This course is about Numerical Methods and covers some of the popular methods and approaches being used daily by mathematicians and everyone involved in the computation.



00:00:00 Introduction
00:04:20 Machine Representation of Numbers
00:32:22 Basic Concepts (Function Continuity, Rolle's Theorem, First Mean Value Theorem, Bolzano's Theorem)
00:49:10 OnePoint Iterative Methods
01:57:44 TwoPoint Iterative Methods
02:14:12 Interpolation and Curve Fitting
03:35:19 Differentiation
03:17:46 Integration (Quadrature)


Topics Covered :
Base 2 Representation
FloatingPoint Representation
Machine Epsilon
RoundOff and Truncation Errors
Quiz: RoundOff and Truncation Errors
Function Continuity
Rolle's Theorem
First Mean Value Theorem
Bolzano's Theorem
Acceleration of Convergence
Acceleration of сonvergence
Order of Convergence
Newton's Method (a.k.a. NewtonRaphson)
Newton's Method
Multidimensional Extensions of Newton's Method
Multidimensional extensions of Newton's method
Approximate Newton's Method
Approximate Newton's Method
Horner's Algorithm for Polynomial Equations
Horner's Algorithm
Bisection Method
Bisection method
Regula Falsi Method
Secant Method

Secant method
Polynomial Interpolation
Newton Basis
Divided Differences
Divided Differences: Examples
Forward Differences
Lagrangian Interpolation
Lagrangian interpolation
Neville's Algorithm
Neville's algorithm
First Derivative Approximations
Second Derivative Approximations
Error Terms by Taylor Series Expansion
Richardson Interpolation
Introduction
Trapezium Rule
Midpoint Rule
GaussHermite
GaussLaguerre


Requirements :
Basic math knowledge
Fundamental knowledge of computing
Some familiarity with #MATLAB is required to follow the examples


This course will teach you about


How computers store numbers: what is floatingpoint, what is precision and accuracy.
The kinds of errors you are likely to encounter when applying numerical methods, and how to minimize them.
One and TwoPoint iterative methods
Interpolation and Curve Fitting
Numerical Differentiation and Integration


Who this course is for:
This course is designed for anyone interested in numerical methods and their applications for solving realworld problems
Engineers, computer scientists, mathematicians, and finance people will enjoy this course