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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, Tn = An cos(nt) + Bn sin(nt). I believe this should be Tn = An cos(3nt) + Bn 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) =B0 /2 + (a sum). Then u(1,θ) = A0 /2 + (a sum). I'm not sure how B0 turned into A0 in this.
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, Tn = An cos(nt) + Bn sin(nt). I believe this should be Tn = An cos(3nt) + Bn 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) =B0 /2 + (a sum). Then u(1,θ) = A0 /2 + (a sum). I'm not sure how B0 turned into A0 in this.
Thank you!