Math Help - Residues

1. Residues

hi my lecture notes were very vague this semester and nine o'clock in the morning isnt the easiest for a student that works till 1am each night.

i need some help with Residues, if anyone knows of a good website that has a good explanation and example of residue calculus it would help out.

the question im working on now is

us residue calculus and appropriate contours to evaluate real integrals

integral from 0 to infinity of 1/(x^4 +1) dx

2. Originally Posted by Reece
hi my lecture notes were very vague this semester and nine o'clock in the morning isnt the easiest for a student that works till 1am each night.

i need some help with Residues, if anyone knows of a good website that has a good explanation and example of residue calculus it would help out.

the question im working on now is

us residue calculus and appropriate contours to evaluate real integrals

integral from 0 to infinity of 1/(x^4 +1) dx

I know four: Art of Problem Solving, Physic Forum, SOS, and here. You just need to search the sites for complex analysis problems and study the solutions.

Anyway, use:

$\mathop\oint\limits_{H_u}\frac{dz}{z^4+1}$ where $H_u$ is the upper half-disc contour. The big denominator assures you that the integral over the semi-circle component of the contour goes to zero and the integral over the real axis component is twice your integral. There are only two poles in the contour right: $e^{\pi i/4}$ and $e^{3\pi i/4}$. Now calculate the residues for these poles and use Residue Theorem.

3. Originally Posted by Reece
hi my lecture notes were very vague this semester and nine o'clock in the morning isnt the easiest for a student that works till 1am each night.

i need some help with Residues, if anyone knows of a good website that has a good explanation and example of residue calculus it would help out.

the question im working on now is

us residue calculus and appropriate contours to evaluate real integrals

integral from 0 to infinity of 1/(x^4 +1) dx