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Final Thoughts on the Symbolic Toolbox Engineering 161

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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

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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 : 16x 2 +32x+4y 2 -24y-52 = 0 and eqn2 : 3x –y -2 = 0

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Trigonometric Identities In this example we will use MATLAB to help us do some trig identities. sin(3x)=3sin(x)-4sin 3 (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)

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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* ∫ v 2 cos 2 (wt)dt from from 0 to T ( i.e., over one period )

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Area of an ellipse In this example we’ll use MATLAB to compute the area of an ellipse Recall that x 2 /a 2 + y 2 /b 2 = 1 where dA = 2ydx and y = (b/a)sqrt(a 2 – x 2 )

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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 = 0.8x 3 + e (0.5x) Y = v 2 e (at/g)

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In this section, we will look at integrating more complicated trigonometric expressions and introduce the idea of trigonometric substitution.

In this section, we will look at integrating more complicated trigonometric expressions and introduce the idea of trigonometric substitution.

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