new course plan math-102 m(1)

8/20/2019 New Course Plan MATH-102 M(1)

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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 PLANProgramme : B. Tech

Course : MATHEMATICS-II

Subject Code : MATH-102

No. of credits : 4

Semester : II

Session : Jan 2016 - June 2016

Batch : 2015-2019

Prepared by : Dr. Nitin Uniyal, Dr. Vipin Kumar, Dr. Pradeep Malik,

Dr. Sanoj Kumar and Dr. Anupam Bhandari

Email : (nuniyal, vipin, pmalik, sanoj.kumar, abhandari)@upes.ac.in

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

http://www.upes.ac.in/http://www.upes.ac.in/


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COURSE PLAN

A. PREREQUISITE:

a. Basic concepts of Mathematics taught up to B. Tech Semester-I level.

b. Basic concepts of differential equations and its solution.

c. Basic knowledge of differentiation and integration rules.

d. Basic knowledge of Mean, Median and Mode of data.

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, formulates, and solves 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. Recognition of the need for and an ability to engage in life-long learning

PO10. Knowledge of contemporary issues

PO11. An ability to use the techniques, skills, and modern engineering tools necessary for

engineering practice


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C.

COURSE OUTCOMES FOR MATHEMATICS-II: At the end of this course student

should be able to

CO1. Develop insight into the concept of Integral transformations (Laplace and Fourier

Transforms) and their applicability in solving various equations.

CO2. Understand the dynamical behavior of real world systems by the concept of

differential equations, their formulation, solution, physical interpretation and applications

in various engineering disciplines. This includes the study of various techniques to solve

first and second order differential equations with constant and variable coefficients.

CO3. Discuss the fundamental concepts of probability and statistics from an engineering

perspective emphasizing mainly on applications.

CO4. Work with the fundamental differential operators of vector calculus, compute

integrals over a variety of regions of space, understand the relation between line and

surface integrals, surface and volume integrals, use the integral theorems to move from

one type of integral to another, and applications to various physical problems.

CO5. Develop technical writing skills of students by means of practical assignments

bridging mathematical theory and engineering applications.

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

1. WEAK 2. MODERATE 3. STRONG

D. PEDAGOGY

The course will be taught using lecture method. The concepts will be adequately

illustrated with examples to make applications of theoretical concepts clear. Students will

be required to sole relevant problems.


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E.

COURSE COMPLETION PLAN

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%

5.3 End term Examination - 50%

F1. INTERNAL ASSESSMENT: WEIGHTAGE – 30%

Internal Assessment shall be done based on the following:

Sl. No. Description % of Weightage out of 30%

1 Common Class Tests 40%

2 Assignments/Tutorials

(Problems/Presentations)

40%

3 Attendance and Discipline in the class 20%

F2. 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.

F3. CLASS TESTS: Two Common Class Tests based on descriptive type theoretical &

numerical questions based on objective type questions will be held; one common classtest at least ten days before the Mid Term Examination and second common class test

at least ten days before the End Term Examination. Those who do not appear in test

examinations shall lose their marks.

The marks obtained by the students will be displayed on Black-Board a week before

the start of Mid Term and End Term Examinations respectively.

Total Class room 43

Total Tests 02

Total Assignment 04


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F4. 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.

F5. GENERAL DISCIPLINE: Based on student’s regularity, punctuality, sincerity and

behavior in the class.

The marks obtained by the students will be displayed on Black-Board at the end of

semester.

F6. 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 Term examination.

F7. 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.

Date of showing End Term Examination Answer Sheets: Within three week after

completion of End Term examination.

F8. GRADING:

The overall marks obtained at the end of the semester comprising all the above three

mentioned shall be converted to a grade.

G. COURSE DELIVERY PLAN

Topics/Subtopics No. of

Sessions

Course

Outcomes

addressed

Assignments/

Tests

Unit 1

Ordinary Differential Equations 9 CO2, CO5 Assignment 1

Unit 2

Integral Transform11

CO1, CO5 Assignment 2

Unit 3

Vectors9


Unit 4

Statistics14



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S.N. Unit Contents

1.

Unit I

Ordinary

Differential

Equations

1. Linear Differential Equations with Constant Coefficients

2. Cauchy-Euler Differential Equations

3. Solution of Second Order Differential Equations (when a part of

complementary function is known, by reduction to Normal Form, by

changing the Independent Variable and by Variation of Parameters)

2.

Unit II

Integral

Transform

1. Laplace Transform2.Unit Step Function and Dirac-Delta Function

3. Periodic Functions

4. Differentiation and Integration of Laplace Transform

5. Inverse Laplace Transform

6. Convolution Theorem

7. Solution of Linear Differential Equations

8. Fourier Transform

3.

