engr 1181 midterm 2 review

review.m

clear;clc
disp('ENGR 1181')
disp('Midterm 2 Review')
disp('----------------')

disp('Problem 1')
x = 10;
y = (log10(x) * log(x)) / exp(1.1); % log10 is log and log is ln
fprintf('The answer is %.2f.\n', y)
x = 45;
y = (cosd(x) + sind(x)) / (x - 44); % cosd and sind for degrees
fprintf('The answer is %.2f.\n', y)
disp('---------')

% Part of problem 2 is in a seperate function file (problem2.m).
disp('Problem 2')
t = input('Input the values of t.\nt = ');
k = input('Input the values of k.\nk = ');
[y, df] = problem2(t, k);
fprintf('y(t) = ')
fprintf('%.2e ', y)
fprintf('\ndf(k) = ')
fprintf('%.2f ', df)
fprintf('\n');
disp('---------')

% Problem 3
subplot(1, 2, 1)
fplot('P + P^2 + 2', [-2 2])
subplot(1, 2, 2)
fplot('(P + 1) / (P - 1)', [-2 2])
% ---------

% Problem 4
fMeasured = [3.8 1.01 15.2 32.8 10.6];
m = [1 0.25 4 9 3];
a = 3.7;
fCalculated = m .* a;
figure
hold on
plot(m, fCalculated, 'r-')
plot(m, fMeasured, 'bx')
hold off
title('Force v. Mass on Mars')
xlabel('Mass (kg)')
ylabel('Force (N)')
legend('Calculated force', 'Measured force')
% ---------

disp('Problem 5')
x = 1:10;
y = x .^ 2 + x;
y2 = y .* x + x .^ 2 + y;
y3 = y2 .* (y ./ 2) + (2 ./ x) + ((x .* y) ./ y2) + x;
figure
hold on
plot(x, y, 'r-')
plot(x, y2, 'b--')
plot(x, y3, 'k:')
hold off
legend('y', 'y2', 'y3')
axis([1 10 0 1000])
fprintf('| x |   y  |  y2  |  y3  |\n')
fprintf('| %i | %.2f | %.2f | %.2f |\n', [x; y; y2; y3])
disp('---------')

% Problem 6
temp = 10:10:50;
expA = [1.15 2.86 3.11 4.1 5.2];
expB = [1.11 2.8 3.05 3.9 6.9];
figure
subplot(1, 2, 1)
hold on
plot(temp, expA, 'rx')
plot(temp, expB, 'bo')
hold off
title('Data v. Temperature')
legend('Experiment A', 'Experiment B')
xlabel('Temperature')
ylabel('Data')
error = ((expA - expB) ./ expA) * 100;
subplot(1, 2, 2)
plot(temp, error)
title('Error v. Temperature')
xlabel('Temperature')
ylabel('Error Percent')
% ---------

% Problem 7
V = 100:50:900;
y = 1.4;
a = 1000;
p_ptCalc = zeros(1, length(V));
for i = 1:length(V)
    p_ptCalc(i) = (1 + ((y - 1) / 2) * (V(i) / a)^2) ^ -(y / (y - 1));
end
p_ptExp = [.99 .97 .93 .9 .83 .75 .72 .64];
M = .1:.1:.8;
figure
hold on
plot(V / a, p_ptCalc, 'r-')
plot(M, p_ptExp, 'b*')
hold off
legend('Calculated', 'Experimental')
title('Pressure v. Mach')
xlabel('Mach')
ylabel('Pressure')
% ---------

disp('Problem 8')
a = input('What is a?\na = ');
rho = 0.0023;
R = 1716;
% I didn't really understand the directions on what it wanted for T
T = randi([480 520]);
if a == 1
    P = rho * R * T;
elseif a == 2
    P = rho * R * T ^ 1.01;
elseif a == 3
    P = rho ^ 1.01 * R * T;
elseif a > 1.2 && a <= 1.5
    P = rho * R * T ^ 1.05;
else
    disp('Input error. Invalid value for a.')
end
% In the else case, P is never set, which would cause the fprintf
% to throw an error when it tries to access P, so I check to see if
% P is set before I call fprintf.
if exist('P', 'var')
    fprintf('P = %.2f\n', P)
end
disp('---------')

disp('Problem 9')
a = zeros(4);
for i = 1:size(a, 1)
    for j = 1:size(a, 2)
        if i == j
            a(i, j) = j;
        elseif j > i
            a(i, j) = 2 * j;
        elseif j < i
            a(i, j) = -j;
        end
    end
end
disp(a)
disp('---------')

