## Fourier Series

In this section we are providing pdf of Fourier Series which includes, Introduction of Fourier Series, Full Series, Half-Range Expansions, Bessel's Inequality and Parseval's Identity, Complex Fourier Series

## Complex Analysis

In this section we are providing pdf of complex analysis which includes, Origin of a complex number, Euler’s equation, Singularity, Complex Variable Functions, Harmonic function Laplace Equation, Taylor Series Analytic Series, Laurent’s Series, Complex Integration or Contour Integration, Real integral using contour integration, Branch Point and Branch Cut

## Matrices

In this section we are providing pdf of Matrices which includes, Matrices, Operations of Matrices, Name of matrices and their properties, in this section we give special emphasis on unitary matrix, Hermitian matrix, Symmetric and Anti-symmetric matrix, Elementary Row Transformation, Linear Dependence and Independence, The Rank of the Matrix, The Inverse of a Matrix, Eigenvalues and Eigenvectors, Pauli Spin Matrices, Similarity Transformation, Diagonalization, Functional Matrices, Spectral Decomposition Law

## Fourier Transformation

In this section we are providing pdf of Fourier Transformation which includes definition, properties (linearity, time shifting, frequency shifting, scaling etc.) and applications of Fourier Transformation. We also discuss inverse Fourier transformation of all functions. We mainly solve problems related to Dirac Delta Function, sinusoidal Function, Unit Step Function, Barrier function Gaussian, Lorentzian Function etc.

## Differential Equation

In this section we are providing pdf of Differential Equation which includes, Ordinary Differential Equations (ODEs), First Order First Degree, Homogeneous and Reducible, Linear differential Equation, Reducible Linear Bernoulli’s Form, Exact Differential Equation, Coupled Differential Equation, Second Order Differential Equation, Non-Homogeneous Linear ODEs of Second Order (RHS≠0), Linear Dependence and Independence of Solutions

## Multiple Variable Calculus

In this section we are providing pdf of Multiple Variable Calculus which includes, Function of Multiple Variable, Jacobian, The Jacobian in Three Dimensions, Cartesian to Spherical Polar Coordinates, Taylor Series, Taylor Series in 2D, Partial Derivatives, Other Relations

## Dirac Delta Function

In this section we are providing details about Dirac Delta Function including its properties, we discuss integration and differentiation of Dirac delta function which is use full in quantum mechanics and electromagnetic theory.

## Laplace Transform

In this section we are providing pdf of Laplace Transform which includes, Definition of Laplace Transform, Inverse Laplace Transform, Properties of Laplace Transformation, Laplace transform of integral, Second Shifting Theorem

## Vector Analysis

In this section we are providing pdf of Vector Analysis which includes, Definition of Vectors, The Rectangular Coordinate System, Vector Components and Unit Vectors, Vector Field, The Dot Product, The Cross Product, The Circular Cylindrical Coordinate System, The Spherical Polar Coordinate System. There are separate pdf of all formula and identity use in vector and vector calculus. The material is design such that it will help to build concept in Electromagnetic Theory and Mechanics.

## Group Theory

In this section we are providing pdf of Group Theory which includes, Definition of Introduction, Order of a group, Group Multiplication Table, The salient features of Cayley table.

## Numerical Method

In this section we are providing pdf of Numerical Technique which includes, Bisection Method, Iteration Method, Newton-Raphson Method, Interpolation, Numerical Integration, Simpson 1 by 3 Rule, Numerical Solution of Ordinary Differential Equations, Runge Kutta Method

## Special Function

In this section we are providing pdf of Special Function which includes, Special Function Legendre Function, Special Function Bessel Function, Special Function Hermite Functions, Special Function Laguerre Functions, Special Function Euler Functions

## Tensor Analysis

In this section we are providing pdf of Tensor Analysis which includes, Introduction, Spaces of N Dimensions, Contravariant and Covariant Vectors, Contravariant, Covariant, and Mixed Tensors, Tensors of Rank Greater Than Two, Tensor Fields, Fundamental Operations with Tensors, Matrices, Line Element and Metric Tensor, Associated Tensors, Christoffel's Symbols, Length of a Vector, Angle between Vectors, Geodesics, Covariant Derivative, Permutation Symbols and Tensors, Tensor Form of Gradient, Divergence, and Curl, Intrinsic or Absolute Derivative, Relative and Absolute Tensors

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