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Format No. QSP/7.1/01.F01 Issue No.04 Rev. No 3 Dated: Jan 25, 2010

UNIVERSITY OF PETROLEUM & ENERGY STUDIES

COURSE PLAN

SUBJECT Mathematics I PROGRAMME B. Tech.

SUBJECT CODE MATH 101 SEMESTER I

CREDIT POINTS 4 DURATION OF

SEMESTER Aug 2010- Dec 2010 (16 W)

PREREQUISITE

SUBJECTS Mathematics up to 10+2 SESSION

DURATION 60 Minutes

: Faculty Member :

Dr. S. K. Banerjee, Dr D K Banerjee, Dr. Mukesh Kumar, Dr. Nidhi Verma,

Ms Shweta Sachdeva, Mr. Pankaj Kumar Mishra, Dr. Komal, Ms. Shalley Gupta,

Mr. R. K. Pavan Kumar Pannala, Mr. Ravi Kiran Maddali, Ms. Geetika Sharma

and Dr. Maheshwar Pathak.

APPROVED BY:

(HOD) (DEAN)

UPES Campus | Energy Acres| P.O. Bidholi via Prem Nagar| Dehradun-248007(UK)

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Tel: +91-135-2261090/91 | Fax: +91-135-2694204 | URL: www.upes.ac.in

1.01.01.01.0 LEVEL OF KNOWLEDGE REQUIRED:LEVEL OF KNOWLEDGE REQUIRED:LEVEL OF KNOWLEDGE REQUIRED:LEVEL OF KNOWLEDGE REQUIRED:

1.11.11.11.1 PREREQUISITEPREREQUISITEPREREQUISITEPREREQUISITE : : : : Students should have knowledge of basic concepts of Mathematics taught up to senior secondary level.

1.21.21.21.2 CORECORECORECORE REQUISITEREQUISITEREQUISITEREQUISITE: : : :

2.02.02.02.0 OBJECOBJECOBJECOBJECTIVES OF COURSE:TIVES OF COURSE:TIVES OF COURSE:TIVES OF COURSE:

The objectives of this course are:

A. To make students understand and appreciate the role of Mathematics in Engineering through modeling approach.

B. To develop an understanding of the fundamental concepts of Matrices, Differential Calculus, Multiple Integrals and Fourier Series and connect them to the applied problems from other disciplines.

C. To enhance students problem solving and mathematical reasoning abilities. D. To develop technical writing skills of students by means of practical assignments bridging

mathematical theory and engineering applications

3.03.03.03.0 SYLLABUS SYLLABUS SYLLABUS SYLLABUS

Sl.NoSl.NoSl.NoSl.No UnitUnitUnitUnit CoCoCoContentsntentsntentsntents

1.1.1.1.

Unit Unit Unit Unit 1111

MatricesMatricesMatricesMatrices

1. Introduction: Revision of Prerequisites. 2. Elementary Row and Column Transformations (Reduction of a

Matrices into Echelon and Normal form) 3. Linear Dependence of columns and rows. 4. Rank of a Matrix 5. Consistency of System of Linear Equations and its Solution. 6. Characteristic Equation, Eigen values and Eigenvectors 7. Applications of Cayley-Hamilton Theorem. 8. Diagonalisation

2222

Unit Unit Unit Unit 2222

Differential Calculus

1. Higher order derivatives, Successive Differentiation 2. Leibnitz Theorem, Maclaurin's and Taylors Theorem 3. Expansion of Functions of one variable 4. Partial Differentiation 5. Eulers Theorem and its Applications. 6. Jacobian 7. Expansion of Functions of two variables 8. Extrema of Functions of two variables 9. Asymptotes 10. Curve Tracing (Cartesian, Polar & Parametric Curves)

3333

Unit Unit Unit Unit 3333

Multiple Integrals

1. Double and Triple Integrals 2. Change of Order of integration, 3. Change of Variable. 4. Beta and Gamma Functions 5. Applications of I(Area, Volume, Center of Gravity & Moment of

Inertia)

4444

Unit Unit Unit Unit 4444 1. Introduction to Periodic Functions 2. Fourier Series Expansion of functions of period 2.

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Fourier Series 3. Change of Interval 4. Half Range Sine and Cosine series.

4.04.04.04.0 PEDAGOGY:PEDAGOGY:PEDAGOGY: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 solve relevant problems and to give presentations.

5.05.05.05.0 EVALUATION OF GRADING:EVALUATION OF GRADING:EVALUATION OF GRADING:EVALUATION OF 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%

5.1.5.1.5.1.5.1. IIIINTERNALNTERNALNTERNALNTERNAL AAAASSESSMENTSSESSMENTSSESSMENTSSESSMENT:::: WWWWEIGHTAGEEIGHTAGEEIGHTAGEEIGHTAGE 30%30%30%30%

Internal Assessment shall be done based on the following:

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

1 Class Tests/Quizzes 10%

2 Assignments (Problems/Presentations) 10%

3 General Discipline 10%

Internal Assessment Record SheetInternal Assessment Record SheetInternal Assessment Record SheetInternal Assessment Record Sheet (including Mid Term Examination marks)(including Mid Term Examination marks)(including Mid Term Examination marks)(including Mid Term Examination marks) will be displayed on LMS at the end of semester i.e. last week of regular classroom teaching.

