NUMERICAL & STATISTICAL METHODS

Paper Code: 
GBCA 401
Credits: 
06
Periods/week: 
06
Max. Marks: 
100.00
Objective: 

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 of computers.
  2. Develop the ability to apply numerical and quantitative techniques

 

Course  Outcomes (COs):

 

Learning Outcome (at course level)

 

Learning and teaching strategies

Assessment Strategies

CO 167 Compute the error estimates for the numerical method.

CO 168 Describe aspects of computer programming.

CO 169 Solve an algebraic or transcendental equation using an appropriate numerical method.

CO 170 Solve a differential equation using an appropriate numerical method.

CO 171 Evaluate a derivative at a value using an appropriate numerical method.

CO 172 Calculate a definite integral using an appropriate numerical method.

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstrations, Team teaching, Teaching using advanced IT audio-video tools, G-suite.

Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation.

This module is designed to help students to know about the concepts of numerical methods and how they are useful in the study of computers.

18.00
Unit I: 

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.

18.00
Unit II: 

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.

18.00
Unit III: 

 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.


 

18.00
Unit IV: 

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.


 

18.00
Unit V: 

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.


 

ESSENTIAL READINGS: 
  1. Rajaraman, “Computer Oriented Numerical Methods” 3rd Edition, Prentice Hall of India Pvt. Ltd.
  2. E.Balagurusami,  “Numerical Methods”, Tata McGraw Hill, 1988.
REFERENCES: 
  1. Schaum’s Series, “Numerical Methods”, TMH   
  2. S.S.Sastry, “Introductory Methods of Numerical Analysis”, second ed., Prentice Hall of -India Pvt. Ltd, 1997.


 

Academic Year: 
2020-21
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