Introduction to PDE's: (Strauss, 1.1) (Haberman, 1.1)
t const coeff(e ) undetermined coefficients
PDE's vs. ODE's methods of solution
variation of parameters
PDE's have the complication of more than 1 independent variable For PDE's: more difficult to "

Instructions: Print your name and student ID number in the spaces below. Name: _ Student ID:_
Exam 1, PDE I (Math 4347) 9/23/2009, Wednesday All problems have equal weigh! You are not allowed to use your notes and calculators. Show your work clearly and c

Name:
110 MIDTERM 2
Some potentially useful formulae: 1x (e + ex ). 2 (ii ) The Fourier coecients of f (x) for the eigenfunctions cos(nx/) and sin(nx/) on the interval (, ) are nx 1 f (x) cos An = dx (i ) cosh x = Bn = 1
f (x) sin
nx dx.
In this case th

ECE 470: I R H 1 S Solution (Problem 2.1)
S B O 10, 2009
Not depending on choice of frames implies that for any rotation, the dot product between two vectors will remain constant. Thus, we need to show for any R that is a rotation matrix that vT v2 = (Rv1