Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Computational Mathematics with SageMath

Institute of Chemical Technology (ICT) and NPTEL via Swayam

Go to class Write review

Overview

Computational Mathematics with SageMath: This twelve week course aims to use SageMath, a Python based free and open source computer algebra system (CAS) to explore concepts in Calculus, Applied Linear Algebra, Numerical Methods and basic Linear Programming Problems. The course will begin with the introduction of basic Python programming language. Next, we shall provide a quick introduction to SageMath software along with plotting 2D and 3D objects. The focus will be on using SageMath to explore topics in Calculus, Applied Linear Algebra, Numerical Method and Linear Programming Problems along with several applications.INTENDED AUDIENCE :UG and PG students of Mathematics and BE Students, Teachers teaching in UG/PG Level.PREREQUISITES : Basic knowledge of Calculus, Linear Algebra and ODE and Numerical Methods.INDUSTRIES SUPPORT :Any industry dealing with Data Science and Numerical Computations.

Syllabus

Week 1:

Installation of Python
Getting Started with Python
Python as an advanced calculator
Lists in Python
Tuple, Sets and Dictionaries in Python
Functions and Branching

Week 2:

For loop in Python
While loop in Python
Creating Modules and Introduction to NumPy
Use of NumPy module
Python Graphics using MatplotLib

Week 3:

Use of SciPy and SymPy in Python
Classes in Python - Part 01
Classes in Python - Part 02
Introduction and Installation of SageMath
Exploring integers in SageMath

Week 4:

Solving Equations in SageMath
2d Plotting with SageMath
3d Plotting with SageMath
Calculus of one variable with SageMath - Part 1
Calculus of one variable with SageMath - Part 2
Applications of derivatives

Week 5:

Integration with SageMath
Improper Integral using SageMath
Application of integration using SageMath
Limit and Continuity of real valued functions
Partial Derivative with SageMath
Local Maximum and Minimum

Week 6:

Application of local maximum and local minimum
Constrained optimization using Lagrange multipliers
Working with vectors in SageMath
Solving system of linear Equations in SageMath
Vector Spaces in SageMath
Basis and dimensions of vector spaces in SageMath

Week 7:

Matrix Spaces with SageMath
Linear Transformations Part 1 with SageMath
Linear Transformations Part 2 with SageMath
Eigenvalues and Eigenvectors Part 1 with SageMath
Eigenvalues and Eigenvectors Part 2 with SageMath

Week 8:

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

Week 9:

Google Page Rank Algorithm using SageMath
Finding Roots of algebraic and transcendental equations in SageMath
Numerical Solutions of System of linear equations in SageMath
Interpolations in SageMath
Numerical Integration in SageMath
Numerical Eigenvalues

Week 10:

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

Week 11:

Introduction to Linear Programming Problems (LPP)
Solving Linear Programming Problmes using Graphical Methods
Basics Definitions and Results in LPP
Theory of Simplex Method
Simplex Methods in SageMath - Part 01
Simplex Methods in SageMath - Part 02
Simplex Methods in Matrix Form

Week 12:

Revised Simplex Method in SageMath
Two Phase Simplex Method in SageMath
Big-M Method in SageMath
Duality of Linear Program
Dual Simplex Method in SageMath
Review and What next in SageMath?

Taught by

Prof. Ajit Kumar

Tags

india

Reviews

Start your review of Computational Mathematics with SageMath