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September 23, 2023

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Description

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)

Course Curriculum

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

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