## C program to evaluate the 1st derivative of a function at any given point

Writing C programs for numerical differentiation is interesting and fun. Here is one that I wrote years back. Enjoy!

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# Category: Numerical Analysis

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## C program to evaluate the 1st derivative of a function at any given point

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Writing C programs for numerical differentiation is interesting and fun. Here is one that I wrote years back. Enjoy!

Advanced Mathematics
## Gregory Newton Backward Interpolation Method

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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 –

Advanced Mathematics
## C Program to evaluate forward difference

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

Advanced Mathematics
## Reducing Lagranges interpolation formula to Linear interpolation

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

Advanced Mathematics
## Discussing Convergence of Iteration and Newton Raphson Methods

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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!

Advanced Mathematics
## Solving Equations by Jacobi’s Iteration Method

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

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

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

Advanced Mathematics
## Finding Inverse of a Matrix using Gauss Elimination Method

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

Advanced Mathematics
## Gauss Jordan Elimination Method

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

Advanced Mathematics
## Gauss Elimination Method

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

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

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

Advanced Mathematics
## Find a root of x = e^{-x} using Regular Falsi Method

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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 –

Advanced Mathematics
## Find a root of x = e^{-x} using Bisection Method

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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!!

Advanced Mathematics
## Newton Raphson Method Example – Find root of e^{-x} = Sin X

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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 –

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

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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 –

Advanced Mathematics
## Numerical solution by method of Iteration

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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 –