# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Mon, Oct 31, 2016 9:10 AM (1 year ago)

### vectors, dot, and cross

assigned today:
• standard-dot and cross:

I can manipulate vectors and their products.

1. 9.1.38 (any 2)
2. 9.2.35 (perpendicular diagonals of parallelogram
3. Prove that the velocity of a point on a spinning solid object is given by $$\vec{\omega}\times\vec{r}$$.

Due today:
• standard-Laplace transforms:

I can use Laplace transforms to solve differential equations.

1. Compare and contrast the Laplace transform and eigensystem approach to second order differential equations with constant coefficients.
2. Any problems from chapter 6 review 29-33.
3. For a spring system with m=1, viscosity=2, and k=10, determine a plot of the trajectory of the system if x(0)=x'(0)=0 and the driving function is 2 from t=0 to t=1, -2 from t=2 to t=3 and zero otherwise. Use a convolution approach.

# in class

• Decided to do new material after all (instead of review day)
• Had them do Corinne's dot product activity on the board (in 3 groups)
• good discussion about how doing the axes first really helps
• Talked about the 3 problems and decided to focus on the third one for the last 20 minutes
• used a stool as the rigid body
• verified the direction predicted by $$\vec{\omega}\times\vec{r}$$.
• worked on the magnitude by considering the circle that location would make when spinning

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