A MATLAB companion for multivariable calculus by Jeffery Cooper
By Jeffery Cooper
Designed for a path in multivariable calculus, this publication offers a suite of MATLAB courses and routines, in addition to uncomplicated suggestions, computations, and pix. Chapters concentrate on the command line, mfiles, vectors, curves, services of 2 and 3 variables, fixing equations, optimization, a number of integrals, scalar integrals, and electrostasis and fluid circulation, workouts contain functions to economics, physics, engineering, and biology. Cooper teaches arithmetic on the college of Maryland.
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X/n); y = y+term; end [x’, y’, exp(x)’, (y-exp(x))’] maxerror = max(abs(y-exp(x))) plot(x,y,x,exp(x), ’--’) title(’Figure 1. 5-term approx, and true exp(x) (dashed line)’) The values of the approximation are put in the vector y and compared with the MATLAB exponential. 6000 . . 2704 . . 2019 . . 0685 . . 3891 Comments: As we can see from Figure 1 (attached), the 5-term approximation does quite well in the interval [-1, 1]. 0099. 8 Figure 1. 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.
This puts an x axis in green in the ﬁgure and makes it easier to see where the roots are located. After plotting the graph, the program waits for the user to enter four numbers in the form of a vector [a; b; c; d]. Entering Comments In a function mﬁle or a script mﬁle that involves several steps, it is very helpful for you, or for another reader, to identify the steps with comment lines. A comment line begins with the percent sign,%. When a script or function mﬁle is executed, the comment lines are ignored.
To compute the deﬁnite integral, over, say, [0; 3], we use the command >> int(f,0,3) ans = 9*a +9/2*b +c*c+2*sin(3) 14 Basic MATLAB: The Command Line Here we assumed that we wanted to integrate the expression with respect to the variable x. If instead, we wanted to consider a as the variable of integration, we must specify that, with the command int(f,a) ans = 1/2*a^2*x^2 +b*x*a +c*a+2*cos(x)*a Many other variations are possible. m. Evaluating symbolic expressions Next, how do we specify the values of the parameters in the expression, and how do we evaluate the symbolically deﬁned function at a point?