MATH 4220, Homework 5
Due date: Wed 9 November
1. Let D = cfw_(x, y ) : x (0, 1), y (0, 1) R2 . Find the solution to the problem:
u = 0 inside D
= 0 when y = 1; u = 0 when y = 0;
u = g (y ) when x = 0; u = 0 when x = 1.
2. Let D = cfw_(x, y ) : x (0,
MATH 4220, Homework 7
Due date: Wed 7 Dec
1. Consider the PDE ut = ux whose general solution is u(x, t) = u(x + t). Now consider the following
three schemes for this PDE:
MATH 5230/4230, Homework 8
Not to be handed in.
1. Consider the system
ut + (2 u)ux = 0;
u(x, 0) = 1 + tanh(x).
(a) Determine the characteristic curves for this PDE.
(b) Show that the solution develops a shock and compute the time t = ts at which the shoc
Math 4420/5220 supplemental practice questions
1. Consider a chemical diusing along a thin pipe that has variable thickness.
At any given location x along the pipe, suppose that its cross-sectional
area is given by A(x). Assume also that the chemical dius
Math 4220/5220 midterm
(a) Let u(x, t) be the vertical displacement of an elastic homogenous string undergoing small transverse vibrations. Carefully derive the wave equation utt = T uxx , where T is the tension magnitude and is its linear density.
How to prepare for the nal exam
Review the topics covered [see below]
Go over all the homework, sample and midterm questions.
Do all the questions in this handout.
Concentrate mostly on topics that you are having diculty with.
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