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Format No. QSP/7.1/01.F01 (B)
Issue No.04 Rev. No 5 Dated: June 2, 2015
________________________________________________________________
UNIVERSITY OF PETROLEUM & ENERGY STUDIES
College of Engineering Studies
Dehradun
COURSE PLAN
Programme : B. Tech
Course : MATHEMATICS-III
Subject Code : MATH-201
No. of credits : 4
Semester : III
Session : 2015-16
Batch : 2014-18
Prepared by : DEPARTMENT OF MATHEMATICS
Email : [email protected]
Approved By
_______________________ _______________________
HOD Associate Dean
UPES Campus Tel : +91-135-2770137
“Energy Acres” Fax : +91 135- 27760904
P.O. Bidholi, Via Prem Nagar, Dehradun Website : www.upes.ac.in
COURSE PLAN
A. PREREQUISITE: a. Basic concepts of differentiation and integration. b. Basic concepts of differential equations and its solution.
B. PROGRAM OUTCOMES (POs) for B.Tech:
PO1. An ability to apply knowledge of mathematics, science, and engineering
PO2. An ability to design and conduct experiments as well as to analyze and interpret data
PO3. An ability to design a system, component, or process to meet desired needs within
realistic constraints such as economic, environmental, social, political, ethical, health and
safety, manufacturability, and sustainability
PO4. An ability to function on multidisciplinary teams
PO5. An ability to identify, formulate, and solve engineering problems
PO6. An understanding of professional and ethical responsibility
PO7. An ability to communicate effectively
PO8. The broad education necessary to understand the impact of engineering solutions in
a global, economic, environmental, and societal context
PO9. A recognition of the need for and an ability to engage in life-long learning
PO10. A knowledge of contemporary issues
PO11. An ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice
C. COURSE OUTCOMES FOR MATHEMATICS-III: At the end of this course
student should be able to
CO1. Understand the basic operations of the calculus of finite differences.
CO2. Apply generating function method technique and Matrix method to solve a difference equation
with constant coefficients.
CO3. Understand the use of Legendre’s polynomials and Bessel’s functions in various engineering
problems.
CO4. Understand the concept of Partial differential equation and its solution by Charpit’s method.
CO5. To formulate certain practical problems like 1-D Wave and Heat Equations in terms of Partial Differential Equations, solve them and practically interpret the results.
CO6. Understand the concept of differentiability in complex plane with the help of analytic function
and its properties.
CO7. Understand the various interesting properties of a conformal mapping with the help of Mobius
transformations
Table: Correlation of POs v/s COs
PO/CO PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11
CO1 2 - - - 3 - - - - - 2
CO2 3 - - 3 - - - 2
CO3 3 - - - 3 - - - - - 2
CO4 3 - - - 3 - - - - - 2
CO5 3 - - - 3 - - - - - 2
CO6 2 - 3 - - - 2
CO7 3 - - - 3 - - - - 2
1. WEAK 2. MODERATE 3. STRONG
D. PEDAGOGY
Write description about the planned pedagogy for the coverage
E. COURSE COMPLETION PLAN
Total Class room sessions 40 Total Quizzes 02 Total Test 02 Total Assignment 04
One Session =60 minutes
F. EVALUATION & GRADING
Students will be evaluated based on the following 3 stages.
5.1 Internal Assessment - 30%
5.2 Mid-term Examination - 20%
5.2 End term Examination - 50%
E1. INTERNAL ASSESSMENT: WEIGHTAGE – 30%
Internal Assessment shall be done based on the following:
Sl.
No.
Description % of Weightage out of 30%
1 Class Tests and Quizzes 50%
2 Assignments (Problems/Presentations) 20%
3 Attendance and conduct in the class 30%
E2. Internal Assessment Record Sheet (including Mid Term Examination marks) will be
displayed online at the end of semester i.e. last week of regular classroom teaching.
E3. CLASS TESTS/QUIZZES: Two Class Tests based on descriptive type theoretical &
numerical questions and Two Quizzes based on objective type questions will be held;
one class test and one quiz at least ten days before the Mid Term Examination and
second class test and second quiz at least ten days before the End Term Examination.
