed Nov 09:
Fri Nov 11:
Mon Nov 14:
Wed Nov 16:
Fri Nov 18:
Mon Nov 21:
Wed Nov 23:
Fri Nov 25:
THANKSGIVING BREAK
Mon Nov 28:
Wed Nov 30:
FIRST STUDY DAY
Fri Dec 02: SECOND STUDY DAY
Wed Dec 07: FINAL EXAM 12:30-02:30
(scheduled by university policy)
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