MT414.01 ASSIGNMENT 1
DUE 17 JANUARY 2013
1.5. Consider the following dictionary of keywords:
chocolate, ice cream, sprinkles,
and
D1.
D2.
D3.
D4.
the following list of documents:
I eat only the chocolate icing o the cake
I like chocolate and vanilla ice
MT414.01 ASSIGNMENT 5SOLUTIONS
DUE 21 MARCH 2013
7.4 Assume that a matrix A satises P A = LU , where
100
001
231
1
P = 1 0 0
L = 2 1 0
U = 0 1 2 .
1
1
010
002
1
3
4
Use these factors, without forming the matrix A or taking any inverses, to solve the
T
sys
MT414.01 ASSIGNMENT 4SOLUTIONS
DUE 28 FEBRUARY 2013
4.3 Newtons method can be used to compute reciprocals, without division. To compute
1/R, let f (x) = x1 R so that f (x) = 0 when x = 1/R. Write down the Newton
iteration for this problem and compute (by
MT414.01 ASSIGNMENT 2SOLUTIONS
DUE 04 FEBRUARY 2013
2.3 Use Matlab to produce a single plot displaying the graphs of the functions sin(kx)
across [0, 2 ], for k = 1, . . . , 5.
Solution. The following Matlab code generates the plot after.
% Generate 500 e
MT414.01 ASSIGNMENT 3SOLUTIONS
DUE 18 FEBRUARY 2013
3.2 Wriate a Matlab code to simulate rolling fair die; that is, it should generate a
discrete random variable that takes on the values 1 through 6, each with probability
1/6. Run the code 1000 times and
MATH4414.01 ASSIGNMENT 13SOLUTIONS
10.4 Find a formula of the form
Z 1
xf (x) dx A0 f (x0 ) + A1 f (x1 ),
0
that is exact for all polynomials of degree 3 or less.
Solution. This exercise is asking for a Two-point Gaussian Quadrature rule for integrands of