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--- math121b:midterm2 [2020/04/11 19:01]
pzhou [2. Legendre Function (25 points)]
+++ math121b:midterm2 [2020/04/19 23:06] (current)
pzhou [3. Bessel Function (30 points)]
@@ Line 39: / Line 39: @@
 . Problem 12.1. (7 points)
-. Problem 15.6 (7 points)
+. Problem 15.6 (7 points) Making the computer plot is optional.
 . Problem 19.1 (10 points)
 . Problem 20.3, 20.6, 20.7 (6 points)
+  * 20.3:  $4/\pi$
+  * 20.6: $-1/(2n+1)$.
+  * 20.7:  $(1/x) e^{i (x - (n+1) \pi /2)}$
 ===== 4. Solving PDE with separation of variables (30 points) =====
@@ Line 63: / Line 66: @@
  $u(0, \theta) = \cos^2(\theta).$
+Hint: you may find the following formula useful
+ $\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) = 2 \cos^2 \theta - 1.$

Lecture Notes