Complex Analysis for Integrals in Physics

In summary, the conversation discusses the usefulness of complex analysis in computing integrals of real valued functions. The speaker, a physics student, is looking for a textbook that takes a practical approach to the subject, focusing on understanding how to do the integral rather than the underlying theory. They mention that any book on mathematical methods in physics would cover this topic, with some specific recommendations. They also mention using Fundamentals of Complex Analysis by Saff and Snyder, which is geared toward physics students and focuses on applications.
  • #1
go quantum!
54
0
Hello!
I know that the theory of complex analysis is useful to compute integrals of real valued functions. I am a Physics student and I followed a Complex Analysis course but we did not have time to cover this up.

I am looking for a textbook that takes a practical approach to this subject. I am more concerned about knowing how to do the integral, then to understand why the rules to do the computations work. In few words, I am looking for textbook with a physicist's approach to complex analysis.

Thanks.

PS- I could reformulate this post and just claim that I am looking for a book that explains the complex analysis that is necessary to study quantum field theory.
 
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  • #2
Almost any book on mathematical methods in physics will have a chapter or two devoted to this. The first three that came up on Amazon were Mathews & Walker, Boas and Arfken, all of them old and reliable. Plus many more.
 
  • #3
We used Fundamentals of Complex Analysis by Saff and Snyder in our Complex Analysis course. It's aimed at physics students and others interested in applications. I found it quite good.
 

1. What is Complex Analysis for Integrals in Physics?

Complex Analysis for Integrals in Physics is a branch of mathematics that deals with the study of complex numbers and their functions. It is used in physics to solve integrals involving complex functions, which are often encountered in the study of electromagnetic fields, quantum mechanics, and fluid dynamics.

2. Why is Complex Analysis important in Physics?

Complex Analysis is important in physics because it provides a powerful tool for solving integrals involving complex functions. These integrals are often encountered in physical systems and cannot be solved using traditional methods. Complex Analysis also allows for the simplification of complex expressions, making it easier to analyze and interpret physical phenomena.

3. What are some applications of Complex Analysis in Physics?

Some common applications of Complex Analysis in Physics include solving integrals in electromagnetism, quantum mechanics, and fluid dynamics, as well as analyzing and interpreting physical phenomena such as wave propagation, electric circuits, and fluid flow.

4. How does Complex Analysis differ from Real Analysis?

Complex Analysis and Real Analysis are both branches of mathematics, but they differ in their focus. Real Analysis deals with real numbers and their functions, while Complex Analysis deals with complex numbers and their functions. Additionally, Complex Analysis allows for the use of techniques such as contour integration and Cauchy's theorem, which are not applicable in Real Analysis.

5. What are some common techniques used in Complex Analysis for Integrals in Physics?

Some common techniques used in Complex Analysis for Integrals in Physics include contour integration, Cauchy's theorem, and the residue theorem. These techniques allow for the evaluation of complex integrals by reducing them to simpler integrals and making use of the properties of complex functions.

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