Inspired by Prof. Strang's CSE, beautiful Ocw courses: 85 and 86, videos: 85 (*), 86, and MIT homes: 85, 86.

HW:

1/17/2012
Illustrate modeling with the mass-spring oscillations example                 HW: finish the problems started in class

Start with the simplest model that makes sense and successively refine.
Guessing and checking solutions.

Linearity and superposition principle.

1/19
Review DE and LA (matrices).                                       Work through Sect 1.1

Watch MIT Lect. 1. Four Special Matrices                        1.1 p9 / 1-5 try

1/24

We like simple models, because we can solve them. Then we critique them - find what important aspect of reality they fail to capture.       

In the process, it may happen that the model becomes hard to solve.                                             HW. illustrate with growth model, exponential --> logistic

Generalize the mass-spring model to several masses and springs -> stiffness matrix K.

K2 = [2 -1; -1 2]

1/26

Watch Linear Algebra (Vectors and Matrices) Review             
Continue with HW; come ready with questions to next class.

1/31
Wave equation u_tt = c^2 u_xx as an example of a PDE.
Finding / checking solutions by "guess and check".

Systems of ODEs as models of time dependent problems - eigenvalues and eigenvectors.     p60 / 23-25 try

2/2
Practice for Test 1

2/7  Test 1

2/9

Difference Equations - another way to introduce Kn, Tn, Bn and Cn.

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Skim through the rest of the book - you may find ideas for projects that you can present at hrumc