## Mathematics revision sheet for class 11 and class 12 physics

This mathematics sheet would be helpful for quick revision of most of maths formulas needed before class 11 and 12 physics examination. It covers quick and much needed formulas on differentiation , integration, trigonometry, AP, GP etc.

## Vector Differentiation full length notes

Full notes on vector Differentiation is now available at the website physicscatalyst.com covering following topics
1. Differentiation of vectors
2. Scalar and vector fields
3. Gradient of a scalar field

## Complex Numbers

Complex numbers are the numbers of the form a+ib where a and b are real numbers.

Definition:- Complex numbers are defined as an ordered pair of real numbers like (x,y) where

z=(x,y)=x+iy

and both x and y are real numbers and x is known as real part of complex number and y is known as imaginary part of the complex number.

## Vector Algebra 2

In this post we’ll lern Vector algebra in component form.
Component of any vector is the projection of that vector along the three coordinate axis X, Y, Z.

In component form addition of two vectors is

## 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 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 but not necessary) … Continue reading Fourier Series »
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 »