MATH 110 EXAM #1
Please answer the following questions. Because this test is open book and open note, you will not get credit for answers unless you demonstrate how you arrived at them. In short, please show all work.
Problem 1. Please nd the specic solut
M ATH 1 52, FALL 2004: MIDTERM # 2
Problem #1 a) Using Fourier Transform solve the initial value roblem with diffusion equation with variable dissipation
for K > 0 , -cc < x < cc and t > 0. b) Write the solution u above more explicitly when 4 ( x ) = e
MATH 152, FALL 2004: MIDTERM # I
Problem $1 (5 1 Let u ~ ( xt , and u 2(x,t ) denote the solutions of the equation )
with initial and b oundary conditions respectively u1 ( x, 0) = gl ( x), u1 ( 0, t ) = f l ( t), u l ( L , t ) = h l(t) a nd u 2(x,0) = g
MATH 152, FALL 2004: FINAL
There are five problems. Do all of them. Total score: 160 points.
Problem # 1, ( 25 p oints) For both of the following functions f on [0, 11, s tate whether the Fourier cosine series on [0, I] converges in each of the following