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 CO1 CO2 CO3 CO4 CO5 CO6 CO7
PO1 2 3 3 3 3 2 3
PO2 -
PO3 PO4 PO5 3 3 3 3 3 3 3
1. WEAK
PO6 -
2. MODERATE
PO7 -
PO8 PO9 PO10 -
3. STRONG
D. PEDAGOGY Write description about the planned pedagogy for the coverage
E. COURSE COMPLETION PLAN Total Class room sessions Total Quizzes Total Test Total Assignment
40 02 02 04
PO11 2 2 2 2 2 2 2
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.
Description
% of Weightage out of 30%
No. 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 UNIT I: DIFFERENCE AND DIFFERENTIAL EQUATIONS 1.Difference Equations: Introduction, formulation, solution by generating function and matrix method. 2.Series solution of ODEs of second order 3.Legender Polynomials and Bessel Functions UNIT II: PARTIAL DIFFERENTIAL EQUATIONS 1.Introduction to PDE 2.Solution of Linear PDE of second order with constant coefficients 3.Solutions of 1D heat & wave equations by the method of separation of variables UNIT III: FUNCTIONS OF COMPLEX VARIABLES I 1.Function of complex variable 2.Analytic functions
No. of Sessions
Course Outcomes addressed
Assignment(s)/Quizzes/Tests
4 CO1, CO2, CO3 Assignment – 1 Class test/Quiz-1 2 6
4 1 4
1 1
CO4, CO5 Assignment – 1 Class test/Quiz-1
3.Cauchy-Riemann Equations (Cartesian Polar forms) 4.Line integral in complex form, Cauchy’s Integral theorem and Cauchy’s Integral formula 5.Taylor & Laurent’s series expansions of functions of complex variable UNIT IV: FUNCTIONS OF COMPLEX VARIABLES II 1.Singularities with special reference to poles and zeros 2.Cauchy Residue Theorem 3.Evaluation of contour integrals 4.Conformal mappings: translation, magnification, rotation, inversion and bi-linear transformation
1
CO6 Assignment – 1 Class test/Quiz-1
2
3
4 CO7 Assignment -1 Class test/Quiz-1
2 3 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
L1 Ref 1,2,3,4 L2 Ref 1,2,3,4,
3.Solution by generating function L3-L4 and matrix method. 4.Series solution of ODEs of second order 5. Solution about Singular points,Frobenius method
Assignment – 1
L5
L6
Class test/Quiz-1
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
Ref 1,2,3,4,
L11-L12
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
2.Solution of Linear PDE of second order with constant coefficients
L14-L16
3. Charpit’s method
L17
4.Solutions of 1D heat & wave equations by the method of separation of variables
L18-L21
Ref 1,2,3,4,6
Assignment – 2
UNIT III: FUNCTIONS OF COMPLEX VARIABLES I 1.Function of complex variable
L22
2.Analytic functions
L23
3.Cauchy-Riemann Equations (Cartesian and Polar forms)
L24
4. Harmonic function, Application of Analytic function to Flow Problems, Method to
Assignment – 3 L25
Ref 1,2,4,5
Class test/Quiz-2
find conjugate function. 5. Construction of Analytic function {Milne Thomson Method}
L26
6..Line integral in complex form.
L27
7. Cauchy’s Integral theorem
L28
8. Cauchy’s Integral formula
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
2.Cauchy Residue Theorem
L33
3.Evaluation of contour integrals
L34
a.Integration round the unit circle 2𝜋
∫ 𝑓(𝑐𝑜𝑠𝜃, 𝑠𝑖𝑛𝜃) 𝑑𝜃 0 +∞ 𝑓1 (𝑥)
b. Evaluation of ∫−∞
𝑑𝑥 𝑓 (𝑥) 2
L35 L36
c. Indented semicircular contour 4.Conformal mappings: translation, magnification, rotation, inversion
L37-38
5. Bi-linear transformation
L39-L40
Assignment -4 Ref 1,2,4,5
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
