Numerical Analysis Course | IIT Bombay | Prof. S. Baskar | 12-Week UG/PG Program
Course Details
| Exam Registration | 88 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 26 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Power of Computation: A Deep Dive into Numerical Analysis
In the realm of mathematics and scientific computing, Numerical Analysis stands as the critical bridge between abstract theory and practical, computable solutions. It is the discipline that empowers us to solve complex mathematical problems—from predicting weather patterns to designing aircraft—using computers. If you're an undergraduate or postgraduate student looking to master this essential field, an exceptional opportunity awaits.
We are proud to present a comprehensive 12-week course in Numerical Analysis, meticulously designed and delivered by one of the Indian Institute of Technology Bombay's most distinguished educators.
Learn from an Award-Winning IIT Bombay Expert
This course is led by Prof. S. Baskar from the Department of Mathematics, IIT Bombay. With over 16 years of teaching experience, Prof. Baskar is not just an instructor; he is a mentor who has shaped the minds of countless students.
- Proven Expertise: He has taught Numerical Analysis more than 15 times, ensuring a refined and deeply effective curriculum.
- Broad Knowledge: His teaching portfolio includes advanced courses like Ordinary and Partial Differential Equations, Multivariable Calculus, Probability Theory, and Derivative Pricing.
- Recognized Excellence: Prof. Baskar's dedication to pedagogy has been honored with the IIT Bombay Excellence in Teaching Award (2020) and the Departmental Excellence in Teaching Award (2018).
Learning from such an accomplished academic ensures you gain insights from both profound theoretical understanding and extensive practical teaching experience.
What is Numerical Analysis?
Numerical Analysis is the branch of mathematics concerned with designing, analyzing, and implementing algorithms to obtain numerical solutions to mathematical problems. The core objectives are twofold:
- To develop robust numerical methods for solving problems where exact solutions are impossible or impractical to find.
- To analyze the errors involved in these numerical approximations, ensuring the solutions are reliable and accurate.
This course will guide you through these very goals, using familiar mathematical problems as a foundation before advancing to more complex applications.
Course Prerequisites
To successfully undertake this journey, you should have a solid foundation in:
- A first course in Calculus or Real Analysis.
- A first course in Linear Algebra.
This background will allow you to fully engage with the mathematical concepts and their numerical interpretations.
Detailed 12-Week Course Layout
The course is structured to build your knowledge progressively, from fundamental concepts to advanced applications, with a strong emphasis on practical implementation.
| Week | Topics Covered |
|---|---|
| Week 1 | Motivations, Preliminaries, Order of Convergence. Error Analysis: Floating-point approximations, Significant digits, Stability. |
| Week 2 | Tutorial + Python Intro. Direct Methods for Linear Systems: Gaussian elimination, Pivoting, LU factorization. |
| Week 3 | Matrix Norms, Condition Number. Iterative Methods: Jacobi Method. Tutorial & Python Implementation. |
| Week 4 | Iterative Methods (Cont.): Gauss-Seidel, SOR Method. Tutorial & Python Implementation. |
| Week 5 | Eigenvalues/Eigenvectors: Power method, Inverse Power method, Gerschgorin’s theorem. Tutorial & Python Implementation. |
| Week 6 | Nonlinear Equations: Bisection, Regula-Falsi, Secant, Newton-Raphson methods, Convergence analysis. Tutorial & Python Implementation. |
| Week 7 | Nonlinear Equations (Cont.): Fixed-point iteration, Newton’s method for systems. Tutorial & Python Implementation. |
| Week 8 | Polynomial Interpolation: Lagrange form, Newton’s form, Divided differences, Error analysis. |
| Week 9 | Piecewise Interpolation: Piecewise polynomials, Hermite interpolation, Cubic splines. Tutorial & Python Implementation. |
| Week 10 | Numerical Integration: Rectangle, Trapezoidal, Simpson’s, Gaussian rules. Numerical Differentiation. |
| Week 11 | Tutorial & Python Implementation for Integration/Differentiation. ODEs: Initial Value Problems (Euler, Runge-Kutta methods). |
| Week 12 | ODEs: Boundary Value Problems. PDEs: Linear advection equation, Stability analysis. Final Tutorial & Python Implementation. |
Why This Course Stands Out: Theory Meets Practice
This isn't just a theoretical overview. A key highlight is the integrated practical component using Python. Starting from Week 2, tutorial sessions are dedicated to implementing the learned numerical methods as functional computer code. This hands-on approach ensures you:
- Translate mathematical algorithms into working programs.
- Gain valuable computational skills highly sought after in research and industry.
- Develop a deeper intuition for method behavior and error through practical experimentation.
Recommended Textbook & Study Material
While comprehensive study material will be provided, the course aligns with the classic text:
- Atkinson, K. E. Introduction to Numerical Analysis (2nd Edition).
This book serves as an excellent reference for deepening your understanding of the topics covered.
Who Should Enroll?
This course is perfectly suited for:
- Undergraduate (Junior/Senior) and Postgraduate students in Mathematics, Engineering, Physics, Computer Science, and related fields.
- Any learner seeking a rigorous, application-oriented understanding of numerical methods.
- Professionals looking to strengthen their computational mathematics foundation.
Embark on this 12-week journey with Prof. S. Baskar to master the art and science of obtaining numerical solutions. You will emerge not only with a strong theoretical grasp of Numerical Analysis but also with the practical coding skills to implement these powerful methods, equipping you for advanced studies and a wide array of technical careers.
Enroll Now →