The ‘hold on’ statement makes several curves appear on the same set of axes. If you want to make a
new plot (with a new set of axes) you can use the ‘figure’ statement to open a new set of axes. For
example
figure
syms x
fplot(x*sin(x),[0,4])
You can do far more than just x-y plots with a Matlab Live Script: for example, you can type any of the
following into the matlab help search box:
• fcontour (for contour plots)
• fsurf (for a 3D surface)
• fplot3 (for a 3D parametric curve)
You can explore these when you need them – it is hard to remember all the different plot functions.
6.3 Calculus
MATLAB is good at calculus. For basic differentiation and integration, try
syms x deriv
deriv = diff(x^2,x)
int(deriv)
Notice that MATLAB has not included a constant of integration – you have to remember to add it in
yourself if it is needed. You can do higher order derivatives as well
syms x f dfdx d2fdx2
f = x*sin(x)^2*cos(x)^2
dfdx = diff(f,x)
d2fdx2 = diff(f,x,2)
dfdx = int(d2fdx2)
f = int(dfdx)
Partial Derivatives: You can do partial derivatives
syms f x y
f = sqrt(x^2+y^2);
diff(f,x)
Maximizing a function As an example, let’s try to maximize
()
x
fx
ax
=
+
We can do this using the usual calculus tricks: the maxima must be at points where
/0df dx =
, so we
can solve this for x and then substitute back into f. Here’s the MATLAB
clear all
syms f x a dfdx xatmax
f = x/(a+x^2);
dfdx = diff(f,x);
xatmax = solve(dfdx==0,x)
subs(f,x,xatmax)
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