HW1 - 3101 Matlab -- (INSERT NAME and UNI HERE)

Due 11:59pm on Tuesday, March 11th, 2008

Contents

Goals

Open Matlab, and start using it for simple stuff (instead of your TI-83)

Directions

Please fill in your name at the top of this page and write your answers under their corresponding question. When you are done, publish this file to html using File > Publish To HTML (or the command publish('hw1.m', 'html') and create a new zip file that is labeled with your UNI and homework number (eg. bs2018-hw1.zip), that contains this original m file, and the html directory created from publishing the file. Email this file to cs3101@gmail.com, making sure to include your name, and uni in the subject.

Note

When I say display a variable I mean display it so the output is labeled with the variable name, don't use disp, just leave off the semicolon from the end of the command.

Help

If you get stuck, type the command doc to pull up the documentation window, from there it's easy to search for any other commands or functions you might want to use...

Problem 1 - some basic calculations

1.1

what is 2 to 20th power?

2^20

ans =

     1048576

1.2

what is the square root of 157?

sqrt(157)

ans =

   12.5300

1.3

http://en.wikipedia.org/wiki/Compound_interest#Continuous_compounding if i have 100 dollars in a savings account that is compounded 4 times a year, with 5 percent interest how much money will i have after 12 years?

100*(1 + 0.05/4)^(4*12)

ans =

  181.5355

Problem 2 - mathematical functions on lists of numbers

We are given the heights of 10 people in inches:

heights = [60    64    69    60    61    62    62    67    63    62];

2.1

what are their heights in feet?

heights ./ 12

ans =

  Columns 1 through 5

    5.0000    5.3333    5.7500    5.0000    5.0833

  Columns 6 through 10

    5.1667    5.1667    5.5833    5.2500    5.1667

2.2

what is the mean and standard deviation of the heights (in inches)?

mean(heights)
std(heights)

ans =

    63


ans =

    2.9439

2.3

what is the maximum and minimum height?

max(heights)
min(heights)

ans =

    69


ans =

    60

2.4

we find out that the last 5 heights were measured incorrectly, using only one line and one command (no semicolons allowed), add two inches to the last 5 heights in the list, store the new list in a variable called heights2, and display heights2

heights2 = [heights(1:5), heights(6:10)+2]

heights2 =

  Columns 1 through 9

    60    64    69    60    61    64    64    69    65

  Column 10

    64

2.5

sort and display heights2

sort(heights2)

ans =

  Columns 1 through 9

    60    60    61    64    64    64    64    65    69

  Column 10

    69

2.6

plot the corrected heights2 in a histogram

hist(heights2)

Problem 3 - investigate prime numbers

3.1

print out the help pages for the primes, and isprime function

help primes
help isprime

 PRIMES Generate list of prime numbers.
    PRIMES(N) is a row vector of the prime numbers less than or 
    equal to N.  A prime number is one that has no factors other
    than 1 and itself.
 
    Class support for input N:
       float: double, single
 
    See also FACTOR, ISPRIME.

    Reference page in Help browser
       doc primes

 ISPRIME True for prime numbers.
    ISPRIME(X) is 1 for the elements of X that are prime, 0 otherwise.
 
    Class support for input X:
       float: double, single
 
    See also FACTOR, PRIMES.

    Reference page in Help browser
       doc isprime

3.2

compute a new variable p that contains all prime numbers less then 1000, and suppress the output (do not display, so add a semicolon)

p = primes(1000);

3.3

make a new variable ps which contains the first 10 prime numbers, display them

ps = p(1:10)

ps =

  Columns 1 through 9

     2     3     5     7    11    13    17    19    23

  Column 10

    29

3.4

make a new variable pe which contains the last 10 prime numbers that are smaller then 1000, display pe, (hint: help end)

pe = p(end-9:end)

pe =

  Columns 1 through 9

   937   941   947   953   967   971   977   983   991

  Column 10

   997

3.5

how many primes are less then 1000?

length(p)

ans =

   168

3.5

plot the first 1000 primes

plot(p)

3.6

Mersenne primes are prime numbers of the form 2^x - 1... for example 7 is a mersenne prime because 7 is prime and 7 = 2^3 - 1... let's try to find more mersenne primes. first create a variable x that contains the number 1,2,3,...32, do not display x

x = 1:32;

3.7

now create a variable m that contains all the numbers of the form (2^x) - 1, for x=1,2,3...32, do not display m or x (hint, remember .^ and ^ are different)

m = 2.^x - 1;

3.8

which numbers in m are prime? (hint there is a function that will make a new list which contains a 1 if the number is prime and 0 if its not, store this list in a variable called i, and display the output)

i = isprime(m);

3.9

create a new variable mersenne which contains all of the mersenne primes that are less then 2^32 (hint, you need to use the variables m and i). Then display only the first 5 mersenne primes.

mersenne = m(i);
m(1:5)

ans =

     1     3     7    15    31

3.9.1

what is the biggest meresenne prime that is less then 2^32

max(mersenne)

ans =

   2.1475e+09

Published with MATLAB® 7.4