1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

528 CHAPTER 12 • FOURIER SERIES AND THE LAPLACE TRANSFORM

Figure 12.14

3. U(8)= {
   
   
   • 1,
     1,
     -1,
   
   
   
   

tr -8,

8,

s

for ~ < 8 <tr;

for -;" < 8 < ~;

for - tr < 8 < - 2 ".

for ~ $ 8 $tr;

4. U(8) = {
   
   
   • tr -8,
   
   
   
   

for - 2 • $ (J < ~;

for -tr<8< - 2 ".

5. u (8) = {

tr - 8,

" 2•

tr+ 8 ,

for~$ 8 $ 7r;

for -; .. $ 8 < ~;

for -tr<fJ< - 2 ".

Approximations for U 5 (8) and u 5 (rcos8,rsin9) are shown in Figure 12.15.

s

1'

2 s = U(t)

1.5

r-

I

I

I

-lt 1' lf. 7t

-2 2

Figure 12.15

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