Math 360: MENU Applied Analysis
First Exam, Winter 2012
February 3, 2012
Name:
Answer the questions in the spaces provided on the question sheets. If you
run out of room for an answer, continue on the back of the page. This exam
has 4 questions and 4 page
TRANSPORT EQUATION PROBLEMS
MATH 360: MENU APPLIED ANALYSIS
Consider the transport problem:
ut + F ux = 0
This models the concentration of a contaminant u = u(t, x) owing along a linear channel
with rate F .
(1) Write v (s, x) = L[u(t, x)] and show:
F vx
ODE PROBLEMS ABOUT HEAT
MATH360: MENU APPLIED ANALYSIS
These problems are adapted from chapter 9 of Mathematical Modelling with Case Studies
by B. Barnes and G.R. Fulford, Taylor & Francis, London 2002.
(1) Heat ows through a wall of width L from left to
HEAT ODES
MATH 360: MENU APPLIED ANALYSIS
This document sets up some ODEs related to heat and derives the one-dimensional heat
equation. It is mostly adapted from chapter 9 of the book Mathematical Modelling with Case
Studies by B. Barnes and G.R. Fulford
A FEW HEAT EQUATION PROBLEMS
MATH 360: MENU APPLIED ANALYSIS
This document provides several problems to grow accustomed to using Fourier series to
solve the heat equation
(PDE)
ut = uxx
subject to boundary conditions
(BC)
u(t, 0) = u(L, 0) = 0
and an init
CONVOLUTION OF TWO STEP FUNCTIONS
MATH 360: MENU APPLIED ANALYSIS
Abstract. In this document we calculate explicitly the convolution product of two step
functions.
At the end of class on Friday, we were computing the convolution of two step functions:
f (
MATH 360-2, Winter 2011
MENU Applied Analysis
Test 2
Each question is worth 20 points.
1. A heated rod of length is subject to the heat equation
ut = Kuxx
where K is a constant. The temperature of the rod is kept at 0 when x = ,
but the end at x = 0 is in
MATH 360-2, Winter 2011
MENU Applied Analysis
Test 2 Sample
1. Consider a vibrating string governed the wave equation
utt c2 uxx = 0
subject to the initial condition ut (x, 0) = 0. The string is xed at x = 0, but
at x = we allow the end to move freely, bu
MATH 360-2, Winter 2011
MENU Applied Analysis
Practice Test 1
1. Suppose that the solution to
y + y = A (t )
subject to the initial condition y (0) = 1 and y (0) = 0. Can there exist an
A so that y (t) = 0 for t > ?
2. Solve the partial dierential equatio
MATH 360-2, Winter 2011
MENU Applied Analysis
Test 1
Each question is worth 20 points.
1. A population of sh grows at a rate of 2 percent a year. Let y = y (t)
be the the population of sh at year t measured in millions. At year t = 0
there are 200 million
Math 360: MENU Applied Analysis
First Exam
March 2, 2012
Answer the questions below in the blue book provided.
You do not have to answer the questions in the order listed.
1. Consider the temperature u(t, x) of a heated ring of length 2 .
(a) [5 points] A
TRANSPORT EQUATIONS
MATH 360: MENU APPLIED ANALYSIS
This document is the course supplement for transport problems.
The main example (Section 1) is adapted from Section 12.4 of the book: Barnes, Belinda
and Fulford, Glenn R., Mathematical Modelling with Ca