Week 4 Answers

Feel free to copy the code provided into your own MATLAB scripts to check your work! Please remember that although these are answers, there are multiple ways of doing the problem(s). We encourage you to develop your own method of writing and organizing your code!

Question 1

%Q1
%Defining the Function
numeric_Q1 = @(x) 3.*x.^3 + 42.*x.^2 - 13.*x + 7;

%1a:
ans1a = numeric_Q1(77);

%1b:
ans1b = numeric_Q1(0:100);

plot(0:100,ans1b);
hold on
title('Week 4 Numeric');
xlabel('x-values');
ylabel('y-values');
hold off

Notes:
Notice how I call which values should be evaluated in part b. The values here could also be generalized using linspace as well. For example

x_values = linspace(0,100)
ans1b = numeric_Q1(x_values)

Week 4: Numeric Functions

Question 2

%Q2
%Defining the Symbols
syms x y
%Defining the Function
symb_Q2(x,y) = 7.*x.*y - 12*x.^2 + 8.*y.^4;

%2a
ans2a = symb_Q2(2,4);

%2b
y_val = linspace(0,1,100);
ans2b = symb_Q2(1,y_val);

    %When Evaluating this, your answers may appear as fractions, to remedy
    %this
    ans2b = eval(ans2b);

plot(0:99,ans2b);
hold on
title('Week 4 Numeric');
xlabel('x-values');
ylabel('y-values');
hold off

Notes:
Sometimes when evaluating your answers, MATLAB may give you an answer in terms of a fraction. You can turn the answer in to a number by using the command eval as it is used in the answer above. MathWorks: eval

Here, we define the function using two variables, however, you can also do the same in the numerical case. Similar to how we define it before:

example = @(x,y) x + y

Week 4: Symbolic Function