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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Numerical Analysis Certification course is a 12-week online programme that offers a comprehensive exploration of fundamental numerical methods and techniques essential for solving complex mathematical problems. Students are provided with the theoretical foundations and practical applications of numerical algorithms through the Numerical Analysis Certification by NPTEL.
The Numerical Analysis training equips students with the skills necessary to effectively analyse and solve real-world problems using numerical methods. The course masters the art of numerical computation and analysis. They will gain proficiency in implementing numerical algorithms using programming languages such as Python, MATLAB, or R.
Also Read: Online Programming Certification Courses
The Highlights
- IIT Bombay recognised Completion Certificate
- Learning from Trained Faculty Members
- Free Course Readings
- Hands-on projects
Programme Offerings
- online learning
- Robust curriculum
- Hands-on Learning
- Certified faculty and mentors
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | IIT Bombay |
Eligibility Criteria
Certification Qualifying Details
Candidates for the Numerical Analysis certification course must qualify for the final examination to receive the completion certificate.
What you will learn
After completing the Numerical Analysis Certification syllabus, students will have acquired a comprehensive understanding of fundamental numerical methods and techniques essential for solving a wide array of mathematical problems in various scientific and engineering disciplines. They will develop critical skills in programming languages such as Python, MATLAB, or R.
Who it is for
The Numerical Analysis training is designed for students interested in knowing deeply about mathematics and related disciplines.
The course is apt for the following professionals:
Admission Details
To join the Numerical Analysis classes, candidates must follow the below-mentioned steps:
Step 1: Visit the official course URL:
https://nptel.ac.in/courses/111101165
Step 2: Log in to the website and enrol for the programme.
Step 3: Enter relevant academic and personal details.
Step 4: Pay the course fee to complete the enrollment process
Step 5: Start learning
The Syllabus
- Motivations, Preliminaries, Order of convergence.
- Error Analysis: Floating-point approximations, Significant digits, Stability in computation.
- Tutorial Session for Week 1.
- Introducing Python coding.
- Direct Methods for Linear System of Equations: Gaussian elimination method, Partial pivoting, LU factorization, Operation counting.
- Matrix Norms: Subordinate matrix norms, Condition number of an invertible matrix.
- Iterative Methods for Linear Systems: Jacobi Method
- Tutorial Session for Week 2 and Python implementation.
- Iterative Methods (continued): Gauss-Seidel method, Residual corrector method, Conjugate gradient method.
- Tutorial Session for Week 3 and Python implementation.
- Methods for Computing Eigenvalue and Eigenvectors: Power method, inverse power method, Gerschgorin’s theorem.
- Tutorial Session for Week 4 and Python implementation.
- Nonlinear Equations: Bisection method, Regula-falsi method, Secant method, Newton-Raphson method, Stopping criteria. Convergence analysis
- Tutorial Session for Week 5 and Python implementation.
- Nonlinear Equations (Continued): Fixed-point iteration method, Newton’s method for system of nonlinear equations
- Tutorial Session for Week 6 and 7, and Python implementation.
- Polynomial Interpolation: Lagrange form, Newton’s form, divided differences, error analysis.
- Piecewise Interpolation: Piecewise polynomial interpolation, Hermite interpolation, Cubic spline interpolations.
- Tutorial Session for Week 8 and 9, and Python implementation.
- Numerical Integration: Rectangle rule, Mid-point rule, Trapezoidal rule, Simpson’s rule, Gaussian quadrature rule, error analysis
- Numerical Differentiation: Method of undetermined coefficients, error analysis.
- Tutorial Session for Week 10 and Python implementation.
- Numerical Methods for ODEs: Initial Value Problems for First Order ODEs - Euler methods, Modified Euler, methods, error analysis, Runge-Kutta method of order 2 and 4.
- Numerical Methods for ODEs: Numerical methods for two-point boundary value problems, Numerical Methods for PDEs: Numerical methods for linear advection equation.Stability analysis
- Tutorial Session for Week 11 and 12, and Python implementation.
Evaluation process
Candidates for the Introduction to Numerical Analysis certification course must appear for the examinations to receive the completion certificate.