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Numerical Methods

Numerical Methods. Instructors: Dr. Ameeya Kumar Nayak and Dr. Sanjeev Kumar, Department of Mathematics, IIT Roorkee. This course is a basic course offered to UG student of Engineering/Science background. It contains solution of system of linear equations, roots of nonlinear equations, interpolation, numerical differentiation and integration. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences. (from nptel.ac.in)

Lecture 11 - Introduction to Eigenvalues and Eigenvectors


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Lecture 01 - Introduction to Error Analysis and Linear Systems
Lecture 02 - Gaussian Elimination with Partial Pivoting
Lecture 03 - LU Decomposition
Lecture 04 - Jacobi and Gauss Seidel Methods
Lecture 05 - Iterative Methods
Lecture 06 - Introduction to Nonlinear Equations and Bisection Method
Lecture 07 - Regula Falsi and Secant Methods
Lecture 08 - Newton-Raphson Method
Lecture 09 - Fixed Point Iteration Method
Lecture 10 - System of Nonlinear Equations
Lecture 11 - Introduction to Eigenvalues and Eigenvectors
Lecture 12 - Similarity Transformations, Singular Value Decomposition, Gershgorin Theorem
Lecture 13 - Jacobi Method for Computing Eigenvalues
Lecture 14 - Power Method
Lecture 15 - Inverse Power Method
Lecture 16 - Introduction to Interpolation
Lecture 17 - Interpolation: Some Basic Operators and their Properties
Lecture 18 - Interpolation: Newton's Forward/Backward Difference Formula
Lecture 19 - Interpolation: Error in Approximating a Function by a Polynomial using Newton's Forward/Backward Difference Formula
Lecture 20 - Interpolation: Solving Problems using Newton's Forward/Backward Difference Formula
Lecture 21 - Interpolation: Central Difference Formula
Lecture 22 - Interpolation: Lagrange's Interpolation Formula with Examples
Lecture 23 - Interpolation: Divided Difference Interpolation with Examples
Lecture 24 - Interpolation: Hermite's Interpolation Formula with Examples
Lecture 25 - Introduction to Numerical Differentiation
Lecture 26 - Numerical Differentiation based on Lagrange's Interpolation Formula
Lecture 27 - Numerical Differentiation based on Divided Difference Formula
Lecture 28 - Numerical Differentiation: Maxima or Minima of a Tabulated Function
Lecture 29 - Numerical Differentiation based on Finite Difference Operators
Lecture 30 - Numerical Differentiation: Method of Undetermined Coefficients with Unequal Intervals
Lecture 31 - Methodology of Numerical Integration and Rectangular Rule
Lecture 32 - Numerical Integration: Quadrature Formula and Trapezoidal Rule with Associated Errors
Lecture 33 - Numerical Integration: Simpson's 1/3rd Rule with Associated Errors
Lecture 34 - Numerical Integration: Composite Simpson's 1/3rd Rule and Simpson's 8/3th Rule
Lecture 35 - Numerical Integration: Gaussian-Legendre 2-point and 3-point Formula with Examples
Lecture 36 - Introduction to Ordinary Differential Equations
Lecture 37 - Numerical Methods for ODEs: Picard's Method, Euler's Method
Lecture 38 - Numerical Methods for ODEs: Taylor Series Method and Euler's Modified Method
Lecture 39 - Numerical Methods for ODEs: Runge-Kutta Method
Lecture 40 - Numerical Methods for ODEs: Multi-Step Method