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 | Thursday | 11:00 - 11:50 |
| 2 | Thursday | 14:00 - 14:50 |
| 3 | Friday | 10:00 - 10:50 |
| # | Assessment | Marks | Topics |
|---|---|---|---|
| 1 | Test 1 | 20 | Up to Topics Covered on 31st January 2025 |
| 2 | Test 2 | 20 | Up to Topics Covered on 22nd February 2025 |
| 3 | End Semester | 60 | End Semester |
| # | Topic | |
|---|---|---|
| 1 | Introduction, History, Prerequisites | Lecture-1 |
| 2 | Preliminaries and Asymptotic Notations | Lecture-2 |
| 3 | Asymptotic Notations and Computation Time | Lecture-3 |
| 4 | Master Theorem and Order of Convergence | Lecture-4 |
| 5 | Error Stories | Lecture-5 |
| 6 | Machine Epsilon and Floating Point System | Lecture-6 |
| 7 | Chopping, Rounding and Truncation Errors | Lecture-7 |
| # | Topic | |
|---|---|---|
| 1 | Numerical Interpolation-Introduction | Lecture-8 |
| 2 | Numerical Interpolation-Taylor Polynomial and Newton's Interpolation | Lecture-9 |
| 3 | Numerical Interpolation-Newton's Divided Differences | Lecture-10 |
| 4 | Numerical Interpolation-Lagrange Interpolation and Interpolation Errors | Lecture-11 |
| 5 | Numerical Interpolation-Error Interpolation Theorems and Proof | Lecture-12 |
| 6 | Numerical Interpolation-Hermite Interpolation | Lecture-13 |
| 7 | Numerical Interpolation-Spline Interpolation | Lecture-14 |
| # | Topic | |
|---|---|---|
| 1 | Root Finding Methods: Introduction | Lecture-15 |
| 2 | Root Finding Methods: Closed Methods | Lecture-16 |
| 3 | Root Finding Methods: Open Methods - Fixed Point | Lecture-17 |
| 4 | Root Finding Methods: Open Methods - Newton-Raphson | Lecture-18 |
| 5 | Root Finding Methods: Open Methods - Secant and Polynomial Roots | Lecture-19 |
| 6 | Root Finding Methods: Advanced Methods | Lecture-20 |
| # | Topic | |
|---|---|---|
| 1 | Numerical Linear Algebra-LU Decomposition | Lecture-21 |
| 2 | Numerical Linear Algebra-LU Decomposition-II | Lecture-22 |
| 3 | Numerical Linear Algebra-Cholesky Decomposition | Lecture-23 |
| 4 | Numerical Linear Algebra-Gaussian Elimination | Lecture-24 |
| 5 | Numerical Linear Algebra-Pivoting | Lecture-25 |
| 6 | Numerical Linear Algebra-Norms | Lecture-26 |
| 7 | Numerical Linear Algebra-Matrix Norms | Lecture-27 |
| 8 | Numerical Linear Algebra-Iterative Methods | Lecture-28 |
| 9 | Numerical Linear Algebra-Conjugate Gradient Method | Lecture-29 |
| 10 | Numerical Linear Algebra-QR/SV Decomposition | Lecture-30 |
| 10 | Numerical Linear Algebra-Eigenvalues | Lecture-31 |
| # | Topic | Coverage |
|---|---|---|
| 1 | Exercise-1 | Numerical Errors |
| 2 | Exercise-2 | Numerical Interpolation |
| 3 | Exercise-3 | Root Finding Methods |
| 4 | Exercise-4 | Numerical Linear Algebra |
Associate Professor
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