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
