# Advanced Computational Techniques

By Prof.Somnath Bhattacharyya   |   IIT Kharagpur
Learners enrolled: 353
There are several basic online courses on numerical methods available, however a course which can provide a foundation for the advanced numerical modeling and scientific computing is infrequent. This course is designed as an introductory course on advanced topics on numerical methods for engineering and science students. It is intended to teach the implementation of numerical methods rather than just provide theoretical foundations of the methods. Scientific computing is an integral part of several disciplines including computational mathematics. The completion of this course will equipped the students in handling advanced computational tools. All the methods will be illustrated by working out several examples. Pre-requisite for this course is the basic knowledge of undergraduate calculus and elementary numerical methods.

INTENDED AUDIENCE: UG or PG of any Engineering course, Mathematics,Physics and Postgraduate student of Mathematics/Mechanical/Aerospace/Chemical Engineering

PREREQUISITES: Basic UG course in Mathematics/ Undergraduate Calculus

Summary
 Course Status : Upcoming Course Type : Elective Duration : 4 weeks Start Date : 20 Feb 2023 End Date : 17 Mar 2023 Exam Date : 30 Apr 2023 IST Enrollment Ends : 20 Feb 2023 Category : Mathematics Credit Points : 1 Level : Undergraduate/Postgraduate

### Course layout

Week 1: Overview on Elementary Numerical Methods,  Hermit Interpolation, Cubic Splines, Numerical quadrature, Gauss Quadrature.
Week 2: Least square approximation, Linear system of equations, LU-decomposition, Tri-diagonal system, Iterative Methods, SOR, Conjugate gradient method, Eigen value computation, Power method.
Week 3: Initial value problems, Predictor-corrector methods, Stability, Truncation error, Runge-Kutta method, Linear boundary value problem, Finite Difference Method.
Week 4: Non-linear BVP, Iterative methods, Advection-diffusion equations, Implicit Scheme, Crank-Nicolson Scheme, von-Neumann stability analysis,  Linear hyperbolic PDE, Upwind scheme, Lax scheme, Non-linear Burgers equations, Iterative scheme.

### Books and references

1. Numerical Methods for Engineers and Scientists, J.D.Hoffman.
2. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, P. Knabner & L. Angermann

### Prof.Somnath Bhattacharyya

IIT Kharagpur
Prof. S. Bhattacharyya is a senior professor in the Dept. Mathematics, IIT Kharagpur. His specialization is Applied Mathematics. He is teaching courses on Integral Transform Techniques, Partial Differential Equations, Numerical solutions of PDEs and other related courses on a regular basis for the B.Tech students at IIT Khargpur for the past 28 years. His research works involve numerical solutions of PDEs and he has published more than 160 research papers in reputed international journals. He has undertaken several sponsored research projects and guided 19 PhD students. Prof. Bhattcahrayya has organized and delivered lectures in several Conferences, AICTE sponsored short term courses, NPTEL courses and GIAN courses on topics related to Applied Mathematics. He has received several fellowships for research collaboration in USA, UK and Germany.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: April 30, 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 3 assignments out of the total 4 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team