Computational Mathematics with SageMath from begging to advance in 2020

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About Course

Computational Mathematics with SageMath.

Computational Mathematics with SageMath: This eight-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, and Numerical Methods.

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This Computational Mathematics with SageMath course will begin with the introduction of basic Python programming language in the first two weeks. Next, we shall provide a quick introduction to SageMath software along with plotting 2D and 3D objects. The main focus will be on using SageMath to explore topics in Calculus, Applied Linear Algebra, and Numerical Method along with several applications.

Computational Mathematics with SageMath Course layout

Week 1:
0. Installation  of Python
1. Getting Started with  Python
2. Python as an advanced Calculator
3. Lists in Python
4. Tuples sets and dictionary in Python
5. Functions and Branching
6. For loop in Python
7.  While loop in Python
Week 2:
8. Creating Modules and Introduction to NumPy
9. Use of NumPy module
10. Python Graphics using matplotlib
11. Use of SciPy and SymPy in Python
12. Classes in Python
13. Classes in Python
Week 3:
00. Introduction and Installation of SageMath
14. Exploring integers in SageMath
15. Solving Equations in SageMath
16. 2d Plotting with SageMath
17. 3d Plotting with SageMath
18. Calculus of one variable with SageMath Part 1
19.  Calculus of one variable with SageMath Part 2
Week 4:
20. Applications of derivatives
21. Integrals in SageMath
22. Applications of Integrals
23. Partial Derivatives and gradients, jacobians
25. Local maximum-minimum
26. Application of local maximum and minimum
27 Applications to least-square problems
Week 5:
28. Lagrange Multipliers
29. Working with vectors in SageMath
39. RREF and Solving system of Linear Equations
31. Vector Spaces in SageMath
32. Vector Spaces in SageMath (cont..)
33. Linear Transformations with SageMath
34. Linear Transformations with SageMath (cont..)
Week 6:
35. Eigenvalues and Eigenvectors with SageMath
36. Eigenvalues and Eigenvectors with SageMath (cont..)
37. Inner Product Spaces in SageMath
38. Inner Product Spaces in SageMath (cont..)
39. Gram-Schmidt Process and QR-factorization
40. Singular Value Decomposition (SVD)
Week 7:
41 Applications of SVD & Least Square Methods
42. Applications of linear algebra with SageMath
43. Numerical Solution of algebraic equations
44. Numerical Solutions of system linear equations
45. Interpolations
46. Numerical Integration
47. Numerical Integration (Cont..)
Week 8:
48. Numerical Eigenvalues
49. Solving ODE with SageMath
50. Initial Value ODE with SageMath
51. Initial Value ODE with SageMath (cont..)
52. Solving system of ODE
53. Solving ODE with Laplace Transforms
54.  Applications of ODE with SageMath
55. What next with SageMath?
Computational Mathematics with SageMath INTENDED AUDIENCE: UG and PG students of Mathematics and BE Students, Teachers teaching in Degree colleges.

 

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Course Content

Computational Mathematics with SageMath

  • mod08lec57 – Review and What next in SageMath?
    00:00
  • mod06lec41 – Orthogonal Decomposition with SageMath
    00:00
  • mod06lec40 – Inner Product Part 2 with SageMath
    00:00
  • mod06lec39 – Inner Product Part 1 with SageMath
    00:00
  • mod06lec38 – Eigenvalues and Eigenvectors Part 2 with SageMath
    00:00
  • mod06lec37 – Eigenvalues and Eigenvectors Part 1 with SageMath
    00:00
  • mod05lec36 – Linear Transformations Part 2 with SageMath
    00:00
  • mod05lec35 – Linear Transformations Part 1 with SageMath
    00:00
  • mod05lec34 – Matrix Spaces with SageMath
    00:00
  • mod05lec33 – Basis and dimensions of vector spaces in SageMath
    00:00
  • mod05lec32 – Vector Spaces in SageMath
    00:00
  • mod05lec31 – Solving system of linear Equations in SageMath
    00:00
  • mod05lec30 – Working with vectors in SageMath
    00:00
  • mod06lec42 – Least Square Solution with SageMath
    00:00
  • mod06lec43 – Singular Value Decomposition (SVD) with SageMath
    00:00
  • mod07lec44 – Application of SVD to image processing
    00:00
  • mod08lec56 – Solving ODE using Laplace Transforms in SageMath
    00:00
  • mod08lec55 – RK4 method for System of ODE and Applications
    00:00
  • mod08lec54 – Fourth Order Runge-Kutta Method
    00:00
  • mod08lec53 – Euler’s Method to solve 1st order ODE with SageMath
    00:00
  • mod08lec52 – Solving 1st and 2nd order ODE with SageMath
    00:00
  • mod08lec51 – Numerical Eigenvalues
    00:00
  • mod07lec50 – Numerical Integration in SageMath
    00:00
  • mod07lec49 – Interpolations in SageMath
    00:00
  • mod07lec48 – Numerical Solutions of System of linear equations in SageMath
    00:00
  • mod07lec47 – Finding Roots of algebraic and transcendental equations in SageMath
    00:00
  • mod07lec46 – Google Page Rank Algorithm using SageMath
    00:00
  • mod07lec45 – Solving System of linear ODE using Eigenvalues and Eigenvectors
    00:00
  • mod05lec29 – Constrained optimization using Lagrange multipliers
    00:00
  • mod04lec28 – Application of local maximum and local minimum
    00:00
  • mod02lec12 – Classes in Python – Part 01
    00:00
  • mod02lec11 – Use of SciPy and SymPy in Python
    00:00
  • mod02lec10 – Python Graphics using MatplotLib
    00:00
  • mod02lec09 – Use of NumPy module
    00:00
  • mod02lec08 – Creating Modules and Introduction to NumPy
    00:00
  • mod01lec07 – While loop in Python
    00:00
  • mod01lec06 – For loop in Python
    00:00
  • mod01lec05 – Functions and Branching
    00:00
  • mod01lec04 – Tuple, Sets and Dictionaries in Python
    00:00
  • mod01lec03 – Lists in Python
    00:00
  • mod01lec02 – Python as an advanced calculator
    00:00
  • mod01lec01 – Getting Started with Python
    00:00
  • mod02lec13 – Classes in Python – Part 02
    00:00
  • mod03lec14 – Introduction and Installation of SageMath
    00:00
  • mod03lec15 – Exploring integers in SageMath
    00:00
  • mod04lec27 – Local Maximum and Minimum
    00:00
  • mod04lec26 – Partial Derivative with SageMath
    00:00
  • mod04lec25 – Limit and Continuity of real valued functions
    00:00
  • mod04lec24 – Application of integration using SageMath
    00:00
  • mod04lec23 – Improper Integral using SageMath
    00:00
  • mod04lec22 – Integration with SageMath
    00:00
  • mod04lec21 – Applications of derivatives
    00:00
  • mod03lec20 – Calculus of one variable with SageMath – Part 2
    00:00
  • mod03lec19 – Calculus of one variable with SageMath – Part 1
    00:00
  • mod03lec18 – 3d Plotting with SageMath
    00:00
  • mod03lec17 – 2d Plotting with SageMath
    00:00
  • mod03lec16 – Solving Equations in SageMath
    00:00
  • mod01lec00 – Installation of Python
    00:00

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