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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

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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