NOC:Numerical Methods


Lecture 1 - Introduction to error analysis and linear systems


Lecture 2 - Gaussian elimination with Partial pivoting


Lecture 3 - LU decomposition


Lecture 4 - Jacobi and Gauss Seidel methods


Lecture 5 - Iterative methods-II


Lecture 6 - Introduction to Non-linear equations and Bisection method


Lecture 7 - Regula Falsi and Secant methods


Lecture 8 - Newton-Raphson method


Lecture 9 - Fixed point iteration method


Lecture 10 - System of Nonlinear equations


Lecture 11 - Introduction to Eigenvalues and Eigenvectors


Lecture 12 - Similarity Transformations and Gershgorin Theorem


Lecture 13 - Jacobi's Method for Computing Eigenvalues


Lecture 14 - Power Method


Lecture 15 - Inverse Power Method


Lecture 16 - Interpolation - Part I (Introduction to Interpolation)


Lecture 17 - Interpolation - Part II ( Some basic operators and their properties)


Lecture 18 - Interpolation - Part III (Newton’s Forward/ Backward difference and derivation of general error)


Lecture 19 - Interpolation - Part IV (Error in approximating a function by a polynomial using Newton’s Forward and Backward difference formula)


Lecture 20 - Interpolation - Part V (Solving problems using Newton's Forward and Backward difference formula)


Lecture 21 - Interpolation - Part VI (Central difference formula)


Lecture 22 - Interpolation - Part VII (Lagrange interpolation formula with examples)


Lecture 23 - Interpolation - Part VIII (Divided difference interpolation with examples)


Lecture 24 - Interpolation - Part IX (Hermite's interpolation with examples)


Lecture 25 - Numerical differentiation - Part I (Introduction to numerical differentiation by interpolation formula)


Lecture 26 - Numerical differentiation - Part II (Numerical differentiation based on Lagrange’s interpolation with examples)


Lecture 27 - Numerical differentiation - Part III (Numerical differentiation based on Divided difference formula with examples)


Lecture 28 - Numerical differentiation - Part IV (Maxima and minima of a tabulated function and differentiation errors)


Lecture 29 - Numerical differentiation - Part V (Differentiation based on finite difference operators)


Lecture 30 - Numerical differentiation - Part VI (Method of undetermined coefficients and Derivatives with unequal intervals)


Lecture 31 - Numerical Integration - Part I (Methodology of Numerical Integration and Rectangular rule )


Lecture 32 - Numerical Integration - Part II (Quadrature formula and Trapezoidal rule with associated errors)merical Integration Part-I (Methodology of Numerical Integration and Rectangular rule )


Lecture 33 - Numerical Integration - Part III (Simpsons 1/3rd rule with associated errors)


Lecture 34 - Numerical Integration - Part IV (Composite Simpsons 1/3rd rule and Simpsons 3/8th rule with examples)


Lecture 35 - Numerical Integration - Part V (Gauss Legendre 2-point and 3-point formula with examples)


Lecture 36 - Introduction to Ordinary Differential equations


Lecture 37 - Numerical methods for ODE-1


Lecture 38 - Numerical Methods - II


Lecture 39 - R-K Methods for solving ODEs


Lecture 40 - Multi-step Method for solving ODEs