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Course11110710540 lectures

Numerical methods

Prof. Ameeya Kumar Nayak and Prof. Sanjeev Kumar · IIT Roorkee

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About

This course is a basic course offered to UG student of Engineering/Science background. It contains solution of system of linear equations, roots of non-linear 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.

Intended audience: UG students of technical universities/colleges.

Lectures

Week 1

  1. Introduction to error analysis and linear systems YouTube
  2. Gaussian elimination with partial pivoting YouTube
  3. LU decomposition YouTube
  4. Jacobi and Gauss Seidel methods YouTube
  5. Iterative methods-II YouTube

Week 2

  1. Introduction to Non-linear equations and Bisection method YouTube
  2. Regula Falsi and Secant methods YouTube
  3. Newton-Raphson method YouTube
  4. Fixed point iteration method YouTube
  5. System of Nonlinear equations YouTube

Week 3

  1. Introduction to Eigenvalues and Eigenvectors YouTube
  2. Similarity Transformations and Gershgorin Theorem YouTube
  3. Jacobi's Method for Computing Eigenvalues YouTube
  4. Power Method YouTube
  5. Inverse Power Method YouTube

Week 4

  1. Interpolation Part I (Introduction to Interpolation) YouTube
  2. Interpolation part-II ( Some basic operators and their properties) YouTube
  3. Interpolation part-III (Newton’s Forward/ Backward difference and derivation of general error) YouTube
  4. Interpolation part-IV (Error in approximating a function by a polynomial using Newton’s Forward & Backward difference formula) YouTube
  5. Interpolation part-V (Solving problems using Newton's Forward & Backward difference formula) YouTube

Week 5

  1. Interpolation part-VI (Central difference formula) YouTube
  2. Interpolation part-VII (Lagrange interpolation formula with examples) YouTube
  3. Interpolation part-VIII (Divided difference interpolation with examples) YouTube
  4. Interpolation part-IX (Hermite's interpolation with examples) YouTube
  5. Numerical differentiation part-I (Introduction to numerical differentiation by interpolation formula) YouTube

Week 6

  1. Numerical differentiation part-II (Numerical differentiation based on Lagrange’s interpolation with examples) YouTube
  2. Numerical differentiation part-III (Numerical differentiation based on Divided difference formula with examples) YouTube
  3. Numerical differentiation part-IV (Maxima and minima of a tabulated function and differentiation errors) YouTube
  4. Numerical differentiation part-V (Differentiation based on finite difference operators) YouTube
  5. Numerical differentiation part-VI (Method of undetermined coefficients & Derivatives with unequal intervals) YouTube

Week 7

  1. Numerical Integration part-I (Methodology of Numerical Integration & Rectangular rule ) YouTube
  2. Numerical Integration part-II (Quadrature formula and Trapezoidal rule with associated errors) YouTube
  3. Numerical Integration part-III (Simpsons 1/3rd rule with associated errors) YouTube
  4. Numerical Integration part-IV (Composite Simpsons 1/3rd rule & Simpsons 3/8th rule with examples) YouTube
  5. Numerical Integration part-V (Gauss Legendre 2-point and 3-point formula with examples) YouTube

Week 8

  1. Introduction to Ordinary Differential equations YouTube
  2. Numerical methods for ODE-1 YouTube
  3. Numerical Methods-II YouTube
  4. R-K Methods for solving ODEs YouTube
  5. Multi-step Method for solving ODEs YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Roorkee
Department
Mathematics
Taught by
Prof. Ameeya Kumar Nayak, Prof. Sanjeev Kumar
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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