5.1.15.1.15.1.15.1.1 CLASS TESTSCLASS TESTSCLASS TESTSCLASS TESTS/QUIZZES/QUIZZES/QUIZZES/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 atleast ten days before the Mid Term Examination and second class test and second quiz atleast 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.

5.1.25.1.25.1.25.1.2 ASSIGNMENTASSIGNMENTASSIGNMENTASSIGNMENTSSSS:::: 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. The marks obtained by the students will be displayed on LMS after each submission and subsequent evaluation.

5.1.3 5.1.3 5.1.3 5.1.3 GENERAL DISCIPLINEGENERAL DISCIPLINEGENERAL DISCIPLINEGENERAL DISCIPLINE:::: Based on students regularity, punctuality, sincerity and

behaviour in the class.

The marks obtained by the students will be displayed on LMS at the end of semester.

5.2.5.2.5.2.5.2. MMMMIDIDIDID TTTTERMERMERMERM EEEEXAMINATION:XAMINATION:XAMINATION:XAMINATION: WWWWEIGHTAGEEIGHTAGEEIGHTAGEEIGHTAGE 20%20%20%20% Mid Term examination shall be Two Hours duration and shall be a combination of Short

and Long theory Questions.

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Date of showing Mid Term Examination Answer Sheets: Oct. 26/27, 2010

5.3.5.3.5.3.5.3. EEEEND ND ND ND TTTTERMERMERMERM EXAMINATION:EXAMINATION:EXAMINATION:EXAMINATION: WWWWEIGHTAGEEIGHTAGEEIGHTAGEEIGHTAGE 50%50%50%50%

End Term Examination shall be Three Hours duration and shall be a combination of

Short and Long theory/numerical Questions.

6.06.06.06.0 GRADING:GRADING:GRADING:GRADING:

The overall marks obtained at the end of the semester comprising all the above three mentioned shall be converted to a grade.

7.0.7.0.7.0.7.0. ATTENDANCE:ATTENDANCE:ATTENDANCE:ATTENDANCE:

Students are required to have a minimum attendance of 75% in the subject. Students

with less than the stipulated percentage shall not be allowed to appear in the End Term

Examination

8.08.08.08.0 DETAILED SESSION PLANDETAILED SESSION PLANDETAILED SESSION PLANDETAILED SESSION PLAN

Sl. No

No. of Sessions Pedagogy

Detail of References Coverage

Pictorial Depiction (if any)

1. 9 Assignments:1

Class Test /Quiz:1

Ref.1,4,5,6 UNIT-1: Matrices

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2 16

Assignments:1 Class Test

/Quiz:1 Ref.3,4,5

UNIT-2: Differential Calculus

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3 10 Assignments:1

Class Test /Quiz:1

Ref. 1,2,4,5

UNIT-3: Multiple Integrals

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7

Assignments:1 Class Test

/Quiz:1

Ref. 1,2,4,6

UNIT-4: Fourier Series

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9.09.09.09.0 SUGGESTED READINGS:SUGGESTED READINGS:SUGGESTED READINGS:SUGGESTED READINGS:

9.19.19.19.1 TEXT BOOK:TEXT BOOK:TEXT BOOK:TEXT BOOK:

1. Jain, R. K., Iyengar, S. R. K., "Advanced Engineering Mathematics", 3e, Narosa Publications, India, 2009 9.29.29.29.2 REFERRENCE BOOKS:REFERRENCE BOOKS:REFERRENCE BOOKS:REFERRENCE BOOKS:

2. Ramana, B. V., "Higher Engineering Mathematics", Tata McGraw Hill publications, 2007 3. Shanthi Narayan., "Differential Calculus", 30e, S. Chand & Company Ltd, India, 2005 4. Grewal, B. S., "Higher Engineering Mathematics", 40e, Khanna Publications, India, 2009 5. Bali, N. P., Narayana Iyengar, N. Ch., "A Text Book of Engineering Mathematics", 6e, Laxmi Publication, India, 2003 6. Kreyszig, Erwin., "Advanced Engineering Mathematics", 9e, Wiley Publications, 2006

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10.010.010.010.0 OTHER RESOURCESOTHER RESOURCESOTHER RESOURCESOTHER RESOURCES

10.110.110.110.1 VVVVIDEOIDEOIDEOIDEO RRRRESOURCES:ESOURCES:ESOURCES:ESOURCES:

10.210.210.210.2 WWWWEBEBEBEB RESOURCESRESOURCESRESOURCESRESOURCES::::

11.011.011.011.0 MINOR AND MAJOR PROJECTSMINOR AND MAJOR PROJECTSMINOR AND MAJOR PROJECTSMINOR AND MAJOR PROJECTS (DESI(DESI(DESI(DESIGN ASSIGNMENTS) GN ASSIGNMENTS) GN ASSIGNMENTS) GN ASSIGNMENTS)

11.111.111.111.1 PPPPROJECTSROJECTSROJECTSROJECTS USINGUSINGUSINGUSING SSSSOFTWARES:OFTWARES:OFTWARES:OFTWARES:

11.211.211.211.2 CCCCONVENTIONAL ONVENTIONAL ONVENTIONAL ONVENTIONAL PPPPROJECTS:ROJECTS:ROJECTS:ROJECTS: