Madlab work

ICS/TBB Dr. Mustafa BAYSAL Fall 2017

Homework

Write the scripts (m-files) in Matlab for the following questions. Write only one

script using cell structure.

Q1. A Fibonacci sequence is composed of elements created by adding the two

previous elements. The simplest Fibonacci sequence starts with 1, 1 and proceeds

as follows: 


1, 1, 2, 3, 5, 8, 13, ... 


However, a Fibonacci sequence can be created with any two starting

numbers.
Prompt the user to enter the first two numbers in a Fibonacci sequence

and the total number of elements requested for the sequence. Find the sequence

and store it in an array by using a for loop. Now plot your results on a polar graph.

Use the element number for the angle and the value of the element in the sequence

for the radius. 


Q2. The value of cos(x) can be approximated using a Maclaurin series

which can be expressed more compactly as

(recall that the symbol ! stands for factorial).


Use a midpoint break loop to determine how many terms must be included in the

summation, in order to find the correct value of cos(2) within an error of 0.001.

Limit the number of iterations to a maximum of 15.

ICS/TBB Dr. Mustafa BAYSAL Fall 2017

Q3. A Fibonacci sequence is composed of elements created by adding the two

previous elements. The simplest Fibonacci sequence starts with 1, 1 and proceeds

as follows: 


1, 1, 2, 3, 5, 8, 13, ... 


One interesting property of a Fibonacci sequence is that the ratio of the values of

adjacent members of the sequence approaches a number called “the golden ratio”

or (phi). Create a program that accepts the first two numbers of a Fibonacci

sequence as user input and then calculates additional values in the sequence until

the ratio of adjacent values converges to within 0.001. You can do this in a while

loop by comparing the ratio of element k to element k – 1 and the ratio of element

k – 1 to element 
k – 2. If you call your sequence x, then the code for the while

statement is 


while abs(x(k)/x(k-1) - x(k-1)/x(k-2))>0.001 


Q4. The value of sin(x) can be approximated as 


Create a function called my_sin, using a midpoint break loop to approximate the

value of sin(x). Determine convergence by comparing successive values of the

summation as you add additional terms. These successive sums should be within an

absolute value of 0.001 of each other. Limit the number of iterations to a maximum

of 30.

Q5. The le lake_powell.dat contains data on the water level in the reservoir of

Lake Powell for the 8 years from 2000 to 2007. By using a nested loop structure,

Determine the average elevation of the water level for each year and for the

eight-year period over which the data were collected. 


Q6. Consider the following method to approximate the mathematical

constant, e. Start by generating K uniform random integers between 1 and K.

Compute J, the number of integers between 1 and K, which were never

generated. We then approximate e by the ratio

𝐾

𝐽

ICS/TBB Dr. Mustafa BAYSAL Fall 2017

Consider the following example for K = 5. Assume that the following five

integers are randomly generated between 1 and 5.

The number of times the integers are generated is given by

Integers 1 2 3 4 5

Number of instances 2 2 1 0 0

In this example, there are two integers, namely 4 and 5, which were never

generated. This means that J = 2. Consequently, e is approximated by

5

2 = 2.5

Write a function called eapprox that takes the value of K as input, and which

then approximates e using the method described above.

Q7. The le lake_powell.dat contains data on the water level in the reservoir of

Lake Powell for the 8 years from 2000 to 2007. By using a nested loop structure,

Determine how many months each year exceed the overall average for the eight-

year period. 


Q8. Most major airports have separate lots for long-term and short-term parking.

The cost to park depends on the lot you select, and how long you stay. Consider this

rate structure from the Salt Lake International Airport during the summer of

2008.

• Long-Term (Economy) Parking

➢ The first hour is $1.00, and each additional hour is
$1.00

➢ Daily maximum $6.00

➢ Weekly maximum $42.00

• Short-Term Parking

➢ The first 30 minutes are free and each additional 20 minutes is $1.00

➢ Daily maximum $25.00


Write a program that asks the user the following:

• Which lot are you using?

• How many weeks, hours, days, and minutes did you park? Your program

should then calculate the parking bill.

ICS/TBB Dr. Mustafa BAYSAL Fall 2017

Q9. The le lake_powell.dat contains data on the water level in the reservoir of

Lake Powell for the 8 years from 2000 to 2007. By using a nested loop structure,

Create a report that lists the month (number) and the year for each of the months

that exceed the overall average. For example, June is month 6.

Q10. Develop a function called diagonal to find the main diagonal vector of a

matrix with nested loops. Developed function should have the same result as

Matlab built-in function diag.

Group 17

Q1-Q2 Q3-Q4 Q5-Q6 Q7-Q8 Q9-Q10

S tu

d e n t

N u m

b e r

10042025 15065221 16012060 16012132 16065209 14012610 16012010 16012067 16012620 16073005 14035023 16012016 16012068 16015057 17012040 15012010 16012031 16012078 16041024 17012071 15012022 16012032 16012081 16051002 17012609 15024909 16012033 16012109 16065025 17012907 15035014 16012044 16012116 16065081 17041029 15065108 16012051 16012127 16065089 17056010 15065149 16012054 16012130 16065154 17065075