Let's cover all the points in no particular order:

• The e is known as Euler's constant, where e ~ 2.71828...
  Something like e^x, i.e. raising e to the power of x is known as the exponential function. While you could in theory compute e and then use the power operator (^ in matlab) to raise e to that power accordingly, this is in fact a less precise way of calculating the exponential function, and therefore matlab provides the exp function for that purpose. If you pass an array [x1, x2,...] to exp, it will perform this function "elementwise", and return [e^x1, e^x2,...] appropriately.

• The sin function, similarly, if given an array of numbers, will calculate the sin for each of those numbers, and return an array of the same shape as its input.

• You could use fplot with an anonymous function as Neo suggested, but I find that beginners find that confusing. So instead I would suggest you create an array of values between [-2,2], and obtain the value of y for each of them, which in matlab can be done as a single operation because it's good at working with arrays and performing such 'vectorized' operations:

  Copyx = [-2:0.1:2];  % Create an array of values from -2 to 2, with a step of 0.1
                   % Note: the ';' at the end suppresses output; if you want to
                   % see the contents of your array, remove it at the end.
  

• Now that you have your array x you can perform operations on it. By convention, matlab uses "dot-operators" to denote "elementwise" operations, as opposed to 'undotted' ones denoting primarily "matrix" operations. Therefore to raise all elements of the array x to the power of 6, you would do x .^ 6
  With that in mind, you can now calculate your f(x) for each point in the array x, by using elementwise operations:

  Copyy = exp( sin(x).^3 ) + x.^6 - 2*(x.^4) - x.^3 - 1;
  

  The result is an array y of the same size as x.

• You can now plot this using the plot command, which takes two arrays of the same size and plots all points in the first array against their equivalent points in the second array, as (x,y) pairs:

  Copyplot( x, y );
  

Output:

As you can see, matlab 'connects' the points by default. If you wanted to see just the individual points of your array instead, you can specify this as the third argument:

Copyplot(x, y, 'o');

Type help plot at the matlab terminal to see more options for the plot command.

---

PS: The above plots were made in octave rather than in matlab, because I don't have matlab at home. Your own plots may look slightly different.

Try this (using LaTeX): figure plot(rand(50,1), rand(50,1), 'p') axis([0 1 0 1]) title('$y = x \times e^{- \frac{x^2}{2}}$', 'Interpreter','latex', 'FontSize',16) prodcing: .

If you want to do the element-wise exponential operation, the following will work on R2016b and onward versions B = A.^reshape((0:0.1:1),1,1,[]); For matrix exponentiation B = arrayfun(@(k) {A^k}, 0:0.1:1)

Just put your negative values in brackets: (-1.5)^2 = 2.2500 In your case Matlab is applying the sign afterwards, as it sees it as a standard operator and is following the usual operation order by calculating the power before subtraction.

I enjoy going to farmers markets.

Hi Ricardo, min3 = min.^3 It's not a good idea to name a variable 'min' because that is the name of a built-in Matlab function.

Hi @Carlos Thanks for the update. Which specific method did you use? Was it ? Regardless of the method employed, you should be aware that even if the simulation runs smoothly, it does not necessarily mean that the result is valid according to the laws of physics. Therefore, you should carefully verify whether the result makes sense. For example, in a common mechanical engineering problem where the friction or drag force model exhibits nonlinear behavior and is proportional to velocity, students often use the power law when the object is moving through non-Newtonian fluids. What would happen if the velocity is a negative value? Mathematically, this results in a complex output. However, the negative sign of the velocity does not imply a "negative" amount. Rather, it indicates the opposite direction of velocity when the reference frame is defined in the model. v = linspace(-2, 2, 4001); k = 1; lambda = 1.2; Fd = - k*(v.^lambda); figure plot(v, Fd), hold on plot(v, -v, '--'), hold off grid on, ylim([-2.5, 2.5]) legend('Nonlinear Friction', 'Linear Friction') title('Case 1: Power law') xlabel('v') ylabel('F_{d}') To avoid complex outputs, students typically use the absolute value operator. However, do the magnitude and direction of the friction force make sense? Fd = - k*(abs(v).^lambda); figure plot(v, Fd), hold on plot(v, -v, '--'), hold off grid on, ylim([-2.5, 2.5]) legend('Nonlinear Friction', 'Linear Friction') title('Case 2: Power law with absolute value') xlabel('v') ylabel('F_{d}') To ensure the inverse symmetric property in the nonlinear friction model, the signum function can be used. Fd = - k*(abs(v).^lambda).*sign(v); figure plot(v, Fd), hold on plot(v, -v, '--'), hold off grid on, ylim([-2.5, 2.5]) legend('Nonlinear Friction', 'Linear Friction') title('Case 3: Absolute power law with sign function') xlabel('v') ylabel('F_{d}')