MATLAB Introduction

Exercise 2.1 fibonacci1 script

(1/(5^0.5))*((((1+(5^0.5))/2)^n)-(((1-(5^0.5))/2)^n))

This seems like a lot of parenthesis for just this line of code.  If there's a more efficient way to write this, I would be glad to hear comments about it.  I could alternatively write this through variables like:

a = (1/(5^0.5));

b(((1+(5^0.5))/2)^n;

c((1-(5^0.5))/2)^n;

a*(b-c)

But it doesn't seem as efficient either.

Exercise 2.3: car_update script

For this, I initially assigned a and b to be equal to 150 and stored the values through the prompt.  My script is as follows:

%car_update updates the number of cars in each location from

%one week to the next.  Precondition: variables aStor and bStor contain

%the number of cars in each location at the beginning of the week

%Postcondition: a and b have been modified to reflect the number of cars

%that have moved

aStor=(b*0.03)+a - (a*0.05)

bStor=(a*0.05)+b - (b*0.03)

a = aStor

b = bStor

a represented the number of cars in Albany while b represented the numbers of cars in Boston.  Since there is a 2% difference between the transfer of cars in each city, Boston ended up with the majority of cars after a few weeks.

Exercise 3.1: car_loop script

%car_loop updates the number of cars in each location via a for loop from

%one week to the next.  Precondition: variables aStor and bStor contain

%the number of cars in each location at the beginning of the week

%Postcondition: a and b have been modified to reflect the number of cars

%that have moved

a = 150

b = 150

for i = 1:52

    aStor=(b*0.03)+a - (a*0.05)

    bStor=(a*0.05)+b - (b*0.03)

    a = aStor

    b = bStor

end

I borrowed the code that I used from exercise 2.3 but I've always preferred for loops over recursion.

Exercise 3.2: car_loop script with plotting

a = 10000 % or 150

b = 10000 % or 150

for i = 1:52

    aStor=(b*0.03)+a - (a*0.05)

    bStor=(a*0.05)+b - (b*0.03)

    a = aStor

    b = bStor

    hold on

    plot (i, a, 'o')

    plot (i, a, 'ro')

    plot (i, b, 'bd')

end

Exercise 3.5: fibonacci2 sequence script

%creates the Fibonacci sequence using for loops instead of recursion.

%Precondition: n represents the level that the sequence is on.  a, b, and

%c represent sections of the Fibonacci sequence while Fx represents the

%entire equation.  Postcondition: the 10th element is assigned to the

%answer.

for i = 3:10

    n = i

    a = (1/(5^0.5));

    b = (((1+(5^0.5))/2)^n);

    c = (((1-(5^0.5))/2)^n);

    Fx = a*(b-c);

end

Fx = a*(b-c)

I later adjusted the code to allow users to compute the nth element for any value of n.  However, users must set the n before the script is run.

n = 3   %user can change this number

for i = n

    a = (1/(5^0.5));

    b = (((1+(5^0.5))/2)^n);

    c = (((1-(5^0.5))/2)^n);

    Fx = a*(b-c);

end

Fx = a*(b-c)