Final Thoughts on the Symbolic Toolbox

Engineering 161

Documentation

Download from the Mathworks site the complete set of documentation for the symbolic toolbox, or at least acquaint yourself with the contents so you can use it for reference in the future.

Go to MATLAB help, symbolic toolbox, and download the documentation

Intersection Example

In this example we want to determine the intersections of a line with an ellipse, plot the two using ezplot, and calculate the intersection points where eqn1 : 16x2+32x+4y2-24y-52 = 0

andeqn2 : 3x –y -2 = 0

Trigonometric Identities In this example we will use MATLAB to

help us do some trig identities. sin(3x)=3sin(x)-4sin3(x) sin(x)sin(y)=1/2(cos(x-y) – cos(x+y)) cos(x+y+z)=cos(x)cos(y)cos(z)

- sin(x)sin(y)cos(z)- sin(x)cos(y)sin(z)- cos(x)sin(y)sin(z)

Root Mean Square (rms)

In this example we’ll use MATLAB to compute the Vrms for a sinusoidal voltage v = Vcos(wt).

Vrms = sqrt(1/T*∫v2cos2(wt)dt from

from 0 to T ( i.e., over one period )

Area of an ellipse

In this example we’ll use MATLAB to compute the area of an ellipse

Recall that x2/a2 + y2/b2 = 1 where dA = 2ydx and y = (b/a)sqrt(a2 – x2)

Substitution Command: subs

Here we will look at a couple examples of using the subs command. The first where we have an expression in one variable, the second where we have an expression in several variables.

S = 0.8x3 + e (0.5x)

Y = v2e (at/g)