Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=10.

> plot(sin(10.5*t)/(2*sin(t/2)),t=-Pi..Pi, title=`Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=10`);

> Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=50.

> plot(sin(50.5*t)/(2*sin(t/2)),t=-Pi..Pi,title=`Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=50`); Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=100.

> plot(sin(100.5*t)/(2*sin(t/2)),t=-Pi..Pi,title=`Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=100`); Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=1000.

> plot(sin(1000.5*t)/(2*sin(t/2)),t=-Pi..Pi,title=`Plot of D_k(t)=sin((k+1/2)/(2*sin(t/2) from t=-Pi to Pi, for k=1000`); Plot of first 6 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*sum(sin((2*j-1)*t)/(2*j-1),j=1..5),t=-Pi..Pi, title=`Plot of first 6 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of first 11 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*sum(sin((2*j-1)*t)/(2*j-1),j=1..10),t=-Pi..Pi, title=`Plot of first 11 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of first 101 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*sum(sin((2*j-1)*t)/(2*j-1),j=1..100),t=-Pi..Pi, title=`Plot of first 101 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of first 1001 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*sum(sin((2*j-1)*t)/(2*j-1),j=1..1000),t=-Pi..Pi, title=`Plot of first 1001 nonzero terms in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of average of first 5 partial sums in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*(1/5)*sum(sum(sin((2*j-1)*t)/(2*j-1),j=1..k), k=1..5),t=-Pi..Pi, title=`Plot of average of first 5 partial sums in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of average of first 10 partial sums in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*(1/10)*sum(sum(sin((2*j-1)*t)/(2*j-1),j=1..k), k=1..10),t=-Pi..Pi, title=`Plot of average of first 10 partial sums in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of average of first 101 partial sums in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi).

> plot(1/2+(2/Pi)*(1/101)*sum(sum(sin((2*j-1)*t)/(2*j-1),j=1..k), k=1..100),t=-Pi..Pi, title=`Plot of average of first 101 partial sums in Fourier series for f(t)= 0 (-Pi< t <0) and f(t)=1 ( 0 < t < Pi)`); Plot of sinc function sinc(t)=sin(Pi*t)/(Pi*t) from t=0 to t=10.

> plot(sin(Pi*t)/(Pi*t),t=0..10, title=`Plot of sinc function sinc(t)=sin(Pi*t)/(Pi*t) from t=0 to t=10`);

> Plot of sum of first 5 nonzero terms in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi).

> plot(sum(sin(j*t)/j,j=1..5),t=0..2*Pi, title=`Plot of sum of first 5 nonzero terms in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi)`); Plot of sum of first 10 nonzero terms in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi).

> plot(sum(sin(j*t)/j,j=1..10),t=0..2*Pi, title=`Plot of sum of first 10 terms in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi)`); Plot of sum of first 100 nonzero terms in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi).

> plot(sum(sin(j*t)/j,j=1..100),t=0..2*Pi, title=`Plot of sum of first 100 terms in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi)`); Plot of average of first 100 partial sums in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi).

> plot((1/100)*sum(sum(sin(j*t)/j,j=1..k),k=1..100),t=0..2*Pi, title=`Plot of average of first 100 partial sums in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi)`); Plot of average of first 1000 partial sums in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi).

> plot((1/1000)*sum(sum(sin(j*t)/j,j=1..k),k=1..1000),t=0..2*Pi, title=`Plot of average of first 1000 partial sums in Fourier series for h(t)= (Pi-t)/2 ( 0 < t < 2*Pi)`); >

Maple TM is a registered trademark of Waterloo Maple Inc.
Math rendered by WebEQ