Category Archives: Mathematical Physics

Quick Vector Algebra Summary

Here in this post we will go through a quick recap of vector algebra keeping in mind that reader already had detail knowledge and problem solving skills related to the topic being discussed. Here we are briefing Vector Algebra because concepts of electrostatics , electromagnetism and many more physical phenomenon can best be conveniently expressed using this tool.

Fourier Series

Fourier series is an expansion of a periodic function of period $2\pi$ which is representation of a function in a series of sine or cosine such as $f(x)=a_{0}+\sum_{n=1}^{\infty }a_{n}cos(nx)+\sum_{n=1}^{\infty }b_{n}sin(nx)$     where $a_{0}$ , $a_{n}$ and $b_{n}$ are constants and are known as fourier coefficients.   In applying fourier theorem for analysis of an complex periodic function , given function must satisfy following condition  (i) It should be single valued  (ii) It should be continuous.   Drichlet’s Conditions(sufficient but not necessary) … Continue reading Fourier Series »

Complex Analysis Part 2

Liouville’s Theorem If a function $f(z)$ is analytic for all finite values of z, and is bounded then it is a constant.Note:- $e^{z+2\pi i} = e^z$ Taylor’s TheoremIf a function $f(z)$ is analytic at all points inside a circle C, with its centre at point a and radius R then at each point z inside C$f(z)=f(a)+(z-a)f'(a)+\frac{1}{2!}(z-a)^2f”(a)+…….+\frac{1}{n!}(z-a)^nf^n(a)$Taylor’s theorem is applicable when function is analytic at all points inside a circle.  Laurent SeriesIf $f(z)$ is … Continue reading Complex Analysis Part 2 »