README.md

# 01_ME3255_repo
First repository (first homework assignment) for ME3255
# HW 2 table
| solver | initial guess(es) | ea | number of iterations|
| --- | --- | --- | --- |
|falsepos   | 0 1  |0.01  | 21  |
|mod_secant | 1 | 0.009 | 5 |
|bisect     | 0 1 | 0.011 | 19  |

#Answer to Homework Question
I hope to learn more matlab tricks and about the backgrounds and goals of engineering
students.

#Problem 3 - first script for loops

```matlab

A_66=zeros(6,6);
for i=1:6
    for j=1:6
        A_66(i,j)=i*j;
    end
end

fprintf('mean of A_66 =%1.2f\nstdev of A_66=%1.2f\n',mean(A_66(:)),std(A_66(:)))
```

output:

- mean of A_66 = 12.25

- stdev of A_66 = 9.07

#Problem 4 - US Energy Consumption

```matlab

mean=mean(A_66(:));
mode=mode(A_66(:));
std=std(A_66(:));
set(0, 'defaultAxesFontSize', 16);
set(0, 'defaultAxesFontSize', 16);
set(0, 'defaultLineLineWidth', 3);

figure(1)
data=dlmread('US_energy_by_sector.csv',',',2,0);
data(1,:);
plot(data(:,1), data(:,3), data(:,1), data(:,9)) %residential in column 3 %transportation in column 9
xlabel('Year');
ylabel('Trillions of BTU');
legend('Residential', 'Transportation', 'Location', 'NorthWest');
title('US Energy Consumption');
size(data);
print('figure_01.png','-dpng');

```

![US Energy By Sector](./figures/figure_01.png)

```matlab

figure(2)
plot(data(:,1), cumtrapz(data(:,3)/(10^6)), data(:,1), cumtrapz(data(:,9)/(10^6))) %residential in column 3 %transportation in column 9
xlabel('Year');
ylabel('Quintillions of BTU');
legend('Residential', 'Transportation', 'Location', 'NorthWest');
title('Cumulative US Energy Consumption');
size(data);
print('figure_02.png','-dpng');

```

![Cumulative US Energy By Sector](./figures/figure_03.png)

#Problem 5 - Freefall

```matlab

function [v_terminal,t]=freefall_comparison(h, timespan)
    % help file for freefall_comparison.m
    % N is number of timesteps between 0 and 12 sec
    % v_numerical is numerical approximation
   
    % Enter "freefall_comparison(0.1,30)" to initiate program
    
    t=(0:h:timespan);
    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c)
    v_numerical=zeros(length(t),1);
    delta_time =diff(t);
    
    for i=1:length(t)-1
        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);
    end
    
    plot(t,v_numerical,'-');
    hold on

    h=1;
    t=(0:h:timespan);
    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c)
    v_numerical=zeros(length(t),1);
    delta_time =diff(t);
    for i=1:length(t)-1
        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);
    end
    plot(t,v_numerical,'-');
    
    h=5;
    t=(0:h:timespan);
    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c)
    v_numerical=zeros(length(t),1);
    delta_time =diff(t);
    for i=1:length(t)-1
        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);
    end
    plot(t,v_numerical,'-');
    
    legend('h=0.1','h=1','h=5','Location','southeast');
    print('figure_03.png','-dpng')
    
end

   xlabel('Time (Seconds)');
    ylabel('Calculated Velocities v(t)');
    title('Calculated Velocities over Time');
    legend('h=0.1','h=1','h=5','Location','southeast');
    print('figure_03.png','-dpng')

```
![Analytical vs Numerical Solution of Freefall Velocity](./figures/figure_02.png)

#Problem 6 - Velocity and Acceleration

```matlab

function [vx,vy,vz] = my_velocity(x,y,z,t)
    % Help documentation of "my_velocity"
    % This function computes the velocity in the x-, y-, and z-directions given
    % three vectors of position in x-, y-, and z-directions as a function of time
    % x = x-position
    % y = y-position
    % z = z-position
    % t = time
    % output
    % vx = velocity in x-direction
    % vy = velocity in y-direction
    % vz = velocity in z-direction
    
    vx=zeros(length(t),1)';
    vy=zeros(length(t),1)';
    vz=zeros(length(t),1)';

    vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t
    vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t
    vz(1:end-1) = diff(z)./diff(t); % calculate vz as delta z/delta t

    vx(end) = vx(end-1);
    vy(end) = vy(end-1);
    vz(end) = vz(end-1);
    
    % In the command window, the user must enter vectors for x, y,
    % z, and t, in either lists of numbers in square brackets or
    % parentheses and colons. An example is shown below: 
    %[vx,vy,vz]=my_velocity((1:3),[2 4 5],(2:4),(6:8))

end

```

```matlab

function [ax,ay,az]=my_acceleration(x,y,z,t)
    % Help documentation of "my_acceleration"
    % This function computes the acceleration in the x-, y-, and z-directions given
    % three vectors of position in x-, y-, and z-directions as a function of time
    % x = x-position
    % y = y-position
    % z = z-position
    % t = time
    % output
    % ax = acceleration in x-direction
    % ay = acceleration in y-direction
    % az = acceleration in z-direction

    function v=diff_match_dims(x,t)
      v=zeros(length(t),1);
      v(1:end-1)=diff(x)./diff(t);
      v(end)=v(end-1);
    end

    [vx,vy,vz]=my_velocity(x,y,z,t);

    ax = diff_match_dims(vx,t);
    ay = diff_match_dims(vy,t);
    az = diff_match_dims(vz,t);
    
    % In the command window, the user must enter vectors for x, y,
    % z, and t, in either lists of numbers in square brackets or
    % parentheses and colons. An example is shown below: 
    %[ax,ay,az]=my_acceleration((1:3),[2 4 5],(2:4),(6:8))

end

```