1. Create a vector with 15 elements: 1, 2, 3, . . . , 15. Then compute
(a) y =
t−1
t+1
(b) z =
sin(t
2
)
t
2
2. Calculate the following quantities:
(a) e
3
, ln(e
3
), log10(103
), and log10(105
).
(b) e
π

163
.
3. You know how to compute x
n element by element for a vector x and a scalar exponent n. How about
computing n
x
, and what does it mean? The result, again, is a vector with elements n
x1
, nx2
, nx3
, etc.
The sum of a geometric series 1 + r + r
2 + r
3 + . . . + r
n approaches the limit 1
1−r
for r < 1 as n → ∞.
Create a vector n of 11 elements from 0 to 10. Take r = 0.5 and create another vector x =
[r
0
r
1
r
2
. . . rn] with the x=r.^n command. Now take the sum of this vector with the command
s=sum(x) (s is the sum of the actual series). Calculate the limit 1
1−r
and compare the computed sum
s. repeat the procedure taking n from 0 to 50 and then from 0 to 100.
4. First read the MATLAB tutorial that I have posted on the Canvas site (and refer to the class notes).
Now create a vector and a matrix with the following commands:
v=0:0.2:12; and M=[sin(v); cos(v)];.
Find the sizes of v and M using the size command. Extract the first 10 elements of each row of the
matrix and display them as column vectors.
5. In class I showed you how to plot y = sin x, 0 ≤ x ≤ 2π, by taking 100 linearly spaced points in
the given interval. Now make the same plot again, but rather than displaying the graph as a curve,
show the unconnected data points. To display the data points with small circles, use plot(x,y,’o’).
[Hint: use the help plot command to learn about the different plotting options.] Now combine the
two plots with the command plot(x,y, x,y, ’o’) to show the line through the data points as well
as the distinct data points.
6. Plot y = e
−0.4x
sin(x), 0 ≤ x ≤ 4π, taking 10, 50, and 100 points in the interval. [Be careful about
computing y. You need array multiplication between exp(-0.4*x) and sin(x).]

 

 

 

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