Category Archives: 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 should be single valued (ii) It should be continuous. Drichlet’s Conditions … Continue reading Fourier series notes »

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 De moivre’s theorem Cube Root of unity Complex Variables A … Continue reading complex analysis notes »

Gradient of a scalar field and its physical significance

Learn about what is Gradient of a scalar field and its physical significance. The gradient of a scalar field Let us consider a metal bar whose temperature varies from point to point in some complicated manner. So, temperature will be a function of x, y, z in Cartesian co-ordinate system. Hence temperature here is a scalar field represented by the function T(x,y,z). Since temperature depends on … Continue reading Gradient of a scalar field and its physical significance »

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 go farther away from the charge. So we can say that electric field here is the … Continue reading Scalar and Vector fields »

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 should be single valued (ii) It should be continuous.  Drichlet’s Conditions(sufficient … Continue reading Fourier Series formula sheet »