Verifying Stroke's Theorem & Fourier Series

[installer2001]

Strokes theorem & Fourier series

Respected guys.
i need ur help ...urgent help bcoz tomorow is my paper.


1);Verify strokes thorem for F=6zi+(2x+y)j-xk where S is upper half of circle x^2+y^2+z^2=1 bounded by close curve c x^2+y^2=1 at z=0 plane

2):With the help of Fourier Sine series and Fourier Cosine series
f(x)=x+1 0<x<Π(pie)
Deduce 1-1/3+1/5-1/7 --------------------- = Π(pie)/4
1+1/(3^2)+1/(5^2)+1/(7^2)--------= Π^2/8

 

[quasar987]

1) They want you to avaluate the surface integral. Then the path integral, and show that they have the same value, as predicted by Stoke's thm.

2) Try evaluating both sides of the equation (i.e. f(x) = its Fourier series) series at a precise point, such as x=0 for which all the sines vanish and all the cos become 1.

 

[installer2001]

well thz but can u explain it in more detail

 

[HallsofIvy]

Respect the problem as well as the 'guys'! What work have you done yourself? Quasar987 told you what you need to do. Do you know what Stoke's Theorem says? What is the line integral you need to do? What is the path integral.