By Jeffery Cooper

ISBN-10: 0080489362

ISBN-13: 9780080489360

ISBN-10: 012187625X

ISBN-13: 9780121876258

Designed for a path in multivariable calculus, this booklet presents a set of MATLAB courses and routines, besides simple techniques, computations, and photos. Chapters specialize in the command line, mfiles, vectors, curves, features of 2 and 3 variables, fixing equations, optimization, a number of integrals, scalar integrals, and electrostasis and fluid movement, routines contain purposes to economics, physics, engineering, and biology. Cooper teaches arithmetic on the college of Maryland.

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**Example text**

For example, >> syms x >> f = cos(x)^2*exp(x) >> ezplot(f, [1,5]) This can be most useful after a symbolic calculation leads to a complicated expression. cos x/2 exp x, if we want to quickly graph the second derivative of f , we could add the lines >> g = diff(f,2) >> ezplot(g, [1,5]) The ezplot command picks its own points for graphing, using more where the function changes rapidly and fewer where it changes more slowly. 2 and higher of MATLAB, the ezplot feature has been extended to graph curves given parametrically in two or three dimensions (with animation).

We can ﬁnd the equation of this plane in the previous form by ﬁnding a normal direction N. Let v be the vector from P0 to P1 and w be the vector from P0 to P2 . Componentwise, v D [x 1 x 0 ; y1 y0 ; z 1 z 0 ] w D [x 2 x 0 ; y2 y0 ; z 2 z 0 ]: Now set N D v ð w. N will be orthogonal to both v and w. Using this N and P0 we generate the equation of the plane as before. , N does not lie in the x; y plane, then we can solve for z in Eq. y y0 //: c In Chapter 5 we shall learn how to graph functions of two variables.

13. A TV antenna is mounted on a roof. The roof has a slope of 20 degrees from the horizontal. Three guy wires are to be stretched from the antenna to the roof. They are attached at a point 25 feet above the roof, and each is to make an angle of 30 degrees with the pole of the antenna. One of the wires is to be as long as possible and thus must go in the direction in which the roof slopes down. 8 Antenna on roof for Exercise 13. x 46 Vectors, Lines, and Planes two wires will be shorter and of equal length.

### A MATLAB companion for multivariable calculus by Jeffery Cooper

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