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. The 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. INTENDED AUDIENCE :UG and PG students of Mathematics and BE Students, Teachers teaching in Degree colleges.PREREQUISITES : Basic knowledge of Calculus, Linear Algebra and ODE and Numerical Methods.INDUSTRIES SUPPORT :Any industry dealing with Data Science and Numerical Computations.
Week 1:0. Installation of Python1. Getting Started with Python2. Python as an advanced Calculator3. Lists in Python4. Tuples sets and dictionary in Python5. Functions and Branching6. For loop in Python7. While loop in PythonWeek 2:8. Creating Modules and Introduction to NumPy9. Use of NumPy module10. Python Graphics using MatplotLib11. Use of SciPy and SymPy in Python12. Classes in Python13. Classes in PythonWeek 3:00. Introduction and Installation of SageMath14. Exploring integers in SageMath15. Solving Equations in SageMath16. 2d Plotting with SageMath17. 3d Plotting with SageMath18. Calculus of one variable with SageMath Part 119. Calculus of one variable with SageMath Part 2Week 4:20. Applications of derivatives21. Integrals in SageMath22. Applications of Integrals23. Partial Derivatives and gradients, jacobians25. Local maximum-minimum26. Application of local maximum and minimum27 Applications to least square problemsWeek 5:28. Lagrange Multipliers29. Working with vectors in SageMath39. RREF and Solving system of linear Equations31. Vector Spaces in SageMath32. Vector Spaces in SageMath (cont..)33. Linear Transformations with SageMath34. Linear Transformations with SageMath (cont..)Week 6:35. Eigenvalues and Eigenvectors with SageMath36. Eigenvalues and Eigenvectors with SageMath (cont..)37. Inner Product Spaces in SageMath38. Inner Product Spaces in SageMath (cont..)39. Gram-Schmidt Process and QR-factorization40. Singular Value Decomposition (SVD)Week 7:41 Applications of SVD & Least Square Methods42. Applications of linear algebra with SageMath43. Numerical Solution of algebraic equations44. Numerical Solutions of system linear equations45. Interpolations46. Numerical Integration47. Numerical Integration (Cont..)Week 8:48. Numerical Eigenvalues49. Solving ODE with SageMath50. Initial Value ODE with SageMath51. Initial Value ODE with SageMath (cont..)52. Solving system of ODE53. Solving ODE with Laplace Transforms54. Applications of ODE with SageMath55. What next with SageMath?