Every story.

Cauchy- Riemann equations

Let (1) where (2) so (3) The total derivative of  with respect to  is then (4) (5) In terms of  and , (5) becomes…

Analytic Functions

Analytic Functions are defined as per the converging series; that revolves around a particular variable x for which the series has…

Stokes theorem and Gauss divergence theorem (without proofs)

Green’s theorem

The idea behind Green’s theorem represents the circulation of FF around CC. If FF were the velocity field of water flow, for example, this integral would…

Line and surface integrals

Gradient of Vector Calculus

The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to…

Taylor’s theorem

Cayley-Hamilton Theorem

Given (1) (2) then (3) where  is the identity matrix. Cayley verified this identity for  and 3 and postulated that it was true…

Matrix Diagonalization

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix–a so-called diagonal matrix–that shares…

Eigenvalues and Eigenvectors

Introduction This page is a brief introduction to eigenvalue/eigenvector problems (don’t worry if you haven’t heard of the latter).  Before…

Determinant of a Matrix

The determinant of a matrix is a special number that can be calculated from a square matrix. A Matrix is an array of numbers: A…

System of linear equations