Contour integration and Calc. of complex functions

[lizzie96]

Hello,

I would like to learn some contour integration and complex analysis at the simplest level possible. My maths education only goes up to A Level, so I haven't covered any "calculus of complex functions" yet, and with the books I'm trying to read at the moment I keep getting stuck because I can't do contour integrals in the complex plane. Could anyone give a brief explanation of contour integration, or link to a document that explains it in simple terms for a beginner?

Thank you!

 

[SteamKing]

Complex integration is usually part of a semester long course in complex variables. You usually need exposure to things like Green's Theorem and other vector calculus theorems as a pre-requisite.

You can google "complex integration" and find various hits for relevant techniques.

 

[lizzie96]

Thank you. I have had a look at some methods online, but I would like to learn in a little more detail. I have also looked at some lecture notes on the topic, but as I mainly want to learn about it in order to understand physics, it is hard to see which parts are the most relevant. Do you know of any undergraduate-level Mathematical methods books for physicists that explain this well?

 

[homeomorphic]

Visual Complex Analysis has the best explanation. Two different explanations, one in terms of Riemann sums, and the other in terms of vector fields.

 

[xiavatar]

If you just want to be able to apply the techniques, and have some vague intuition about it you could try Mathematical Methods in the Physical Sciences by Boas.