1
MATH 745 Fall 2014
HOMEWORK #2
Due: November 14 (Friday) by midnight
Submit your solutions in the form of a single MATLAB m-le via Email to the instructor.
Please embed your narrative answers in this le using the instruction disp(.), or
submit them as a
Spectral Methods belong to the broader category of Weighted Residual Methods
for which approximations are defined in terms of series expansions, such that a
measure of the error known as the residual is set to be zero in some approximate sense
In general,
1
MATH745 Fall 2014
QUIZ #2
9:30am, November 28 (Friday), 20 minutes, 10 points max
(no books, no notes)
Write your name and Email address on the top of this sheet
Write your answers on the reverse side and/or attach additional sheets as
necessary.
1. You
1
MATH 745 Fall 2014
HOMEWORK #1
Due: October 8 (Wednesday) by midnight
Submit your solutions, i.e., your brief report in the form of a single PDF le (no Word les
will be accepted!) and your MATLAB code(s) in the form of a single m-le via Email to
the ins
1
MATH745 Fall 2014
QUIZ #1
9:30am, October 24 (Friday), 20 minutes, 8 points max
(no books, no notes)
Write your name and Email address on the top of this sheet
Write your answers on the reverse side and/or attach additional sheets as
necessary.
1. Consi
The finite difference is the discrete analog of the derivative. The finite forward difference of a
function f_p is defined as
Deltaf_p=f_(p+1)-f_p,
(1)
and the finite backward difference as
del f_p=f_p-f_(p-1).
(2)
The forward finite difference is impleme
An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality
involving a function and its derivatives. An ODE of order n is an equation of the form
F(x,y,y^',.,y^(n)=0,
(1)
where y is a function of x, y^'=dy/dx is
The continuous Fourier transform is defined as
f(nu)
=
F_t[f(t)](nu)
=
int_(-infty)^inftyf(t)e^(-2piinut)dt.
(1)
(2)
Now consider generalization to the case of a discrete function, f(t)->f(t_k) by letting f_k=f(t_k),
where t_k=kDelta, with k=0, ., N-1. Wr
There are three types of boundary conditions commonly encountered in the solution of partial
differential equations:
1. Dirichlet boundary conditions specify the value of the function on a surface T=f(r,t).
2. Neumann boundary conditions specify the norma
A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series
is an expansion of a real function f(x) about a point x=a is given by
f(x)=f(a)+f^'(a)(x-a)+(f^(')(a)/(2!)(x-a)^2+(f^(3)(a)/(3!)(x-a)^3+.+(f^(n)(a)/(n!)(x-a
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MATH 745 Fall 2012
HOMEWORK #2
Due: November 6 (Tuesday) by midnight
Submit your solutions in the form of a single MATLAB m-file via Email to the instructor.
Please embed your narrative answers in this file using the instruction disp(.), or
submit them