1. Solve Heath Exc 1.4 (page 42). Show your calculations.
2. Solve Heath Exc 1.6 (page 42). Show your calculations.
3. While basking on Seba beach of Wabamun lake (west of Edmonton), in the distance I can just barely see the very top of the three power plant chimneys over at the eastern end of the lake. Determine the height of the chimney's with error margins. Assume the earth radius r=6366km, and make appropriate measurements with error margins in the map below. (You can assume the powerplant is in Kapasiwin. When driving it is also visible from the road, so I think more precisely it is in the north east corner of the map.
4. Solve Heath Exc 2.17 (page 97) Note: Show your solution steps in obtaining the LU factorization. Ie you cannot just type it into matlab, but have to hand-calculate this small LU factorization... (But you may use matlab to check your result.)
5. Farmer McDonald runs an organic and ecological operation on his rural Alberta property. Instead of burning non-renewable fossil fuels, he takes advantage of the heat emitted by the animals. Each cow emits 300 W, and each pig 250 W. He is contemplating building a new three room barn (in the third roomis Hay, which emits no heat), and has enlisted the help of the numerical methods students to help with the calculation of the temperature he can expect in each room. The architect has provided the following drawing of the barn plus inhabitants:
Let the outside temperature T0 be a balmy -20C. The heat conductance between the various rooms are as follows: k12 = k13 = k23 = 45 W/C, k10 = k20 = 25 W/C, k30 = 105 W/C.
From the laws of physics we know that energy is conserved. Hence
for each room, the sum of the total heat energy emitted by the animals
and the heat energy leaking leaking through the walls is zero.
The heat leakage through a wall depends on two things, the temperature
difference across the wall and the heat conductivity of the wall
and is given by P = k(To-Ti).
Hence for each room we can derive one heat balance equation in the unknown T1,T2,T3. Together we have three equations, which can be solved for the temperature in each room. Derive and solve these equations.
6. Open ended question: When was this satellite picture of campus taken? Try to find cues in the image, calculate date and time. Describe your assumptions, conclusions and error analysis.
