# Numerical Methods And Simulation Techniques For Scientists And Engineers

By Prof. Saurabh Basu   |   IIT Guwahati
Learners enrolled: 707
The course contains very important aspects of modern day course curriculum, namely, numerical methods and simulation techniques that are going to be of utmost importance to both undergraduate and graduate level. Most of the real life problems are unsolvable using known analytic techniques, thus depending on numerical methods is imperative. The course introduces basic numerical methods and the key simulation techniques that are going to be useful to academia and industry alike. Even if the software packages, such as Mathematica, Matlab etc are available for most of the numeric computations, yet one should be aware of the techniques that are inbuilt into the softwares.

INTENDED AUDIENCE:  Sudents, Lecturers from Engineering colleges and Universities. Also Industry people may be interested who do simulation

PREREQUISITES:           Basic level Mathematics course

INDUSTRY SUPPORT:
Industry people in the R&D sectors of Fluid Mechanics, Material Science may value the course
Summary
 Course Status : Completed Course Type : Core Duration : 8 weeks Category : Physics Credit Points : 2 Level : Undergraduate/Postgraduate Start Date : 25 Jul 2022 End Date : 16 Sep 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 25 Sep 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1: Introduction to Numerical analysis, Importance of error and their calculations, Examples
Week 2: Root Finding Method of non-linear equations, Bisection Method, Newton Raphson Method, Secant method, Regula- Falsi method, Practical examples.
Week 3: Curve fitting method, linear and non-linear fitting, Linear interpolation, Lagrange interpolation method, Newton Interpolation formula, Practical examples.
Week 4: Numerical differentiation, central difference methods, higher order derivatives, errors, practical examples.
Week 5: Numerical integration, Simpson’s 1/3 rd rule, Simpson’s 3/8 th rule, local and global error analysis ,practical examples.
Week 6: Eigenvalue problems, Heun’s method, Euler’s method, Runge Kutta Method, Gerschgorin disc theorem ,  Jacobi method, Practical examples
Week 7: Simulation Techniques, Random numbers, Monte Carlo Method, Importance Sampling, Metropolis Algorithm, Heat- bath algorithm, practical Examples
Week 8: Molecular dynamics, interaction and forces in molecular systems, MD and Verlet algorithm, correlations, practical examples

### Books and references

1. R.H. Landau, M.J. Paez, and C.C. Bordeianu, Computational Physics: Problem soving with Computers  Wiley VCH (2007)
2. S.C. Chopra and R.P. Canale, Numerical Methods for Engineers, Tata Mcgraw Hill (2002)
3. M.K. Jain, S.R.K. Iyengar, and R.K. Jain, "Numerical Methods for Scientific and Engineering Computation", New Age Pvt. Pub, New Delhi.
4. M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics, Oxford University Press (2010)
5. J.M. Haile, Molecular Dynamics Simulations: Elementary methods, Wiley Professional (1992)

### Prof. Saurabh Basu

IIT Guwahati
Dr. Saurabh Basu is a professor at the Department of Physics, IIT Guwahati. The area ofexpertise is Theoretical Condensed Matter Physics, with special emphasis on the correlatedboson and fermion systems, topological insulators. He has about 90 research publicationsin different refereed international journals.

### 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: 25 September 2022 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 6 assignments out of the total 8 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 Guwahati. 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