Department Events
Numerical & Statistical Methods
Course Objectives:
The course will enable the students to
1. Know about the concepts of numerical methods and how they are useful in the study ofcomputers.
2. Develop the ability to apply numerical and quantitative techniques
Course | Learning Outcome (at course level) | Learning and teaching strategies | Assessment Strategies | |
Course Code | Course Title | |||
25GBCA401 | Numerical & Statistical Methods (Theory) | CO235. Compute the error estimates for the numerical methods. CO236. Apply numerical methods to find the solution of algebraic equations using different methods. CO237. Analyse solution Of algebraic equations. CO238. Apply various interpolation methods and finite difference concepts. CO239. Work out numerical differentiation and integration whenever and wherever routine methods are not applicable. CO240.Contribute effectively in course- specific interaction | Approach in teaching: Interactive Lectures, Discussion, Reading assignments, Demonstration.
Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation. | Class test, Semester end examinations, Quiz, 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 TabulatedFunction (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.
ESSENTIAL READINGS:
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:
1.https://global.oup.com/uk/orc/biosciences/maths/reed/01student/numerical_tutori als/
2. https://programming-techniques.com/2013/12/numerical-methods-tutorials.html
3. https://numericalmethodstutorials.readthedocs.io/en/latest/
4. https://www.slideshare.net/musadoto/numerical-methods-1-tutorial-questions- 95544883
JOURNALS:
1. https://www.elsevier.com/mathematics
2. https://msp.org/apde/about/journal/about.html
3. https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis- sinum
4. https://journal.r-project.org/
5. https://onlinelibrary.wiley.com/journal/10970207
6. https://msp.org/memocs/about/journal/about.html
