Computational Project # 1
Due January 26
1. Develop, debug, and test a program (MATLAB m-file) that for arbitrary m and n
(input parameters):
a) Defines vector
(
)
1
11 cos , 1,
2 1
i
i
x i m
m
Ļ
ļ£« ļ£¶
āļ£« ļ£¶
= ā =
ļ£¬ ļ£·
ļ£¬ ļ£·
ļ£¬ ļ£·
ā
ļ£ ļ£ø
ļ£ ļ£ø
ā¦
using single loop.
b) Define vector
(
)
( )
1
sin , 1,
2 1
j
j
y j n
n
Ļ
ļ£« ļ£¶
ā
= =
ļ£¬ ļ£·
ļ£¬ ļ£·
ā
ļ£ ļ£ø
ā¦
using Matlab vector
operations instead of using loop.
c) Define two-dimensional array
2 2
1 1
, 1, , 1,
2 3
ij i j
a x y i m j n
ļ£« ļ£¶ ļ£« ļ£¶
= ā + ā = =
ļ£¬ ļ£· ļ£¬ ļ£·
ļ£ ļ£ø ļ£ ļ£ø
ā¦ ā¦
using double loop.
d) Define two-dimensional array
2 3
1 2 , 1, , 1,
4 3
ij i j
b x y i m j n
ļ£« ļ£¶ ļ£« ļ£¶
= ā + ā = =
ļ£¬ ļ£· ļ£¬ ļ£·
ļ£ ļ£ø ļ£ ļ£ø
ā¦ ā¦
using āmeshgridā Matlab
command instead of using double loop.
e) Plot y vs. x. Define the names for the axes using on-line commands. Create
legends.
f) Plot two-dimensional array aij as 3-dimensional surface. Use two different
styles for the surface: āshading interpā and āshading facetedā.
g) Create a filled contour plot of two-dimensional array bij. Use jet as a
colormap.
For items (a)-(g) create a single function that performs all the tasks with n and m as
input parameters. Run and test the program for (n,m)=(11,6), (51,26) .
2. Using the Symbolic Math Toolbox create, debug, and test another program
(MATLAB m-file) that
a) finds first 7 terms of Taylor series expansion for
( )
2
sin
x
x e
about x=0.
b) differentiates the function
(
)
4 cos
sin
x
x e
P.S. Email your code to [email protected]. The program that you send should be
a working program All the codes will be checked whether they run or not. . If they are
erroneous, but run, points will be taken for the errors. If the code is not running (it has
some syntax errors), an additional 25% will be taken out. The goal of this class is for
you to be comfortable solving engineering problems. Please take your time and learn
how to trust the computer.