Department Events
NUMERICAL & STATISTICAL METHODS
The course will enable the students to
- Know about the concepts of numerical methods and how they are useful in the study of computers.
- Develop the ability to apply numerical and quantitative techniques
Course Outcomes (COs):
Course Outcome (at course level) | Learning and teaching strategies | Assessment Strategies |
|---|---|---|
The students will: CO183. Apply numerical methods to find the solution of algebraic equations using different methods and numerical solution of system of algebraic equations. CO184. Compute the error estimates for the numerical methods. CO185. Apply various interpolation methods and finite difference concepts. CO186. Work out numerical differentiation and integration whenever and wherever routine methods are not applicable. CO187. Solve a differential equation using an appropriate numerical method. | Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstrations, G-suite. | Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation. |
Computer Arithmetic: Introduction, Floating point representation of numbers, Arithmetic operation with normalized floating point numbers, Consequences of normalized floating point representation of numbers, binary representation of numbers.
Iterative Methods: Introduction, Beginning an iterative method, Method of successive bisection, Method of false position, Newton-Raphson iterative method, Secant method, Method of successive approximation, Comparison of iterative methods.
Solution of simultaneous Algebraic equations: Gauss elimination method, Pivoting, Ill conditioned equations, Refinement of the solution obtained by Gaussian Elimination, Gauss- Seidel Iterative Method, Algorithm to implement Gauss-Seidel method, Comparison of Direct and Iterative Methods.
Interpolation: Theory of interpolation, polynomial forms, difference Table (Forward, Backward& Divided difference table), Methods of Equal spaced function: - Newton’s forward interpolation, Newton’s Backward interpolation.
Methods of unequal spaced function: - Lagrange interpolation, Newton’s Divided difference interpolations.
Numerical Integration: Trapezoidal Rule, Simpson’s rule, Algorithm for Integration of Tabulated Function (Using Trapezoidal rule& Simpson’s rule).
Numerical solution of Differential Equations: Euler's method, Euler’s modified method, Runge- Kutta Fourth Order Formula, Predictor-Corrector Method (Milne Simpson’s methods), Comparison of Predictor-Corrector and Runge-Kutta Methods
NOTE:Problem will be solved by using Scientific Calculators (Non Programmable). Candidates must know about all functions and operations of scientific calculator.
NOTE:
1. Rajaraman, “Computer Oriented Numerical Methods” 4rd Edition, Prentice Hall of India Pvt. Ltd.
2. E.Balagurusami, “Numerical Methods”, Tata McGraw Hill, 2017.
Suggested READINGS:
1. Richard Hamming, “Numerical Methods for Scientists and Engineers”, Dover Publications
2. Mahinder Kumar Jain and R. K. Jain, “Numerical Methods for Scientific and Engineering Computation”, Fourth ed., New Age International (P) Ltd, Publisher, 2004
3. Eugene Isaacson and Herbert Keller, Analysis of Numerical Methods, Dover Publications, 2012
E-RESOURCES:
- https://global.oup.com/uk/orc/biosciences/maths/reed/01student/numerical_tutorials/
- https://programming-techniques.com/2013/12/numerical-methods-tutorials.html
- https://numericalmethodstutorials.readthedocs.io/en/latest/
- https://www.slideshare.net/musadoto/numerical-methods-1-tutorial-questions-95544883
