Learn · NPTEL

Course11110614973 lectures

Computational Mathematics with SageMath

Prof. Ajit Kumar · Institute of Chemical Technology, Mumbai

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Installation of Python Video
  2. Getting Started with Python Video
  3. Python as an advanced calculator Video
  4. Lists in Python Video
  5. Tuple, Sets and Dictionaries in Python Video
  6. Functions and Branching Video

week-02

  1. For loop in Python Video
  2. While loop in Python Video
  3. Creating Modules and Introduction to NumPy Video
  4. Use of NumPy module Video
  5. Python Graphics using MatplotLib Video

week-03

  1. Use of SciPy and SymPy in Python Video
  2. Classes in Python - Part 01 Video
  3. Classes in Python - Part 02 Video
  4. Introduction and Installation of SageMath Video
  5. Exploring integers in SageMath Video

week-04

  1. Solving Equations in SageMath Video
  2. 2d Plotting with SageMath Video
  3. 3d Plotting with SageMath Video
  4. Calculus of one variable with SageMath - Part 1 Video
  5. Calculus of one variable with SageMath - Part 2 Video
  6. Applications of derivatives Video

week-05

  1. Integration with SageMath Video
  2. Improper Integral using SageMath Video
  3. Application of integration using SageMath Video
  4. Limit and Continuity of real valued functions Video
  5. Partial Derivative with SageMath Video
  6. Local Maximum and Minimum Video

week-06

  1. Application of local maximum and local minimum Video
  2. Constrained optimization using Lagrange multipliers Video
  3. Working with vectors in SageMath Video
  4. Solving system of linear Equations in SageMath Video
  5. Vector Spaces in SageMath Video
  6. Basis and dimensions of vector spaces in SageMath Video

week-07

  1. Matrix Spaces with SageMath Video
  2. Linear Transformations Part 1 with SageMath Video
  3. Linear Transformations Part 2 with SageMath Video
  4. Eigenvalues and Eigenvectors Part 1 with SageMath Video
  5. Eigenvalues and Eigenvectors Part 2 with SageMath Video

week-08

  1. Inner Product Part 1 with SageMath Video
  2. Inner Product Part 2 with SageMath Video
  3. Orthogonal Decomposition with SageMath Video
  4. Least Square Solution with SageMath Video
  5. Singular Value Decomposition (SVD) with SageMath Video
  6. Application of SVD to image processing Video
  7. Solving System of linear ODE using Eigenvalues and Eigenvectors Video

week-09

  1. Google Page Rank Algorithm using SageMath Video
  2. Finding Roots of algebraic and transcendental equations in SageMath Video
  3. Numerical Solutions of System of linear equations in SageMath Video
  4. Interpolations in SageMath Video
  5. Numerical Integration in SageMath Video
  6. Numerical Eigenvalues Video

week-10

  1. Solving 1st and 2nd order ODE with SageMath Video
  2. Euler's Method to solve 1st order ODE with SageMath Video
  3. Fourth Order Runge-Kutta Method Video
  4. RK4 method for System of ODE and Applications Video
  5. Solving ODE using Laplace Transforms in SageMath Video

week-11

  1. Introduction to Linear Programming Problems (LPP) Video
  2. Solving Linear Programming Problmes using Graphical Methods Video
  3. Basics Definitions and Results in LPP Video
  4. Theory of Simplex Method Video
  5. Simplex Methods in SageMath - Part 01 Video
  6. Simplex Methods in SageMath - Part 02 Video
  7. Simplex Methods in Matrix Form Video

week-12

  1. Revised Simplex Method in SageMath Video
  2. Two Phase Simplex Method in SageMath Video
  3. Big-M Method in SageMath Video
  4. Duality of Linear Program Video
  5. Dual Simplex Method in SageMath Video
  6. Review and What next in SageMath? Video

Live Session

  1. Live Session 29-01-2021 Video
  2. Live Session 22-02-2021 Video
  3. Live Session 08-03-2021 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
Institute of Chemical Technology, Mumbai
Department
Mathematics
Teacher
Prof. Ajit 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. Coordinated by IIT Madras.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed