1

**Test 2 / 2022 midterm 2 solution: Possible typos?**

« **on:**March 22, 2023, 10:02:57 PM »

I've been looking through the midterm solutions from 2022 to study for the midterm coming up. I was wondering if it's possible there are typos in the solutions, or if you can explain the following if I am misunderstanding something:

1. In problem 1 of Main Sitting 2022, there is the equation T' + 4λT = 0. I believe this should be T'' + 4λT = 0, with the first T as a second derivative.

2. In problem 1 of Morning Sitting 2022, there is equation 4T'' + λT = 0. I believe this should be T'' + 9λT = 0.

In the same question, T

In the same question, there are initial boundary conditions dependent on the value of t. I believe in the solution when plugging these in, they are swapped.

3. In problem 3 of Main Sitting 2022, there u(r,θ) =B

Thank you!

1. In problem 1 of Main Sitting 2022, there is the equation T' + 4λT = 0. I believe this should be T'' + 4λT = 0, with the first T as a second derivative.

2. In problem 1 of Morning Sitting 2022, there is equation 4T'' + λT = 0. I believe this should be T'' + 9λT = 0.

In the same question, T

_{n}= A_{n}cos(nt) + B_{n}sin(nt). I believe this should be T_{n}= A_{n}cos(3nt) + B_{n}sin(3nt).In the same question, there are initial boundary conditions dependent on the value of t. I believe in the solution when plugging these in, they are swapped.

3. In problem 3 of Main Sitting 2022, there u(r,θ) =B

_{0}/2 + (a sum). Then u(1,θ) = A_{0}/2 + (a sum). I'm not sure how B_{0}turned into A_{0}in this.Thank you!