Main Content

Jan-22-2015
First Meeting
ODEs: Classification, Examples, Euler's Method (first look)
[Notes #1]
Movies:

• [unforced]
• [forced]
• [geocentric]

Jan-27-2015
Calculus and Math 541 Review
[Notes #2]
Movies:

• Calc. – Differentiability
• Calc. – Rolle's Theorem
• Calc. – MVT

Jan-29-2015
Euler's Method, a second look
[Notes #3] [HW#1]
Movies:

• [euler_stab]
• [taylor_example]
• [Harmonic Oscillator (Euler Simulation)]

Feb-03-2015
Stability Regions
Runge-Kutta Methods
[Notes #4] [Code]

Feb-05-2015
Runge-Kutta Methods, Modern Approach
[Notes #5] [HW#2]

Feb-10-2015
Application of RK Methods to Lotka-Volterra Models
[Notes #5.5] [Resources]
Movies:

• [lynx_hare_01]
• [lynx_hare_02]

Feb-12-2015
Linear Multistep Methods, I
[Notes #6]

Feb-17-2015
Linear Multistep Methods, II
[Notes #7] [HW#3]
Movies:

• [ab_stabregs]
• [am_stabregs]

Feb-19-2015
Example: The Lorenz System
[Notes #8]
Movies:

• Lorenz 3D
  • [r=0.5], [r=2.5], [r=10], [r=24], [r=28], [r=55], [r=100], [r=101], [r=150], [r=170], [r=220]
• [Lorenz 3D (chaos)]
• [Lorenz 5D]
• [Lorenz 6D]
• [Rossler]

Feb-24-2015
Predictor-Corrector Methods
[Notes #9] [HW #4]

Feb-26-2015
Stiff ODEs -- Multiscale Phenomena
[Notes #10]

Mar-03-2015
Runge-Kutta Methods for Stiff ODEs
[Notes #11] [HW #5]

Mar-05-2015
Linear Multistep Methods for Stiff Systems
[Notes #12]

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]

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]

Mar-26-2015
Boundary Value Problems – Introduction
[Notes #18]

Apr-07-2015
BVP: The Shooting Method, ctd.
[Notes #19]
Movies:

• [beam]

Apr-09-2015
Finite Difference Methods
[Notes #20]

Apr-14-2015
Higher Order Equations (FD)
[Notes #21]

Apr-16-2015
Nonlinear Equations
[Notes #22]
Unopened Cans of Worms
[Topics #1]
Movies:

• [DoublePendulum]

Apr-21-2015
The Finite Element Method – Introduction; Basic Theory
[FEM #1]

Apr-23-2015
The Finite Element Method – Continued; Numerics
[FEM #2]

Apr-28-2015
FEM: Numerics, Triangulation, Element Stiffness Matrix
FEM: Hilbert Spaces --- L₂(D), H¹(D), and H¹₀(D)
FEM: Geometric Interpretation
[FEM #3]