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.

2/14

Lagrangian Dynamics: L = K - P

Euler equation:  d/dt ( dL/d(udot) ) = dL/du ... can recover Newton from here and in addition provides other insights

Ex. rederive the mass spring equations with Lagrange/Euler

Test 1: problem 7 - logistic model - brute force versus phase space (fixed pts) qualitative analysis

2.1 Equliibrium and the Stiffness Matrix                                                                                          

2/21

2.1 Masses and Springs via the Applied Mathematics Framework  K = A'CA                                  p109 / 1,2,3

2/23

2.2 Oscillation: Mu'' + Ku = 0                                                               p60 / 23-25

Spring Break

3/13

Test 2

3/20

3.1 Differential Equations and Finite Elements                                       p242 / 1 try

3/22

4/03

3.1 Finite Elements, Part II                                                                  p242 / 1,2,3,10,11 

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