Annexure ‘CD – 01’
FORMAT FOR COURSE CURRICULUM
Course Title: Mathematics-Vi
Course Code: MATH401
Credit Units:04
Course Objectives:
To enable the students to



L
T
P/S
SW/F
W
3
1
-
-
TOTAL
CREDIT
UNITS
develop critical thinking for the content of mathematics
reconstruct the disciplinary knowledge of mathematics
enrich their knowledge base to allow further study in the discipline of mathematics
Pre-requisites:
Sets; sequence and series
Student Learning Outcomes:
To enable the students to:





describe topological structure of R
classify between sequences and series and their types
solve the problems on continuity and derivability of given functions
formulate mathematical model
identify mathematical models for physical and socio – economic environment
Course Contents/Syllabus:
Weightage (%)
Module I
Descriptors/Topics
Topological structure of R
Topological structure of R, neighbourhoods, open and closed sets, limit points, bounded sets
Module II
Sequences
10
Descriptors/Topics
Sequences and their convergence, monotonic sequences
The number ‘e’ and its properties
Infinite series of positive terms, comparison and ratio tests for convergence of an infinite series
Module III
Descriptors/Topics
20
Limits
Limits, continuity and derivability of functions
Mean value theorems and Taylors expansions
Power series expansions of elementary functions
Indeterminate forms and L’Hospital rule
20
Module IV
Introduction to Mathematical Modeling
Descriptors/Topics
What is a mathematical model?
Need, types and limitations of mathematical modeling
Formulating a model
Solving and interpreting a model
15
Module V
Mathematical Modeling in Physical Environment
Descriptors/Topics
Simple harmonic motion
Projectile motion
Newton’s law of gravitation
Escape velocity, central forces
Modelling planetary motion, Kepler’s law
Modelling air pollution
Module VI
Descriptors/Topics
15
Mathematical Modelling in the Socio- Economic Environment
Some models in economics (utility, demand, production, cost and supply functions etc.)
Investments (Markowitz model – return valuations, risk valuations, diversification, portfolio selection – feasible set,
20
efficient and optimal portfolio, limitations of the models developed)
Queuing – basics concepts, structure and techniques, two queueing models, basics and time series analysis, forecasting
models
Pedagogy for Course Delivery:
Problem Solving
Lecture
Drill
Lab/ Practicals details, if applicable:
List of Experiments:
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

Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term Examination
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop down)
End Term Examination
Viva Voce
Home Assignment
Test
Attendance
08
07
10
05
Weightage (%)
70
Lab/ Practical/ Studio Assessment:
Continuous Assessment/Internal Assessment
Components (Drop down
Weightage (%)
End Term Examination
Text & References:
 Alexander A. Samarskii, Principles of Mathematical Modelling, Routledge, 2001
 Bartle, R.G. and D.R. Sherbert. Introduction to Real Analysis, John Wiley & Sons: New York, 1982
 IGNOU study materials of MTE – 14 course
 Kapur J.N., Mathematical Modelling, PB Books, 6th Edition
 Malik S.C.and Arora Savita, Mathematical Analysis, 2008
 Rutherford Aris, Mathematical Modelling Techniques, Routledge, 2007
 Singal, M.K. and Asha Rani Singal. Topics in Analysis I, R. Chand & Co.: New Delhi, 2000, 6th Edition
 Verma, H.C. Concepts of Physics, Bharti Bhuwan Publications
 Gamow George , Cleveland John M., Physics:foundations and frontiers, Prentice- Hall Publications