Those who do not appear in Viva-Voce and quiz examinations shall lose their marks.
The marks obtained by the students will be displayed on LMS a week before the start
of Mid Term and End Term Examinations respectively.
E4. ASSIGNMENTS: After completion of each unit or in the mid of the unit, there will be
home assignments based on theory and numerical problems. Those who fail to
submit the assignments by the due date shall lose their marks.
E5. GENERAL DISCIPLINE: Based on student’s regularity, punctuality, sincerity and behavior
in the class.
The marks obtained by the students will be displayed on LMS at the end of semester.
E6. MID TERM EXAMINATION: WEIGHTAGE – 20%
Mid Term examination shall be Two Hours duration and shall be a combination of
Short and Long theory Questions.
Date of showing Mid Term Examination Answer Sheets: Within a week after
completion of mid Sem examination.
E7. END TERM EXAMINATION: WEIGHTAGE – 50%
End Term Examination shall be Three Hours duration and shall be a combination of
Short and Long theory/numerical Questions.
E8. GRADING:
The overall marks obtained at the end of the semester comprising all the above three
mentioned shall be converted to a grade.
F. COURSE DELIVERY PLAN
Topics No. of Sessions
Course Outcomes addressed
Assignment(s)/Quizzes/Tests
UNIT I: DIFFERENCE AND DIFFERENTIAL EQUATIONS
1.Difference Equations: Introduction, formulation, solution by generating function and matrix method.
4 CO1, CO2, CO3
Assignment – 1 Class test/Quiz-1
2.Series solution of ODEs of second order
2
3.Legender Polynomials and Bessel Functions
6
UNIT II: PARTIAL DIFFERENTIAL EQUATIONS
1.Introduction to PDE 4 CO4, CO5
Assignment – 1 Class test/Quiz-1
2.Solution of Linear PDE of second order with constant coefficients
1
3.Solutions of 1D heat & wave equations by the method of separation of variables
4
UNIT III: FUNCTIONS OF COMPLEX VARIABLES I
1.Function of complex variable 1
2.Analytic functions 1
3.Cauchy-Riemann Equations (Cartesian Polar forms)
1 CO6
Assignment – 1 Class test/Quiz-1 4.Line integral in complex form,
Cauchy’s Integral theorem and Cauchy’s Integral formula
2
5.Taylor & Laurent’s series expansions of functions of complex variable
3
UNIT IV: FUNCTIONS OF COMPLEX VARIABLES II
1.Singularities with special reference to poles and zeros
4 CO7
Assignment -1 Class test/Quiz-1
2.Cauchy Residue Theorem 2
3.Evaluation of contour integrals 3
4.Conformal mappings: translation, magnification, rotation, inversion and bi-linear transformation
2
G. DETAILED SEESSION PLAN
Topics # Lectures References Pedagogy
UNIT I: DIFFERENCE AND DIFFERENTIAL EQUATIONS
1.Difference Equations:
Introduction and formulation
2.Solution by E and ∆
operators/undetermined
coefficient method
3.Solution by generating function
and matrix method.
L1
L2
L3-L4
Ref 1,2,3,4
Ref 1,2,3,4,
Assignment – 1
Class test/Quiz-1
4.Series solution of ODEs of
second order
5. Solution about Singular
points,Frobenius method
L5
L6
3.Legender Polynomials ,
Rodrigue’s Formula, Generating
function of Legendre’s
polynomial, Orthogonality and
Recurrence Formulae.
4. Bessel Functions, Generating
function and Recurrence
Formulae.
L7-L10
L11-L12
Ref 1,2,3,4,
UNIT II: PARTIAL DIFFERENTIAL EQUATIONS
1.Introduction to PDE,
Formulation of PDE by the
elimination of arbitrary
constants and by elimination of
arbitrary function
L13
Ref 1,2,3,4,6
Assignment – 2
2.Solution of Linear PDE of
second order with constant
coefficients
3. Charpit’s method
L14-L16
L17
4.Solutions of 1D heat & wave
equations by the method of
separation of variables
L18-L21
UNIT III: FUNCTIONS OF COMPLEX VARIABLES I
1.Function of complex variable L22
Ref 1,2,4,5
Assignment – 3
Class test/Quiz-2
2.Analytic functions L23
3.Cauchy-Riemann Equations
(Cartesian and Polar forms)
4. Harmonic function,
Application of Analytic function
to Flow Problems, Method to
L24
L25
find conjugate function.