% Part of problem 10 is in a seperate function file (problem10.m).
disp('Problem 10')
rho = input('What is rho?\nrho = ');
P = input('What is P?\nP = ');
n = input('How many cases?\nn = ');
for i = 1:n
    fprintf('What are the values for velocity for case %i?\n', i)
    V = input('V = ');
    Po = problem10(P, rho, V)';
    fprintf('Case %i Po = ', i)
    fprintf('%.2f ', Po)
    fprintf('\n')
end
disp('----------')

% Problem 11
x = 0:6;
y = zeros(1, length(x));
for i = 1:length(x)
    if x(i) >= 0 && x(i) < 2
        y(i) = x(i) ^ 2 + .5 * x(i);
    elseif x(i) >= 2 && x(i) < 4
        y(i) = 2 * x(i) ^ 2 + 2;
    else
        y(i) = 5 * x(i) - 5;
    end
end
figure
plot(x, y)
% ----------

problem2.m

function [y, df] = problem2(t, k)
    % Usage: problem2(t, k)
    % Returns y(t) and df(k)
    y = (exp(-t) .* sin(2 * t) .^ 2) ./ (2 * (t + 1));
    df = ((k .^ 4 + k .^ 3) ./ (k + 2)) + ((k .^ 2 + k) ./ (k + 1));
end

problem10.m

function Po = problem10(P, rho, V)
    % Usage: problem10(P, rho, V)
    % Returns the bernoulli equation for the given values.
    Po = P + .5 * rho .* V .^ 2;
end

command output

ENGR 1181
Midterm 2 Review
----------------
Problem 1
The answer is 0.77.
The answer is 1.41.
---------
Problem 2
Input the values of t.
t = 0:10
Input the values of k.
k = 1:5
y(t) = 0.00e+00 7.60e-02 1.29e-02 4.86e-04 1.79e-03 1.66e-04 5.10e-05 5.59e-05 1.54e-06 3.48e-06 1.72e-06
df(k) = 1.67 8.00 24.60 57.33 112.14
---------
Problem 5
| x |   y  |  y2  |  y3  |
| 1 | 2.00 | 5.00 | 8.40 |
| 2 | 6.00 | 22.00 | 69.55 |
| 3 | 12.00 | 57.00 | 346.30 |
| 4 | 20.00 | 116.00 | 1165.19 |
| 5 | 30.00 | 205.00 | 3081.13 |
| 6 | 42.00 | 330.00 | 6937.10 |
| 7 | 56.00 | 497.00 | 13924.07 |
| 8 | 72.00 | 712.00 | 25641.06 |
| 9 | 90.00 | 981.00 | 44155.05 |
| 10 | 110.00 | 1310.00 | 72061.04 |
---------
Problem 8
What is a?
a = 2
P = 2172.05
---------
Problem 9
     1     4     6     8
    -1     2     6     8
    -1    -2     3     8
    -1    -2    -3     4

---------
Problem 10
What is rho?
rho = .0023
What is P?
P = 14.7/144
How many cases?
n = 2
What are the values for velocity for case 1?
V = 70:100
Case 1 Po = 5.74 5.90 6.06 6.23 6.40 6.57 6.74 6.92 7.10 7.28 7.46 7.65 7.83 8.02 8.22 8.41 8.61 8.81 9.01 9.21 9.42 9.63 9.84 10.05 10.26 10.48 10.70 10.92 11.15 11.37 11.60
What are the values for velocity for case 2?
V = 100:120
Case 2 Po = 11.60 11.83 12.07 12.30 12.54 12.78 13.02 13.27 13.52 13.77 14.02 14.27 14.53 14.79 15.05 15.31 15.58 15.84 16.11 16.39 16.66
----------

graphs

http://imgur.com/a/LAFHv