# Mathematical Physics

## Fourier series notes

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 a complex periodic function, given function must satisfy the following condition (i) It …

## complex analysis notes

Revise few of most important basics in complex numbers and complex algebra Note :- All pages open in new page What is complex numbers Algebra Of complex Numbers Conjugate of Complex Numbers Modulus of complex numbers Argand Plane Polar Representation of the complex number Rotation of Complex Number Identities for Complex Numbers Eulers formula and …

## Gradient of a scalar field and its physical significance

In this article learn about what is Gradient of a scalar field and its physical significance. We have also written an article on scalar and vector fields which is the topic you must learn before doing this topic. The gradient of a scalar field Let us consider a metal bar whose temperature varies from point …

## Scalar and Vector fields

In this article, learn what are Scalar and Vector fields. We know that many physical quantities like temperature, electric or gravitational field, etc. have different values at different points in space, for example, the electric field of a point charge is large near the charge and it decreases as we got farther away from the …

## Fourier Series formula sheet

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 …