What is Numerical Analysis?

A Quick Intro

Numerical analysis is a branch of mathematics focused on developing and analyzing algorithms for approximating solutions to complex numerical problems in science and engineering. It involves techniques for solving equations, integrating and differentiating functions, and optimizing processes when exact solutions are unattainable or impractical.

All of the topics are covered in detail in our Online Numerical Analysis Course.

https://www.youtube.com/watch?v=e7a3bo22fAc&list=PLrtzypMWdxDE2F5o05FumTKW0vZrQiddU&pp=iAQB

The following sections contain links to our full lessons on all the topics listed below.

Ch # 1: Empirical Laws and Curve Fitting

• Find Linear law using Least Square Method.
• Find Parabola of the form y = a+bx+cx²  using Least Square Method.
• Fit a curve of the form v = ae^kt  using Least Square Method.
• Fit a curve of the form y = ax^b  using Least Square Method.
• Fit a curve of the form y = ab^x  using Least Square Method.
• Fit a straight line y = ax+b  and also parabola  y = ax²+bx+c . Also calculate Sum of Residuals in each case.
• Fit a straight line using Method of Moments.
• Fit a parabola of the form   y = ax²+bx+c .

Ch # 3 : Solution to Numerical Algebraic and Transcendental Equations

• Bisection Method
• Method of False Position (Regula False Method)
• Newton Raphson Method

Ch # 4 : Simultaneous Linear Algebraic Equations

• Jacobi Method of Iteration
• Gauss Seidel Iteration Method

Ch # 6 : Interpolation with Equal Intervals

• Gregory Newton Forward Interpolation Formula
• Gregory Newton Backward Interpolation Formula

Ch # 7 : Central Difference Interpolation Formulae

Ch # 8 : Interpolation with Unequal Intervals

• Gauss’s Forward Interpolation Formula
• Gauss’s Backward Interpolation Formula
• Stirling’s Formula
• Bessel’s Formula

• Divided Difference
• Newton’s Divided Difference Formula
• Lagrange’s Interpolation Formula
• Lagrange Method (Inverse Interpolation)
• Iterative Method (Inverse Interpolation)

Ch # 9 : Numerical Differentiation and Integration

• Derivates using Newton’s Forward Difference Formula
• Derivates using Newton’s Backward Difference Formula
• Derivates using Stirling Formula

Ch # 10 : NUMERICAL INTEGRATION

• Trapezoidal Rule
• Simpson’s 1/3 Rule
• Simpson’s 3/8 Rule
• Weddle’s Rule

Ch # 11 : Numerical Solution to Ordinary Differential Equations

• Power Series Solution
• Point Wise Methods (Solution by Taylor Series)
• Taylor Series Method for Higher Order Differential Equations
• Euler’s Method
• Improved Euler’s Method
• Modified Euler’s Method
• Runge Kutta Methods
• Higher Order Runge Kutta Methods
• Runge Kutta Methods for Simultaneous First Order Equations
• Runge Kutta Methods for Second Order Differential Equations