Peter Blomgren
San Diego State University
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Math 542: Numerical Solutions to Differential Equations Spring 2015
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Evolving Schedule (topics arranged by "target week.")

Week # Tuesday Thursday
1 Jan-20-2015

Martin Luther King, Jr. Day (January 20th)
Jan-22-2015
First Meeting
ODEs: Classification, Examples, Euler's Method (first look)
[Notes #1]
Movies:
2 Jan-27-2015
Calculus and Math 541 Review
[Notes #2]
Movies:
Jan-29-2015
Euler's Method, a second look
[Notes #3] [HW #1]
Movies:
3 Feb-03-2015
Stability Regions
Runge-Kutta Methods
[Notes #4] [Code]
Feb-05-2015
Runge-Kutta Methods, Modern Approach
[Notes #5] [HW #2]
HW#1 Due (Friday)
4 Feb-10-2015
Application of RK Methods to Lotka-Volterra Models
[Notes #5.5] [Resources]
Movies:
Feb-12-2015
Linear Multistep Methods, I
[Notes #6]
5 Feb-17-2015
Linear Multistep Methods, II
[Notes #7] [HW #3]
Movies:
Feb-19-2015
Example: The Lorenz System
[Notes #8]
Movie:
HW#2 Due (Friday)
6 Feb-24-2015
Predictor-Corrector Methods
[Notes #9] [HW #4]
Feb-26-2015
Stiff ODEs -- Multiscale Phenomena
[Notes #10]
7 Mar-03-2015
Runge-Kutta Methods for Stiff ODEs
[Notes #11] [HW #5]
Mar-05-2015
Linear Multistep Methods for Stiff Systems
[Notes #12]
HW#3 Due (Friday)
8 Mar-10-2015
Example: Variable Order LMM Schemes
[Notes #15]
Projects!!! [past]
Example(RK): The Van der Pol Equation
[Notes #13] [Code]
Mar-12-2015
Example: Adaptive RKF45 Solver
[Notes #14]
9 Mar-17-2015
Hybrid Methods
[Notes #16]

Consider (in matlab): syms x; p = 7*x^7 + 5*x^5 + 1; coeffs(p), feval(symengine,'coeff',p,x,'All'), sym2poly(p)
Mar-19-2015
General Linear Methods
[Notes #17]
HW#4 Due (Friday)
10 Mar-24-2015
Professor is coughing, sneezing, non-speaking BIOHAZARD, class and office hours cancelled
Mar-26-2015
Boundary Value Problems – Introduction
[Notes #18]
- Mar-31-2015
Spring Break

Cesar Chavez Day (March 31st)
Apr-02-2015
Spring Break
11 Apr-07-2015
BVP: The Shooting Method, ctd.
[Notes #19]
Movies:
Apr-09-2015
Finite Difference Methods
[Notes #20]
HW#5 Due (Friday)
12 Apr-14-2015
Higher Order Equations (FD)
[Notes #21]
Apr-16-2015
Nonlinear Equations
[Notes #22]
Unopened Cans of Worms
[Topics #1]
Movies:
13 Apr-21-2015
The Finite Element Method – Introduction; Basic Theory
[FEM #1]
Apr-23-2015
The Finite Element Method – Continued; Numerics
[FEM #2]

Presentation Scheduling: Slots arranged by random drawing ON THE DAY of presentation. Volunteer for bonus(*) / penalty for skipping. (*) Bonus can be later presentantion in Math 693B
14 Apr-28-2015
FEM: Numerics, Triangulation, Element Stiffness Matrix
FEM: Hilbert Spaces --- L2(D), H1(D), and H10(D)
FEM: Geometric Interpretation
[FEM #3]
Apr-30-2015
Project Presentations (12–15 min)
01. 11:00p  Pr.Ke. (volunteer)
02. 11:15p  Pi.Wi. (volunteer)
03. 11:30p  Ne.Pa. (volunteer)
04. 11:45p  Ju.Su. (volunteer)
05. 12:00p  He.Hu. (volunteer)
15 May-05-2015
Project Presentations (12–15 min)
06. 11:00p  Uy.Ho. (volunteer)
07. 11:15p  Jo.Mu. (volunteer)
08. 11:30p  Th.Mo. (volunteer)
09. 11:45p  Jo.An. (volunteer)
10. 12:00p  Wi.Ma. (volunteer)
May-07-2015
Project Presentations (12–15 min)
11. 11:00p  Da.Ar. (volunteer)
12. 11:15p  S.Han. (volunteer)
13. 11:30p  Ef.Li. (volunteer)
14. 11:45p  S.Has. (lucky draw)
15. 12:00p  Ju.Wa. (volunteer)
Finals May-12-2015
Project Presentations (12–15 min)
16. 10:30p  __.__.
17. 10:45p  __.__.
18. 11:00p  __.__.
19. 11:15p  __.__.
20. 11:30p  __.__.
21. 11:45p  __.__.
22. 12:00p  __.__.
23. 12:15p  __.__.
May-14-2015

Please verify that I have received all your homeworks (hard or soft copy), and project (code + movies + presentation; soft copy)
Unused
Modules
Spectral Methods See Math 693B - Spring 2015

Reference: Spectral Methods in MATLAB
Spectral Methods, I
Spectral Methods, II
Spectral Methods, III

Homework and Projects will be assigned.

Copyright © 2017 Peter Blomgren.