MATH 3150: Problem Solving with Fourier Series - Problems 2.2.7, 2.2.9, 2.2.11, 2.2.13, Assignments of Mathematics

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• 0.2 0.
• 0.4 0.
• 0.6 0.
• 0.8 0.

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% MATH 3150

F a l l^2008 % Problem

t h i c k L i n e s ( 3 ) ;

% remove

i f^ you^ don ’ t

have^ t h i s

i n

your^ system f i g u r e^ ( 1 ) ;^ c l f

x =^ linspace

(−pi^ , 3^ ∗^ pi

%^ p l o t^ t r u e

f u n c t i o n

f o r^ r e f e r n c e hold^ on ; plot^ ( x ,^ sin

( x ). ˆ 2 ) ; axis^ ([^ −^ pi

, 3^ ∗^ pi^ , 0 , 1 ] ) ; %^ l o o p^ o v e r

number^ o f

terms plot^ ( x , 1 / 2

∗^ o n e s (^ s i z e

( x ) ) , ’ r ’ ) ; plot^ ( x ,1/

∗(1^ −^ cos^ ( 2

∗^ x ) ) , ’ g ’ ) ; f i l e n a m e^

=^ ’ p 2^2 1 1. e p s ’ ; xlabel^ ( ’ x ’ ) ; print^ ( ’−d e p s c 2 ’ , f i l e n a m e ) ;system ( [ ’ e p s t o p d f

’ , f i l e n a m e ] ) ;

% MATH 3150

F a l l^2008 % Problem

t h i c k L i n e s ( 3 ) ;

% remove

i f^ you^ don ’ t

have^ i t^

i n

your^ system f i g u r e^ ( 1 ) ;^ c l f

x =^ linspace

(−pi^ , 3^ ∗^ pi

%^ p l o t^ t r u e

f u n c t i o n

f o r^ r e f e r n c e hold^ on ; %^ t r i c k^ t o

make^2 ∗^ p i

p e r i o d i c

f u n c t i o n

from^ f n

d e f^ on^ [ 0 , 2

∗^ p i ] plot^ ( x , ( mod( x+

pi^ , 2^ ∗^ pi^ )−

pi^ ) ) ; axis^ ([^ −^ pi^

, 3^ ∗^ pi^ ,−^ pi

∗^ 1. 2 ,^ pi^ ∗^ 1. 2 ] ) ; %^ l o o p^ o v e r

number^ o f

terms Ns =^ [ 1 , 2 , 5 , 1 0 , 1 5 ] ;c o l s ={^ ’ g ’ , ’m’ , ’ c ’ , ’ r ’ , ’ k ’

}^ ;

for^ iN =^

1 :^ length^ ( Ns ) ,N=Ns ( iN ) ; % compute^ p a r t i a l^

F o u r i e r^ s e r i e s s=zeros^ (^ s i z e

( x ) ) ; for^ n=1:N,an =^ −^2 ∗

(−1)ˆn/n ;s=s+an∗ sin^ ( n∗x ) ; end^ ; %^ c o m p a r a t i v e

p l o t plot^ ( x , s , c o l s

{^ iN^ }^ ) ; end^ ;%N hold^ o f f ;^ xlabel^ ( ’ x ’ ) ;f i l e n a m e= ’ p 2

2 1 3. e p s ’ ; print^ ( ’−d e p s c 2 ’ , f i l e n a m e ) ;system ( [ ’ e p s t o p d f

’^ f i l e n a m e ] ) ;