By Jeffery Cooper
Designed for a path in multivariable calculus, this publication presents a set of MATLAB courses and routines, in addition to easy ideas, computations, and pictures. Chapters concentrate on the command line, mfiles, vectors, curves, capabilities of 2 and 3 variables, fixing equations, optimization, a number of integrals, scalar integrals, and electrostasis and fluid stream, workouts 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
1 Parametric representation of curves Curves in two- and three-dimensional space are often represented as the image of a vector-valued function of a real variable. This is called a parametric representation. t/, and the vector-valued function t ! t//. These curves are very easy to plot with MATLAB. 1; 3/ and radius r D 2 is >> >> >> >> t = linspace(0, 2*pi, 101); x = 1 +2*cos(t); y = 3 +2*sin(t); plot(x,y) We can also use the feature of the inline function to make such plots. An alternate sequence of commands to graph the circle is >> >> >> >> x = inline(’1 + 2*cos(t)’); y = inline(’3 + 2*sin(t)’); t = linspace(0, 2*pi, 101); plot(x(t), y(t)); 47 48 Curves in Space The inline functions x and y deﬁned in the ﬁrst and second lines are array-smart; when applied to the vector t, they produce the same vectors as in the second and third lines of the previous sequence.
M is a function mﬁle that graphs a plane using the parametric form. Input information consists of the point P0 and the normal direction N. 3. The normal direction is indicated with a red arrow. Notice that the point P0 is located in the center of the planar piece, where the normal vector is attached. The width of the planar piece in the horizontal direction is 2 and the width in the other direction is also 2. To get a planar piece of width 2a in the horizontal direction and width 2b in the other direction, use the longer call >> plane(P0,N,a,b) If two planes have normals N1 and N2 that are not multiples of one another, the planes will intersect.
We shall see this difference often. ezplot is an example of a function mﬁle that can operate on other functions. These function mﬁles have the name of a function as an argument in the call. When the function is given as an inline function, the name of the function is f or g, etc. When the function is given in an mﬁle, the name of the function is ’f’ or ’g’, etc. 3. 3 Function functions MATLAB has a number of routines that operate on functions, called function functions. These are function mﬁles that generally have function names as well as variables as arguments.