Unit III

Vectors

1. Differentiation of vector valued functions and applications

2. Gradient, Divergence, Curl

3. Integration of vector valued functions: Line, Surface and Volume

Integrals

4. Applications of Green’s, Gauss divergence and Stokes Theorems

4. Unit IV

Statistics

1. Random Variable: Discrete and Continuous

2. Probability mass and Probability density Functions

3. Moments, Skewness and Kurtosis

4. Moment Generating Functions and their properties

5. Binomial, Poisson and Normal Distributions

6. Correlation: Carl-Pearson coefficient and Spearman Brown’s Rank

correlation

7. Linear Regression

8. Chi Square Test


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H.

DETAILED SEESSION PLAN

Topics # Lectures References Pedagogy

UNIT I: ORDINARY DIFFERENTIAL EQUATIONS

1. Solution of Linear Differential equation with

constant coefficients

2. Particular integral for non-homogeneous

Linear Differential equation 3. Cauchy-Euler Differential equation

4. Solution of LDE of type:

′′() + ()′() + ()() = (): a. When a part of C.F. is known

b. Reduction to normal form

c. Changing the independent variable

d. Method of variation of parameters.

L1

L2-L3

L4

L5

L6

L7

L8-L9

Ref- 1,2,3

Text- 1,2,3

Assignment – 1

Class test - 1

UNIT II: INTEGRAL TRANSFORMS

1. Laplace transform and sufficient condition of

existence: Piecewise continuous function and

growth restriction.

2. Evaluation of

(), (), (), () where () is an elementary function.3. Unit Step function and Dirac delta

function and their Laplace

transforms and their properties.

4. (), where () is periodic.

5. { ()()}, ∫ ()0 , Initial andfinal value theorems

L10

L11

L12

L13

L14

Ref -1,2,3

Text- 1,2,3,

Assignment – 2


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6. Evaluation of integrals using Laplace

transforms.

7. Inverse Laplace transform using

Shifting theorems, Heaviside’s

expansion formula

8. Convolution theorem and its

applications

9. Solution of Linear Differential

Equation using Laplace transform

10. Fourier transform

L15

L16

L17

L18-L19

L20

UNIT III: VECTORS

1. Scalar and vector fields,

Differentiation of vector valued

function.

2. Gradient of scalar function, divergence and

curl of a vector valued function.3. Line integral and path

independence of conservative field

4. Surface integral

5. Volume integral

6. Green’s theorem in a plane

7. Stokes’ s theorem

8. Gauss’s divergence theorem

L21

L22-L23

L24

L25

L26

L27

L28

L29

Ref- 1,2,3

Text- 1,2,3

Assignment – 3

Class test -2

UNIT IV: STATISTICS

1. Random Variable: Discrete and

Continuous

2. Probability mass and Probability

density Functions

3. a. Moments about mean, origin and

L30

L31-L32

L33


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arbitrary point.

b. Skewness and Kurtosis

c. Moment generating function and

its properties

5. Probability distributions:

a. Binomial distribution

b. Poisson distribution

c. Normal distribution

6. Correlation: Carl-Pearson coefficient

and Spearman Brown’s Rank

correlation

7. Linear Regression

8. Chi-square test

L34

L35-L36

L37

L38

L39

L40-L41

L42

L43

Text -1,2,3,4 Assignment -4

I. SUGGESTED READINGS:

I1. 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

3. Ramana, B. V., "Higher Engineering Mathematics", Tata McGraw Hill publications,

2007

4. Miller, I. and Miller, M., “John E. Freund’s Mathematical Statistics and applications”

7e Pearson, 2003.

I2. REFERRENCE BOOKS:

1. Stewart, James, “Calculus Early Transcendentals”, Cengage Learning, 2013.

2. Jeffery, Alan, “Advanced Engineering Mathematics”, Academic Press, 2005.

3. Greenberg, Michael, “Advanced Engineering Mathematics”, Pearson, 2013.


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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 Black-Board 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 tests, assignment, Mid-term and/or End-term examinations. It is suggestedthat 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 cri teri on: 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


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Sample format for Indirect Assessment of Course outcomes

NAME:

ENROLLMENT NO:

SAP ID:

COURSE:

PROGRAM:

Please rate the following aspects of course outcomes of Mathematics II.

Use the scale 1-4*

Sl.

No.

1 2 3 4

1 CO1. Develop insight into the concept of Integral transformations

(Laplace and Fourier Transforms) and their applicability in solvingvarious equations.

2 CO2. Understand the dynamical behavior of real world systems by theconcept of differential equations, their formulation, solution, physical

interpretation and applications in various engineering disciplines. Thisincludes the study of various techniques to solve first and second order

differential equations with constant and variable coefficients.

3 CO3. Discuss the fundamental concepts of probability and statistics from

an engineering perspective emphasizing mainly on applications.

4 CO4. Work with the fundamental differential operators of vector calculus,

compute integrals over a variety of regions of space, understand therelation between line and surface integrals, surface and volume integrals,use the integral theorems to move from one type of integral to another,and applications to various physical problems.

5 CO5. Develop technical writing skills of students by means of practical

assignments bridging mathematical theory and engineering applications.

* 1

2

3

4

Below Average

Average

Good

Very Good

new course plan math-102 m(1)

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