Computational Science in Engineering

By Prof. Ashoke De | IIT Kanpur

Learners enrolled: 236

The Computational Science in Engineering is a rapidly evolving field that exploits the power of computation as an approach to major challenges on the frontiers of natural and social science and all engineering fields. The primary focus lies on developing problem-solving methodologies and robust tools for numerical simulation. The goal is to present the fundamentals of scientific computing, with short codes to implement the key concepts. This includes a framework for applied mathematics such as Linear Algebra, ODEs and PDEs. To understand phenomena and processes from science and engineering, these simulations require advanced skills in mathematical modelling, numerical analysis, efficient algorithms, computer architecture, software design and implementation, validation, and visualization of results.

INTENDED AUDIENCE : Freshman/Sophomore undergraduate students and postgraduate students of Aerospace/Mechanical/Chemical/Civil Engineering

PREREQUISITES : Basics of Mathematics and programming

INDUSTRIES SUPPORT : Aerospace, Automobile, Chemical and Power Generation and Defense Industries

Summary

Course Status :	Upcoming
Course Type :	Elective
Duration :	8 weeks
Start Date :	21 Feb 2022
End Date :	15 Apr 2022
Exam Date :	23 Apr 2022 IST
Category :	Aerospace Engineering
Credit Points :	2
Level :	Undergraduate/Postgraduate

Course layout

Week 1:Linear Algebra: Introduction to Vectors, Vector spaces and subspaces, Solving Linear systems

Week 2:Linear Algebra: Orthogonality, Determinants, Eigenvalues & Eigen vectors, SVD

Week 3: Ordinary Differential Equations: ODE, homogeneous and non-homogeneous ODEs, second order linear ODE, higher order ODEs

Week 4:Solution of Higher Order ODEs, Fourier Analysis, Fourier Integrals, Laplace Transforms

Week 5:Partial Differential Equations: Classification, 1D & 2D equations, BC, 2^nd order PDEs

Week 6:Basis of numerical analysis, errors, stability, Interpolation and extrapolation

Week 7: System of linear algebraic equations and eigenvalue problems: Direct methods, Iterative methods, convergence analysis, Eigenvalues and Eigenvectors, bounds on eigenvalues, Methods for symmetric matrices and arbitrary matrices

Week 8:Solution of ODEs: Difference equation, Numerical methods, convergence, stability, Single step and multistep methods, Predictor-corrector methods, stability analysis of multistep methods, IVP (shooting methods), BVP (methods and solutions)

Books and references

1. Introduction to Linear Algebra – Gilbert Strang

2. Differential Equations – G. F. Simmons

3. An Introduction to Ordinary Differential Equations – E. A. Coddington

4. Partial Differential Equations for Scientists and Engineers – S. J. Farlow

5. Atkinson, K. E., An Introduction to Numerical Analysis, John Wiley & Sons, 1978.

6. Numerical recipes: the art of scientific computing - William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, Cambridge University Press, 2007

7. Ferzziger, J.H., and Peric, M., Computational Methods for Fluid Dynamics, Springer, 2002.

8. Computational Fluid Dynamics: The Basics with Applications, Anderson

9. Computational Fluid Flow and heat transfer, Tannehill, Anderson, Pletcher

Instructor bio

Prof. Ashoke De

IIT Kanpur

Dr. Ashoke De is currently working as Associate Professor in the Department of Aerospace Engineering at Indian Institute of Technology Kanpur. He leads large scale initiatives in the modeling of turbulent reacting and non-reacting flows at IIT Kanpur. So far, he has authored more than 130 peer reviewed articles in journals and conferences. His primary research focus is the emerging field of computational mechanics with particular interest in combustion and turbulent flows.

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: 23 April 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 Kanpur .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

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