Computer Oriented Numerical Methods (CONM)
Numerical Analysis and Design (NAD)
Computer Oriented Numerical and Otimization Techniques
IT614 | IT 503 Syllabus | IC-504
Assignment Notification
Previous submission- submitted by : Vinayk Singoria CONM Calculator
LAB Assignment
Preamble:
This is M.Tech.(IT)-V Semester's core subject of Computer Science.
It is termed by various names like:
Numerical Analysis and Design (NAD)
Design and Analysis of Numerical Algorithms ( D&A of NM )
Design of Numerical Algorithms ( DNA )
Computer Oriented Numerical and Statistical Methods ( CONSM )
Numerical Analysis ( NA )
These subjects are taught in various courses with different perspective. In this class the subject will be discussed with the perspective of Development and Analysis of algorithms for Numerical Problems.
The Theoretical base/Concept will be discussed in detail with the approach of developing algorithms.
and the result of algorithm will be analysed by various alternatives.A comparative study of these algorithms will be attempted with the focus of efficient algorithms.
The Sequence in which each method will be discussed is:
Derivation,Geometrical Interpretations
Development of Algorithms/Flowchart
Development of program/Coding
Numerical problems
Efficiency comparisons with peer algorithms
UNIT-1: Numeric Information Representation :
Integer Representations
Unsigned integer representations
One's Complement Method
Two's Complement Method
Real Number Representations
Fixed Point Notations
Errors in handling numerical quantities and Measures and types of errors.
UNIT-2 Roots of Polynomials
Concept of roots, Formula approach v/s Iterative approach, Iterative Methods:
Bisection Method/Bolzano's Method/Midpoint subdivision Method
Method of false position/Regula Falsi Method
Secant Method
Newton Raphson Method
Convergence Order Theorem
Order of Convergence of Secant Method
Order of Convergence of Newton Raphson Method
Comparison among various iterative methods
Function with discrete arguments, Basics of Finite difference calculus.
Forward difference operator, Forward difference table,
Algorithm/program/flowchart for construction of forward difference tables.
Backward difference operator,Backward difference table, algorithm/program/flowchart for construction of Backward difference tables.
Divided difference operator,Divided difference table, algorithm/program/flowchart for construction of Divided difference tables.
Shift Operator, Central difference operator, Averaging operator
Relationship among various operators.
Newton Gegory Forward interpolation formula, Newton Gregory Backward interpolation formula, Newton's divided difference interpolation formula,
Lagrangee's interpolation formula,Inverse interpolation.Numerical problems and algorithms/ Programs.
Inverse Interpolation
UNIT-5: Numerical Differentiation and Integration
Newton Cote's formula,General Quadrature Formula,
Derivation of Trapezoidal rule, Simpson's rule (1/3 and 3/8), Weedle's Rule,(Algorithms, programs, numerical)
Numerical Differentiation.
Solution of ordinary differential equations
Solution of differential Equations using:
Picard’s Method, Euler’s Method, Taylor’s Method,Runge - Kutta Methods, Predictor Corrector Methods
LAB Assignment
[Further Reading]
Statistical Computation Algorithms
Study and develop Algorithms for:
Frequency chart,Scatter diagrams,correlations
Curve fitting by method of least squares
fitting of straight lines, polynomials, exponential curves etc,
Data fitting with Cubic splines,
Regression Analysis, Linear and Non linear Regression, Multiple regression
References
Rajaraman V, “Computer Oriented Numerical Methods”, Pearson Education
IGNOU Study Materials
Gerald & Whealey, “Applied Numerical Analyses”, AW
Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age Int.
Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi
T Veerarajan, T Ramachandran, “Theory and Problems in Numerical Methods,TMH
Pradip Niyogi, “Numerical Analysis and Algorithms”, TMH
Francis Scheld, ” Numerical Analysis”, TMH
Sastry S. S, “Introductory Methods of Numerical Analysis”, Pearson Education.
Gupta C.B., Vijay Gupta, “Introduction to Statistical Methods”, Vikas Publishing.
Goyal, M, “Computer Based Numerical and Statistical Techniques”, Firewall Media, New Delhi.
Future Work
Use Python/C to see and demonstrate your computations results graphically
Use MATLAB, NUMPy, SciLab for solving all the problems of Unit1,2,3,4,5
Teaching Aid-(Future Action-2014)
Shifting whole course on Moodle
Video Lectures on DAVV-Tube
Online Calculators
Root Finding techniques
System of equation
Interpolation Method
Forward difference interpolation
Backward difference interpolation
Divided difference interpolation
Lagrangee's interpolation
COVID-19 : Refer following OER and Reference material to boost your studies:
July December 2014:Test-2(Solution by Preeti Sharma, Anjeeneelu -28/10/2014)