Electromagnetic Waves, Materials, and Computation with MATLAB®

298 Electromagnetic Waves, Materials, and Computation with MATLAB

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Another useful function is a triangle function T(x − x

n

) given by

T x x

x x N x x

N

n

n n

−

( )

=

− − +

( )

− <

+

1 1

1

1

0

, ,

,

x x

N

n

− >

+

⎧

⎨

⎪

⎪

⎩

⎪

⎪

1

1

.

(15.73)

This function is sketched in Figure 15.8.

After choosing w

m

and f

n

in Equation 15.70, one can perform the denite integrals with

respect to x and the result may be written as an algebraic equation



mn n

n

N

m

gα

=

∑

=

1

,

(15.74)

where



mn m n

w Lf x=

∫

0

1

d ,

(15.75)

P (x)

x

1

1

N + 1

FIGURE 15.7

Pulse function.

T (x – x

n

)

x

x

n

1

1

N + 1

FIGURE 15.8

Triangle function.

Introduction and One-Dimensional Problems 299

g w g x

m m

=

∫

0

1

d .

(15.76)

Equation 15.74 yields ...