Mission
Our mission is to foster analytical thinking and computational skills to address challenges in science, engineering, and data-driven disciplines with precision and efficiency.
Our mission is to foster analytical thinking and computational skills to address challenges in science, engineering, and data-driven disciplines with precision and efficiency.
Numerical Analysis is a rigorous study of computational algorithms used to approximate solutions to complex mathematical problems. The course delves into the stability, accuracy, and convergence of numerical methods applied to real-world scenarios, including solving nonlinear equations, matrix computations, interpolation, integration and differential equations. It challenges participants to develop efficient algorithms while critically analyzing errors and numerical stability.
Numerical errors arise from limitations in precision, truncation, or propagation during computational processes, affecting the accuracy of results.
Lectures
Tests
End Semester
Major Topics
The only way to solve a real problem is to approximate it, for real problems are always in the nature of the infinite
Numerical methods are the primary tools in computational science, providing the means to predict and analyze phenomena in nature and engineeringt!
Computational methods and numerical analysis are like the plumbing and wiring in a house. Essential, but often hidden, and only noticed when something goes wrong
| # | Topic | |
|---|---|---|
| 1 | Tuesday | 10:00 - 10:50 |
| 2 | Wednesday | 09:00 - 09:50 |
| 3 | Friday | 11:00 - 11:50 |
| # | Assessment | Marks | Topics |
|---|---|---|---|
| 1 | Test 1 | 20 | Up to Topics Covered on 6th February 2026 |
| 2 | Test 2 | 20 | Up to Topics Covered on 24th March 2026 |
| 3 | End Semester | 60 | End Semester |
| # | Topic | Date | |
|---|---|---|---|
| 1 | Introduction, History, Prerequisites | Lecture-1 | 06-01-2026 |
| 2 | Preliminaries | Lecture-2 | 07-01-2026 |
| 3 | Asymptotic Notations | Lecture-3 | 09-01-2026 |
| 4 | Master Theorem | Lecture-4 | 13-01-2026 |
| 5 | Order of Convergence and Error Stories | Lecture-5 | 16-01-2026 |
| 6 | Errors, Machine Epsilon | Lecture-6 | 20-01-2026 |
| 7 | Floating Point System and Error Analysis | Lecture-7 | 21-01-2026 |
| # | Topic | Date | |
|---|---|---|---|
| 1 | Numerical Interpolation - Introduction | Lecture-8 | 23-01-2026 |
| 2 | Numerical Interpolation - Newton's Interpolation | Lecture-9 | 27-01-2026 |
| 3 | Numerical Interpolation - Newton's Divided Differences | Lecture-10 | 27-01-2026 |
| 4 | Numerical Interpolation - Lagrange Interpolation | Lecture-11 | 28-01-2026 |
| 5 | Numerical Interpolation - Error in Interpolation | Lecture-12 | 02-02-2026 |
| 6 | Numerical Interpolation - Osculating Polynomial | Lecture-13 | 02-02-2026 |
| 7 | Numerical Interpolation - Spline Interpolation | Lecture-14 | 02-02-2026 |
| # | Topic | Date | |
|---|---|---|---|
| 1 | Introduction and Closed Method | Lecture-15 | 16-02-2026 |
| 2 | Bracketing Methods | Lecture-16 | 17-02-2026 |
| 3 | Fixed Point Method | Lecture-17 | 19-02-2026 |
| 4 | Newton-Raphson Method | Lecture-18 | 24-02-2026 |
| 5 | Secant Method and Roots of Polynomials | Lecture-19 | 25-02-2026 |
| 6 | Mullers Method and Acceleration | Lecture-20 | 25-02-2026 |
| # | Topic | Date | |
|---|---|---|---|
| 1 | Introduction and LU Decomposition | Lecture-21 | 03-03-2026 |
| 2 | LU Decomposition - Proof and Variations | Lecture-22 | 03-03-2026 |
| 3 | Gaussian Elimination | Lecture-23 | 10-03-2026 |
| 4 | Pivoting | Lecture-24 | 11-03-2026 |
| 5 | Vector Norms | Lecture-25 | 13-03-2026 |
| 6 | Matrix Norms | Lecture-26 | 17-03-2026 |
| 7 | Condition Number and Iterative Methods | Lecture-27 | 18-03-2026 |
| 8 | Iterative Methods | Lecture-28 | 20-03-2026 |
| 9 | Conjugate Gradient | Lecture-29 | 31-03-2026 |
| 10 | QR Decomposition | Lecture-30 | 31-03-2026 |
| 11 | Singular Value Decomposition | Lecture-31 | 09-04-2026 |
| 12 | Power Method | Lecture-32 | 09-04-2026 |
| # | Topic | Date | |
|---|---|---|---|
| 1 | Introduction and Trapezoidal Rule | Lecture-33 | 10-04-2026 |
| 2 | Closed Newton-Cotes Formula | Lecture-34 | 10-04-2026 |
| 3 | Open Newton-Cotes Formula | Lecture-35 | 10-04-2026 |
| 4 | Composite Rule and Romberg Integration | Lecture-36 | 15-04-2026 |
| 5 | Adaptive Quadrature and Summary | Lecture-37 | 17-04-2026 |
| 6 | Gaussian Quadrature | Lecture-38 | 18-04-2026 |
| # | Topic | Date | |
|---|---|---|---|
| 1 | Introduction and Euler's Method | Lecture-39 | 21-04-2026 |
| 2 | Runge-Kutta Method | Lecture-40 | 22-04-2026 |
| 3 | Mult-Step Methods | Lecture-41 | 24-04-2026 |
| 4 | Shooting Methods | Lecture-42 | 27-04-2026 |
| 5 | Finite Difference Methods | Lecture-43 | 28-04-2026 |
| 6 | Final Conclusions | Lecture-44 | 30-04-2026 |
| # | Topic | Coverage |
|---|---|---|
| 1 | Exercise-1 | Numerical Errors |
| 2 | Exercise-2 | Numerical Interpolation |
| 3 | Exercise-3 | Nonlinear Equations |
| 4 | Exercise-4 | Numerical Linear Algebra |
| 5 | Exercise-5 | Numerical Integration |
| 6 | Exercise-6 | Numerical Differentiation |
Associate Professor
Research Scholar
Research Scholar
In case of any doubts, please write to panch.m@iittp.ac.in or meet me in my office room during my office hours
Disclaimer: Contents in this website may have some typos or errors. So, please use it with caution. Some corrections are spelled out during lecture hours. In case, if you find any, please write to panch.m@iittp.ac.in