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
u
= 0 when y = 1; u = 0 when y = 0;
n
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:
(i)
(ii)
(iii)
un+1 un
un un1
j
j
j
j
=
t
x
un+1 un
un+1 un
j
j
j
j
=
t
x
un+1 un
un
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
1.
(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.
(b)
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.
Topics covered
Modellin
Page 1 of 19
Page 2 of 19
Page 3 of 19
Page 4 of 19
Page 5 of 19
Page 6 of 19
Page 7 of 19
Page 8 of 19
Page 9 of 19
Page 10 of 19
Page 11 of 19
Page 12 of 19
Page 13 of 19
Page 14 of 19
Page 15 of 19
Page 16 of 19
Page 17 of 19
Page 18 of 19
Page 19 of 1