Scientific Computing Using Python

Exam Preparation PDF

ABOUT THE COURSE:

Computation has become an essential tool in science and engineering. In this course, we introduce Python programming language, after which we will cover basics of computational methods. The students will be asked to the solution in Python, which the de facto language now. Topics to be discussed include interpolation, integration, differentiation, ODE and PDE solvers, basic linear algebra, and Monte Carlo techniques. These topics form essential computing tools for computational courses in science and engineering.

INTENDED AUDIENCE: PG students of Science and Engineering (Specially Physics, Mathematics, Mechanical, Aerospace, Computer science and Chemical Engineering). Advance UG students too can take this course.

PREREQUISITES: Basic knowledge of calculus, linear algebra, and ordinary and partial differential equations. Basic knowledge of computation is recommended.

Summary

Course Status :	Ongoing
Course Type :	Elective
Duration :	12 weeks
Category :	Physics
Credit Points :	3
Level :	Postgraduate
Start Date :	24 Jul 2023
End Date :	13 Oct 2023
Enrollment Ends :	07 Aug 2023
Exam Registration Ends :	18 Aug 2023
Exam Date :	29 Oct 2023 IST

Course layout

Week 1:
Module 1:About Computers

Module 2:Python variables

Module 3:Python arrays

Week 2:
Module 1:Python Control Structure

Module 2:Python functions

Module 3:Programming style

Week 3:
Module 1:Plotting

Module 2:Data input/output

Module 3:Error analysis and nondimensionalization

Week 4:
Module 1:Lagrange Interpolation

Module 2:Splines

Week 5:
Module 1:Numerical Integration: Newton Cotes

Module 2:Gaussian quadrature

Module 3:Multidimensional and misc integration

Week 6:
Module 1:Differentiation

Module 2:ODE solvers: Euler method

Module 3:ODEs: Implicit schemes

Week 7:
Module 1:ODEs: Higher-order method

Module 2:ODEs: System of eqns, Stiff equations

Module 3:Fourier Transforms

Week 8:
Module 1:Spectral method (PDE solvers): Diffusion equation

Module 2:Spectral method: Wave and Burger eqn solver

Module 3:Spectral: Navier-Stokes eqn solver

Module 4:Spectral: Schrodinger eqn solver

Week 9:
Module 1:Finite Difference (FD) (PDE solvers): Diffusion equation

Module 2:FD method: Wave and Burger eqn solver

Module 3:FD Method: Navier-Stokes eqn solver

Module 4:FD Method: Schrodinger eqn solver

Week 10:
Module 1:Solving Nonlinear Equations (Root finders)

Module 2:Boundary value problems (Shooting method)

Module 3:Eigenvalue solver for diff equatons

Week 11:
Module 1:Lapace equation solvers

Module 2:Lapace equation solvers

Module 3:Poisson equation solvers

Week 12:
Module 1:Linear algebra: Solution of linear equations

Module 2:Linear algebra: Eigenvalues and eigenvectors

Module 3:Intro to Monte Carlo method

Module 4:Summary

Books and references

1. Practical Numerical Computing Using Python : Scientific and Engineering Applications (2021)

2.Mark Newmann: Computational Physics with Python, 2nd Ed.
3.J. M. Stewart: Python for Scientists, Cambridge U. Press (2014)
4.J. H. Ferziger, Numerical Methods for Engineering Applications, John Wiley & Sons (in TB section).
5.M. Lutz, Learning Python 5th Edition, O’Reilly Media (2013)

Exam Preparation PDF

Part : 1

   

Part : 2

   

Part : 3