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Last updated:

September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Description

Numerical Analysis and Computer Programing. Instructor: Prof. P. B. Sunil Kumar, Department of Physics, IIT Madras.

This course covers some of the basic aspects of programming and algorithms. Topics covered in this course include Approximations and round off errors, Truncation errors and Taylor Series, Determination of roots of polynomials and transcendental equations by Newton-Raphson, Secant and Bairstow's method; Solutions of linear simultaneous linear algebraic equations by Gauss Elimination and Gauss-Seidel iteration methods; Curve fitting - linear and nonlinear regression analysis; Backward, Forward and Central difference relations and their uses in Numerical differentiation and integration, Application of difference relations in the solution of partial differential equations; Numerical solution of ordinary differential equations by Euler, Modified Euler, Runge-Kutta and Predictor-Corrector method. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Programming: Basics Unlimited
  • Lecture 02 – Introduction to Pointers Unlimited
  • Lecture 03 – Pointers and Arrays Unlimited
  • Lecture 04 – External Functions and Argument Passing Unlimited
  • Lecture 05 – Representation of Numbers Unlimited
  • Lecture 06 – Numerical Error Unlimited
  • Lecture 07 – Error Propagation and Stability Unlimited
  • Lecture 08 – Polynomial Interpolation Unlimited
  • Lecture 09 – Polynomial Interpolation (cont.) Unlimited
  • Lecture 10 – Error in Interpolation Polynomial Unlimited
  • Lecture 11 – Piecewise Polynomial Interpolation Unlimited
  • Lecture 12 – Cubic Spline Interpolation Unlimited
  • Lecture 13 – Data Fitting: Linear Fit Unlimited
  • Lecture 14 – Data Fitting: Linear Fit (cont.) Unlimited
  • Lecture 15 – Data Fitting: Nonlinear Fit Unlimited
  • Lecture 16 – Matrix Elimination and Solution to Linear Equations Unlimited
  • Lecture 17 – Solution to Linear Equations: LU Decomposition Number Unlimited
  • Lecture 18 – Matrix Elimination with Pivoting and the Condition Number Unlimited
  • Lecture 19 – Eigenvalues of a Matrix Unlimited
  • Lecture 20 – Eigenvalues and Eigenvectors Unlimited
  • Lecture 21 – Solving Nonlinear Equations Unlimited
  • Lecture 22 – Solving Nonlinear Equations: Newton-Raphson Method Unlimited
  • Lecture 23 – Methods for Solving Nonlinear Equations: Newton-Raphson Iterative Method Unlimited
  • Lecture 24 – Systems of Nonlinear Equations Unlimited
  • Lecture 25 – Numerical Derivations Unlimited
  • Lecture 26 – Higher Order Derivatives from Difference Formula Unlimited
  • Lecture 27 – Numerical Integration: Basic Rules Unlimited
  • Lecture 28 – Numerical Integration: Comparison of Different Basic Rules Unlimited
  • Lecture 29 – Numerical Integration: Gaussian Rules Unlimited
  • Lecture 30 – Numerical Integration: Comparison of Gaussian Rules Unlimited
  • Lecture 31 – Solving Ordinary Differential Equations: Euler’s Method Unlimited
  • Lecture 32 – Solving Ordinary Differential Equations: Runge-Kutta Method Unlimited
  • Lecture 33 – Adaptive Step Size Runge-Kutta Scheme Unlimited
  • Lecture 34 – Partial Differential Equations Unlimited
  • Lecture 35 – Explicit and Implicit Methods for Partial Differential Equations Unlimited
  • Lecture 36 – The Crank-Nicolson Scheme for Two Spatial Dimensions Unlimited
  • Lecture 37 – Fourier Transforms Unlimited
  • Lecture 38 – Fast Fourier Transforms Unlimited

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