## Transcribed Text

1. NCM problem 1.8. Be sure ansuer the questions asked in the problem particular,
you figure out what the matrix elements that are being generated are (lock chapter
come
answerl.
2. NCM. problem 1.34. Don't just explain what ench line code the
and what the values should
be
3.
NCM. probless 1.35
4.
NCM. problem Make <]) thoroughly
This best by setting
dome
and x(2) Make sure yom compate the accurate the formula
book
5
NCM.
problem
1.45
Note
the
(a)
blance
6.
According
the
Richter
M
given
formula
where
Ei
the
energy
1044
Joules
the
energy
of
depends
the
function
plot
and
make
ased to
create
7.
The
history
history
mathematics
that
There
many
amazing
formulas
for
computing
which was used by James Gregory 1671 compute many digits. Another
infinite
series
involving
Basel
serins
go-
(2)
which Leonhard Euler proved 1735
(a) Write Matlas function for approximating using the Basel series. Your fuaction
should aumber the Basel series and ostpat an
approximation to z. Using this fuaction othe following
i. Compute an approximation t using 10.10P, 10³. 104. 10². and 10 term in
the serim
report
table
ii. Compute asing the built-in comstant for from MAT-
ad report the
results
same
table.
iii. Plot the function the aumber tesms
used i the sum Use the and axes of your plot obtain
the erron plot a your assignment
(b)
You should motice from part (a) that the series does not converge very This one
ofthe Euler the series
2/6 they zouldn't surm emough terms make guess what the answer might be
Euler grentness, notiond thet the Basel series could follows
(3)
where log here the natural logarithm This rees much more
and Euler (whe was closest thing this world may have seem humm
the
toget
what
might
converge
to
be
later
he resalt)
Write
MATLAR
function
for
Euler's
the
Basel
series Asit part (a). your function the total number
the Basel series Using this function do the
following
Compute approximation using and 2 terms the
series report the results in
table
ii.
the
built-in
constant
for
from
MAT-
report
the results
the same
table.
Plot relative error the approximation function of the number terms
the sum Use a the and y Eyour plot obtain
the error curve Include this plota your assignment
(c)
None a for however. compare the following one
ered by
John
Machin in
1706
(4)
This
formula
particularly
nace
cal
involves
rational
numbers
and
the
term zeto very rapadly. this formula Machin was able to
100
Write Mailab function formula Asi part
and
series and ompet an approximation tox. part 2(b)(i) (iii) using your function
Note that there now mach better than the ones listed abore
8. Let r and y be column polygion (given order that
polygion without repeating vertion, first ones). The
polygion
can
computed
using
formula
where assurmed that the vertices i.e. Fa+l 91
(a) Write a MATLAB function that takes input vectors and
containing
the
vertions
polygon
Computes
the
result.
Try
the use
loops by
being
function
sum
and
vec-
toruzation
Producs
displayed
Labels
polygion
the
title
(b)
Test
your
pentagon,
and
regular
resuats
that
E
one
that
has
9
(Area
(g)
states
think
the
state
border
Use
these
estimate
and thast
total number
1356
polygon
representing
Idaho
problem
obtain
the region
Idaho,
of
for distances betareer
earth Idaho, use some geometrical tricke to
convert
points
values
miles
Compare you answer "official' Idaho Make sure yom explair hom
and
what
between
your
estimate
and
the
the
programas
pi, for, while, sun, if, xlabel ylabel title
these
>>help
MATLAB command

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1.

Matrix X starts as the identity matrix while matrix A is the operation of adding numbers according to the Fibonacci series; that is matrix X updates with the latest Fibonacci numbers. Every time enter is pressed we get the next number sequence in the Fibonacci series. n=0@X(2,2), n=1@X(2,1), n=2@X(1,1)=[X(2,2)+X(2,1)].

The process has to be repeated 1475 until X overflows, at the 1476th time the sum of numbers will be greater than realmax (=inf).

2.

e (expected) = 0 0 0 0 0 0 0 0 0 0

e (calculated) = 1.0e-15 *

0 0 -0.0555 0 0 -0.1110 -0.1110 0 0 0

t is a scalar. n is an array (size 10). Thus n determines the size of e, which is a size 10 array.

Each of n array values is similarly calculated, and should be zero (since: n/10 – n*0.1=0). This however is seen to not be the case.

MATLAB expresses divisions (1/10, etc.) as a binary approximation using an infinite series, up to a 52 bit term precision. In the above the decimal number 0.1 is developed into a series with a representation error, known as a round-off error. That is why, for example, the result of 3/10 differs slightly from 3*(1/10) and we are left with a non-zero result....