Checklist
Month/Date/Year
Material Covered
Assignments and Midtern
Readings
Sep 10, 2007 Intro to ODEs. examples are: 1) Newtons law, 2) Predatory-Prey, 3)
Chemical Kinematics.
Lecture only
Sep 12, 2007 More Chemical Kinematics, waves on a string and BVP.
Assignment #1
AMATH 342/CM 352
Due September 21st, 2007
Questions:
1. Consider a simple pendulum at an angle of 0 /2 from the bottom most position.
(a) Use a balance of forces and Newtons second law to nd the second order nonlinear
ODE for the evolution o
Addendum to Assignment #2
AMATH 342/CM 352
Due October 5th, 2007
Questions:
2 (a),(b). I want you to set up these two problems similarly to what we did in class. For each
you will get a system of 5 linear equations in ve unknowns. Use Matlab, or some othe
Assignment #2
AMATH 342/CM 352
Due October 5th, 2007
Questions:
1. This question will use an alternative means to derive a nite dierence formula for du/dx().
x
Say we want to approximate this using the values of u at x, x h, x 2h. Instead of using
Taylor
clear all;
%
%
%
%
%
I have modified the vandermonde system slightly.
For the approximation to the first derivative I redefine the constants to
have a factor of 1/h in front. This means that the h disappears.
Similarly, for the second derivative, I redefi
Assignment #3
AMATH 342/CM 352
Due October 19th, 2007
Questions:
1. Consider the following general BVP dened on the interval x0 x xend ,
d2 u
du
+ b(x) + c(x)u = f (x)
dx2
dx
with Dirichlet boundary conditions,
a(x)
u(x0 ) =
and
u(xend ) = .
Write a Matl
clear all;
set(0,'defaultaxesfontsize',15);
set(0,'defaulttextfontsize',20);
set(0,'defaultlinelinewidth',2);
% To reproduce the solution from assignment 2
a
b
c
f
=
=
=
=
@(x)
@(x)
@(x)
@(x)
0*x+1;
0*x;
0*x;
sin(x);
[x,u]=GeneralDirichlet(a,b,c,f,0,1,1,2
Assignment #4
AMATH 342/CM 352
Due November 2nd, 2007
1. Consider the system of ordinary dierential equations
du1
= 3u1 + 4u2 ,
dt
du2
= 5u1 6u2 .
dt
Find the general solution of this homogeneous system. State explicitly what the fundamental
matrix is.
2.
Assignment #5
AMATH 342/CM 352
Due November 16, 2007
Questions:
1. For a given system of ordinary dierential equations
dy
= f (y)
dt
consider the -method dened by
yn = yn1 + t [f (yn ) + (1 )f (yn1 )]
for some value of , with 0 1.
a) What are the names of
Poulin, F.J.
AM 342/CM 352
AMATH 342/CM 352: Assignment #6 Due November 30, 2007
Questions:
1. A system is in partitioned form if it can be written as
M
dq
= p,
dt
U
dp
=
(q),
dt
q
for a constant symmetric matrix M . It is also a Hamiltonian system with a
University of Waterloo
Department of Applied Mathematics
AMATH 342/CM 352
Midterm Exam - Fall 2007
Instructor: Francis Poulin
Date: Friday, October 12th, 2007
1: Transform the following 4-th order ordinary dierential equation to a system of ordinary
diere
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PAGE 1
Problem 1 (5p)
Interpolation with Lagrangian Polynomials
Select the correct implementation of the n-th order interpolation function with Lagrangian polynomials lagrint(X,Y,xint), which returns the interpolated value for the given coordinate,