Page 63 - Applied Numerical Methods Using MATLAB

52 MATLAB USAGE AND COMPUTATIONAL ERRORS
Surprisingly, MATLAB gives us the function values without any com-
plaint and presents a nice graph of the sinc function. What is the
difference between (a) and (b)?
(cf) Actually, we would have no problem if we used the MATLAB built-in function
sinc().
1.7 Termwise (Element-by-Element) Operation in In-Line Functions
(a) Let the function f 1 (x) be defined without one or both of the dot(.)
operators in Section 1.1.6. Could we still get the output vector consist-
ing of the function values for the several values in the input vector?
You can type the following statements into the MATLAB command
window and see the results.

>>f1 = inline(’1./(1+8*x^2)’,’x’); f1([0 1])
>>f1 = inline(’1/(1+8*x.^2)’,’x’); f1([0 1])

(b) Let the function f 1 (x) be defined with both of the dot(.) operators as in
Section 1.1.6. What would we get by typing the following statements
into the MATLAB command window?

>>f1 = inline(’1./(1+8*x.^2)’,’x’); f1([0 1]’)
1.8 In-Line Function and M-file Function with the Integral Routine ‘quad()’
As will be seen in Section 5.8, one of the MATLAB built-in functions for
computing the integral is ‘quad()’, the usual usage of which is

b
quad(f,a,b,tol,trace,p1,p2, ..) for f(x, p1,p2,. ..)dx
a
(P1.8.1)
where
f is the name of the integrand function (M-file name should be categorized
by ’’)
a,b are the lower/upper bound of the integration interval
tol is the error tolerance (10 −6 by default [])
trace set to1(on)/0(off)(0 bydefault []) for subintervals
p1,p2,.. are additional parameters to be passed directly to function f

Let’s use this quad() routine with an in-line function and an M-file function
to obtain
m+10

(x − x 0 )f (x)dx (P1.8.2a)
m−10
and
m+10
2
(x − x 0 ) f(x)dx (P1.8.2b)
m−10