5. Construction of Analytic
function {Milne Thomson
Method}
L26
6..Line integral in complex form.
7. Cauchy’s Integral theorem
8. Cauchy’s Integral formula
L27
L28
L29
9.Taylor & Laurent’s series
expansions of functions of
complex variable
L30-L31
UNIT IV: FUNCTIONS OF COMPLEX VARIABLES II
1.Singularities with special
reference to poles and zeroes
L32
Ref 1,2,4,5
Assignment -4
2.Cauchy Residue Theorem L33
3.Evaluation of contour integrals
a.Integration round the unit
circle
∫ 𝑓(𝑐𝑜𝑠𝜃, 𝑠𝑖𝑛𝜃)2𝜋
0
𝑑𝜃
b. Evaluation of ∫𝑓1(𝑥)
𝑓2(𝑥)
+∞
−∞𝑑𝑥
c. Indented semicircular contour
L34
L35
L36
4.Conformal mappings:
translation, magnification,
rotation, inversion
5. Bi-linear transformation
L37-38
L39-L40
H. SUGGESTED READINGS:
H1. TEXT BOOK:
1. Jain, R. K., Iyengar, S. R. K., "Advanced Engineering Mathematics", 3e, Narosa
Publications,
2. Kreyszig, Erwin., "Advanced Engineering Mathematics", 9e, Wiley Publications, 2006
H2. REFERRENCE BOOKS:
1. Ref. 1. Raisinghania, M. D., "Advanced Differential Equations", 18e, S. Chand Group, India, 2009
2. Ref. 2. Ramana, B. V., "Higher Engineering Mathematics", Tata McGraw Hill Publications, 2007
3. Ref. 3. Brown W. B., Churchill R. V., Complex Variable and Application, Mc Graw Hill
4. Ref. 4. Sneddon, Elements of Partial differential Equation, Dover Publication.
GUIDELINES
Cell Phones and other Electronic Communication Devices: Cell phones and other electronic
communication devices (such as Blackberries/Laptops) are not permitted in classes during
Tests or the Mid/Final Examination. Such devices MUST be turned off in the class room.
E-Mail and online learning tool: Each student in the class should have an e-mail id and a
pass word to access the LMS system regularly. Regularly, important information – Date of
conducting class tests, guest lectures, via online learning tool. The best way to arrange
meetings with us or ask specific questions is by email and prior appointment. All the
assignments preferably should be uploaded on online learning tool. Various research
papers/reference material will be mailed/uploaded on online learning platform time to time.
Attendance: Students are required to have minimum attendance of 75% in each subject.
Students with less than said percentage shall NOT be allowed to appear in the end semester
examination.
Course outcome assessment: To assess the fulfilment of course outcomes two different
approaches have been decided. Degree of fulfillment of course outcomes will be assessed in
different ways through direct assessment and indirect assessment. In Direct Assessment, it is
measured through quizzes, tests, assignment, Mid-term and/or End-term examinations. It is
suggested that each examination is designed in such a way that it can address one or two
outcomes (depending upon the course completion). Indirect assessment is done through the
student survey which needs to be designed by the faculty (sample format is given below) and
it shall be conducted towards the end of course completion. The evaluation of the
achievement of the Course Outcomes shall be done by analyzing the inputs received through
Direct and Indirect Assessments and then corrective actions suggested for further
improvement.
Passing criterion: Student has to secure minimum 40% marks of the “highest marks in the
class scored by a student in that subject (in that class/group class)” individually in both the
‘End-Semester examination’ and ‘Total Marks’ in order to pass in that paper.
Passing Criterion for B. Tech: minimum 40% of the highest marks in the class
Passing Criterion for M. Tech: minimum 40% of the highest marks in the class