EE575: HOMEWORK 2 (DUE 02/13/2020)
Problem 1. Simulate 1D metal rod of unit length. Use 1D assumptions (constant
temperature across crossection etc). Initial temperature f(x, 0) = 1
x+0.1
sin(2πx),
boundary conditions f(0, t) = f(L, t) = 0. Run the heat equation and plot the temperature as a function of time. (Hint: Refer to the handout posted on blackboard
for some useful source code). (10pt)
Problem 2. Simulate 2D unit square plate using a 256x256 regular grid, with initial temperature f(x, y, t = 0) = sin(2πx)cos(2πy). Assume the Dirichlet boundary
conditions of 0 temperature on the boundary. Run the heat equation and plot the
temperature distribution as a function of time. Take any black and white 256x256
image and run the heat equation on the intensity values. Show the smoothing
behavior of the heat equation. (Extra credit (2pt): Create a movie showing heat
change over a period of time). Hint: Check delsq function in matlab. (10pt)
Problem 3. (4pt) (Straight Lines as Shortest) Let α : I → R
3 be a parameterized
curve. Let [a, b] ⊂ I and set α(a) = p, α(b) = q.
a. (2pt) Show that, for any constant vector v, |v| = 1,