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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 27 - Numerical Differentiation based on Divided Difference Formula

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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