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ENGS 91
Laboratory 8
Due: in class, Tuesday, Nov. 13
Hyperthermia, or elevated tissue temperature, has been proposed as a cancer therapy. One
approach for inducing hyperthermia that is presently under investigation is microwave heating.
A popular model

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ENGS 91: Fall 2012
Laboratory 6
Due: in class, Tuesday, Oct. 30
20 pts
(1) Solve the initial-value problem
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y
dy
= 2 y2
dt
t
t
on the interval 1 t 2 subject to initial conditions y (1) = 1 using Eulers method
with step-sizes t = 0.2(2n ) for n = 0, 1,

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ENGS 91: Fall 2012
Laboratory 5
Due: in class, Tuesday, Oct. 23
10 pts
(1) Derive Simpsons Rule with error term by using
x2
f (x)dx = a0 f (x0 ) + a1 f (x1 ) + a2 f (x2 ) + kf (4) ( ).
x0
Find a0 , a1 , and a2 from the fact that Simpsons rule is exact f

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ENGS 91: Fall 2012
Laboratory 4
Due: in class, Tuesday, Oct. 9
15 pts
(1) Consider the oscillograph record of the free-damped vibrations of a structure. From vibration theory, it is known that for viscous damping (damping proportional to velocity),
the

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ENGS 91: Fall 2012
Laboratory 3
Due: in class, Tuesday, Oct. 2
15 pts
(1) Approximate the function
f (x) = 10x + ex cos 10x
over the interval x [1, 2] using a polynomial of order N , where N is at least 4. Use
three dierent polynomials (described below)

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ENGS 91: Fall 2012
Laboratory 2
Due: in class, Tuesday, Sept. 25
20 pts
(1) Using Newtons method, Secant method, and Modied Newtons method, nd the root
for the functions listed below that is located between x = 1 and x = 2. For the cases
which converge

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ENGS 91: Fall 2012
Laboratory 1
Due: in class, Tuesday, Sept. 18
Solutions to Laplaces equation in cylindrical coordinates can be described by Bessel functions, Ji (x),
where i = 1, 2, ., N . Although they are built-in functions to many programming lang