By Jeffery Cooper
Designed for a path in multivariable calculus, this ebook offers a set of MATLAB courses and routines, in addition to easy thoughts, computations, and pics. 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 circulate, routines contain functions to economics, physics, engineering, and biology. Cooper teaches arithmetic on the college of Maryland.
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Extra resources for A MATLAB companion for multivariable calculus
For example, to graph the function cos x on the interval [ ³; ³ ], we ﬁrst create a vector of x coordinates. Then we create a vector of y coordinates that are the values of cos x at these points. 1; 2; 3; 4; 5/ and y D . 1; 2; 3; 1; 5/. 7 Two-dimensional graphs 17 If the function f is deﬁned as an inline function, we can graph it with the command plot(x,f(x)). 0 or higher is, by default, blue, but other colors are possible. The desired color is indicated by a third argument, which is a character string.
Rotate the ﬁgure until the line of intersection is clearly visible. Label the axes. 9. 2; 5=2; 0/, and N D [1; 1=2; 1]. a) Graph the planes through P0 and P1 with the same normal N in the same ﬁgure. P1 C P2 /=2 and N3 D [0; 1; 1=2]. Add the graph of this third plane to the previous ﬁgure. Rotate the graph so that you can see the intersections clearly. Label the axes. 10. 0; 0; 1/. P1 C P2 C P3 /=3. b) To see the portion of the plane that lies in the ﬁrst octant, let x be the vector of ﬁrst coordinates of the points P1 ; P2 ; P3 , let y be the vector of second coordinates, and let z be the vector of third coordinates.
1 Figure produced by the script mﬁle myexp. 5 MATLAB documents 31 The diary command in Windows If you are working on a PC with Windows, put the diary into a ﬁle with the extension txt. txt A ﬁle with the extension txt can be immediately viewed and edited with the Notepad editor. This Page Intentionally Left Blank 3 Vectors, Lines, and Planes In this chapter we study some of the elements of “ﬂat geometry,” namely, vectors, lines, and planes. To help with the graphical displays, we have prepared the following mﬁles to be used in this chapter.