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| Professional Mathematics - 00201 |
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| Periods/Week |
|
Periods in one
Session |
|
Full
Marks |
|
Annual
Exam |
|
Internal
Exam |
| L |
T |
P/S |
|
| 3 |
0 |
0 |
|
60 |
|
100 |
|
80 |
|
20 |
Rationale
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A technical diploma holder is engaged generally as first line supervisor. He forms a bridge between workers and management. He has to understand the language of the modern management and communicate with the workers in their language. This subject will help accomplishment of the task in stipulated time, develop attitude towards cost effectiveness, selection of most effective alternative methods. This course will also help the student to tackle different numerical methods and computational techniques for problem solving in research organization as a programmer.
Objectives
The course enables student to:
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develop managerial skills based on mathematical footing.
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develop the ability to find approximate solutions and/or answers to the problems where analytical methods become more complex.
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choose correct numerical techniques for a given problem.
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| CURRICULUM |
| SL |
Group |
Topics |
Periods |
| 1. |
A |
Numerical Methods and Computational Techniques |
20 |
| 2. |
B |
Statistical Techniques |
20 |
| 3. |
C |
Management Techniques |
20 |
| |
|
Total |
60 |
| GROUP-'A' : Numerical Methods and Computational Techniques |
| Topics |
Content |
| 01.01 |
Introduction to Numerical methods: Approximation and errors (Truncation & Round off). Floating point presentation of numbers, arithmetic operations with normalized floating point. |
| 01.02 |
Numeric solutions of non-linear and Transcendental equations: Iterative methods, Newton-Raphson's method, Bisection method and Regula-Falsi method. |
| 01.03 |
Solution of Linear Simultaneous Equations: Gaussian Elimination method and Gauss-Jordan method. |
| 01.04 |
Finite Differences: Backward and forward Differences.Finite Difference Interpolation Formulae, Newton's Forward Difference formulae and Newton's Backward Difference formulae. |
| 01.05 |
Numerical Differentiation and Integration: Newton's forward and backward differentiation formula, Trapezoidal Rule and Simpson's 1/3 rule for numerical integration. |
| 01.06 |
Numerical solution of 1st order ordinary differential equations: Taylor's Series, Euler's method, modified Euler's method, Runga-Kulta methods. |
| GROUP-'B' : Statistical Techniques |
| Topics |
Content |
| 02.01 |
Introduction to Statistics: Measure of central tendencies; measures of dispersions; standard deviation and variance for discrete and grouped data; assumed mean and step deviation methods. |
| 02.02 |
Theory of Probability: Random events and their types, Probability of Events, Definitions, Laws of Probability (Addition and Multiplication Laws). |
| 02.03 |
Probability Distribution: Introduction to Arithmetic Mean and Standard Deviation of a probability distribution. Important probability distribution - Binomial distribution, Poisson's distribution and normal distribution, their means and variance. |
| 02.04 |
Sampling Distribution: Sampling Distribution of Mean and Standard Deviation. |
| 02.05 |
Quality Control: P-Chart and R-Chart. |
| GROUP-'C' : Management Techniques |
| Topics |
Content |
| 03.01 |
Linear Models: |
| 03.01.01 |
Introduction to Operations Research(O.R) Steps of O.R. |
| 03.01.02 |
Linear Programming Problems: Step in formation of a LPP, Mathematical Modelling and Solution Procedure. |
| 03.01.03 |
Solution by Simplex Method : Basic Feasible Solution (Degenerator and Non-degenerator) Procedure including Big-M Method, Example. |
| 03.01.04 |
Transportation problem; Introduction and Solution Procedure:
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| 03.01.05 |
Assignment Problem: Introduction and Solution Procedure-Fundamental theory underlying Hungarian Method. |
| 03.02 |
Network Analysis, CPM & PERT: Introduction. |
| 03.02.01 |
Basic concepts - Activities, Nodes, Edges, Networking of a project, various times calculations, CPM to determine the optimal project schedule. |
| 03.02.02 |
PERT- Definition, difference between CPM & PERT, pessimistic times, optimistic times, most likely times of various activities, probability of meeting the schedule time, standard deviation of the schedule time. |
| 03.03 |
Simulation: Event type simulation - elements of simulation, Generation of random numbers, Monte-O Carlo simulation - Generation and analysis of random observation using random numbers. |
| 03.04 |
Resource Analysis in Network Scheduling: Introduction, project cost, Time cost optimization, Algorithm, Updating (PERT & CPM), Resource Allocation and scheduling. |
| Recommended Books |
| SL |
Title |
Author/Publisher |
| 1. |
Operations Research |
Kanti Swaroop, P.K. Gupta and Man Mohan / Sultan Chand & Sons, New Delhi, 1990. |
| 2. |
Operations Research |
Heera and Gupta / Sultan Chand & Sons, New Delhi, 1990. |
| 3. |
Operations Research |
H.A. Taha / Macmillan Publishing Co., New York, 1982. |
| 4. |
Computer based Numerical Algorithm |
E.V. Krishna Murthy and S.V. Sen / East West Press, 1975. |
| 5. |
Computer Oriented Numerical Methods |
V. Rajaraman / Prentice Hall India, 1980. |
| Scheme of Examination: Final Examination Marks = 80 |
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