User Tools

Site Tools


math121b:midterm2

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
math121b:midterm2 [2020/04/11 19:01]
pzhou [3. Bessel Function (30 points)]
math121b:midterm2 [2020/04/19 23:06] (current)
pzhou [3. Bessel Function (30 points)]
Line 44: Line 44:
  
 4. Problem 20.3, 20.6, 20.7 (6 points) 4. Problem 20.3, 20.6, 20.7 (6 points)
 +  * 20.3: 4/π 4/\pi
 +  * 20.6: $-1/(2n+1)$. 
 +  * 20.7: (1/x)ei(x(n+1)π/2)(1/x) e^{i (x - (n+1) \pi /2)}
  
 ===== 4. Solving PDE with separation of variables (30 points) ===== ===== 4. Solving PDE with separation of variables (30 points) =====
Line 63: Line 66:
 u(0,θ)=cos2(θ). u(0, \theta) = \cos^2(\theta).  u(0,θ)=cos2(θ). u(0, \theta) = \cos^2(\theta).
  
 +Hint: you may find the following formula useful 
 +cos(2θ)=cos2(θ)sin2(θ)=2cos2θ1.\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) = 2 \cos^2 \theta - 1.
  
  
math121b/midterm2.1586656897.txt.gz · Last modified: 2020/04/11 19:01 by pzhou