## Gregory Newton Backward Interpolation Method

Gregory Newton Backward Interpolation Method can be used to derive difference formula when the x values are at equidistant intervals and the value to be interpolated lies towards the end of the table. Below is a detailed explanation of how to apply Gregory Newton Backward Interpolation Method –

## C Program to evaluate forward difference

Below is a C program to evaluate forward difference and thus print a forward difference table for n function values –

## Reducing Lagranges interpolation formula to Linear interpolation

Below is an amazing solution to prove that when n=2, Lagranges interpolation formula reduces to Linear interpolation –

## Testing convergence of a sample Logarithmic series using Leibnitz’s rule

Below is the solution to test convergence of a sample Logarithmic series –

## Discussing Convergence of Iteration and Newton Raphson Methods

We use various Numerical methods to solve algebraic and transcendental equations. All these methods converge the result to a single root after various approximations specific to each method. In this article we delve into details of rate of convergence of two popular methods – Iterative and Newton Raphson method. Enjoy!

## Solving Equations by Jacobi’s Iteration Method

Jacobi’s Iteration method is an interesting method to solve equations by simple iteration method. Here is an example –

## Solving a set of equations using Gauss Seidal Elimination Method

Here is an excellent example of Gauss Seidal elimination method to solve a set of equations –

## Finding Inverse of a Matrix using Gauss Elimination Method

Here is an intelligent and simple way to find the inverse of a matrix using Gauss Elimination method –

## Gauss Jordan Elimination Method

Here is a well explained solution to solve a set of equations using Gauss Jordan Elimination method –

## Gauss Elimination Method

Below is a well explained solution for a set of equations using Gauss Elimination method. Enjoy!

## Finding Roots of equation x3-3×2+x+1=0

We will be using Newton Raphson method to find the root of this equation. Enjoy!

## Finding measure of skewness and kurtosis for Poisson distribution

Here we define what Poisson Distribution is how to measure its skewness and kurtosis.

## Proving Inversion Mapping

Here we venture to prove that Inversion Mapping maps the totality of circles lines in the Z plane on to the same that of W plane –

## Find 4th Root of 1 and Square root of -8i

Here is an interesting solution to find nth root of a complex number Z. Here we use a general equation to find the 4th root of 1 and square of -8i. Enjoy!

## Finding Linear Fractional Transformation

Ok, here is a beautiful mathematical solution to find the Linear Fractional Transformation which maps |Z| <= 1 on to |W| <=1 such that Z = i/4 is mapped onto W=0. Also we will graph out the images of the lines x=c and y=c.

## Transformation of W=eZ

Here we discuss transformation of W = eZ

## Forming a Bi-Linear Transformation which maps a set of points

Here is a mathematical solution for forming a Bi-Linear Transformation which maps the points (1, i,-1) onto the points  (i,0,-i) and hence finding the image of |Z| < 1 and also finding the Invarient points of this Transformation 🙂

## How to determine which mathematical functions are analytic

Here is the solution on how to determine if a mathematical function is analytic –

## Mathematical solution for checking a certain function satisfy Laplace Equation

Here is an attempt to check if a function satisfies Laplace Equation and determining corresponding analytical function –

## Locus of a point Z satisfying condition |Z-1| + |Z+1| = 4

Here is a fun solution for Mathematics students to find the locus of a point Z satisfying condition |Z-1| + |Z+1| = 4 –

## Find a root of x = e-x using Regular Falsi Method

Regular Falsi method is a numerical method to derive the root of a polynomial. The advantage of Regular Falsi over Bisection method is that the convergence is made faster. Below is explanation with a graphical representation and the solution –

## Find a root of x = e-x using Bisection Method

Bisection method is the most simplest method of solving algebraic or transcendental equations. It involves selecting an interval [a,b] in which the root lies such that f(a)f(b) < 1. Below is a detailed solved version to find root of x = e<sup>-x</sup>. Enjoy!!

## Newton Raphson Method Example – Find root of e-x = Sin X

Newton Raphson method is the core in computer Numerical analysis software programs to find root of equations such as e<sup>-x</sup> = Sin X. Complete solution is as below –

## Numerical solution of a transcendental equation 1.5x – tanx – 0.1 = 0

Solving 1.5x – tanx – 0.1 = 0,  using iteration method – Iteration is a method of solving algebraic or transcendental equation and is widely used in computer mechanics and programming algorithms. A hand-written solution is as below –

## Numerical solution by method of Iteration

Solving x = 1/ (1+x)1/2 using iteration method – Iteration is a method of solving algebraic or transcendental equation and is widely used in computer mechanics and programming algorithms. A hand-written solution is as below –