CME381 Homework 5 – This is all to be submitted in a single Excel workbook with a sheet for each problem

- Consider the square heated plate from slide 9 of the PDE slide show, where the top boundary is at 100˚C, the left boundary is 75˚C, the right boundary is 50˚C, and the bottom boundary is 0˚ Find the temperature distribution for the interior of the plate using 49 interior nodes.
- Repeat the above problem (#1), but now use a bottom boundary that is insulated and solve for the temperature of the 49 interior points and the 7 points along the bottom boundary.
- Find the temperature distribution for the L-shaped plate below.

- Consider a long, thin aluminum rod with a length of 10 cm. Initially, the temperature of the rod is 0˚C; the boundary at x=0 is 100˚C and the boundary at x=10 is well insulated. Using a Δx=2cm, solve this system explicitly and implicitly for t=0.1s and t=0.2s.

CME381 Homework 6

This assignment is to be done in Excel and submitted in Isidore. Be sure to have written out the equations either in individual cells or in VBA so we can see where your values are coming from.

- For the following set of data taken at steady state, apply all 3 forms of smoothing discussed in class. Use an interval of 4 for your smoothing. When doing the exponential smoothing, use α=0.2. State your new smoothed data points and their corresponding times for each method. Then graph in Excel what the smoothed data will look like for each method.

t |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

y |
10 | 9 | 8.5 | 10 | 11 | 11 | 10.5 | 9.5 | 11 | 10 | 12 | 10.5 | 9 | 8.5 | 9 | 9.5 |

- Use linear and quadratic interpolation to estimate a function’s value at x=1.5 given that f(1)=2, f(2)=3, and f(3)=2. Compare both values to the true value of 2.75 and state reasoning for which is a better approximation.
- Find the mean and two-tailed confidence interval for the y data given in problem 1.

More ODE&PDE Practice Problems

- Use the following differential equations to compute the velocity and position of a soccer ball that is kicked straight up in the air with an initial velocity of 40m/s. In these equations, y = upward distance (m), t = time (s), v = upward velocity (m/s), c
_{d}= drag coefficient (kg/m), A = area of the ball. Use g=9.81m/s^{2}and diameter = 22cm. Solve using all three numerical ODE methods from lecture.

- Find the temperature distribution in the plate below

- Resolve the parabolic PDE problem from class Tues, Oct. 16, but now use a Δx = 1cm.
- Resolve the parabolic PDE problem from class Tues, Oct. 16, but now let both boundary temperatures be 50°

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