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 SUBJECT CODE CREDIT POINTS PREREQUISITE SUBJECTS
Mathematics – I MATH 101 4 Mathematics up to 10+2
PROGRAMME SEMESTER DURATION OF SEMESTER SESSION DURATION
B. Tech. I Aug 2010- Dec 2010 (16 W) 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)
1
Tel: +91-135-2261090/91 | Fax: +91-135-2694204 | URL: www.upes.ac.in
1.0
LEVEL OF KNOWLEDGE REQUIRED:
1.1 PREREQUISITE : Students should have knowledge of basic concepts of Mathematics taught up to senior secondary level. 1.2
CORE REQUISITE: REQUISITE:
2.0
OBJECTIVES OBJECTIVES 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
3.0 SYLLABUS Sl.No Unit
1.
2
3
4
Unit – 1 Matrices
Unit – 2 Differential Calculus
Unit – 3 Multiple Integrals
1. 2. 3. 4. 5.
Unit – 4
1. 2.
Contents Contents 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 1. Higher order derivatives, Successive Differentiation 2. Leibnitz Theorem, Maclaurin's and Taylor’s Theorem 3. Expansion of Functions of one variable 4. Partial Differentiation 5. Euler’s 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) Double and Triple Integrals Change of Order of integration, Change of Variable. Beta and Gamma Functions Applications of I(Area, Volume, Center of Gravity & Moment of Inertia) Introduction to Periodic Functions Fourier Series Expansion of functions of period 2π. 2
Fourier Series
4.0
3. Change of Interval 4. Half Range Sine and Cosine series.
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.
5.0
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.
INTERNAL ASSESSMENT: SSESSMENT: WEIGHTAGE – 30% Internal Assessment shall be done based on the following: Sl. No. 1 2 3
Description Class Tests/Quizzes Assignments (Problems/Presentations) General Discipline
% of Weightage out of 30% 10% 10% 10%
Internal Assessment Record Sheet (including Mid Term Examination marks) will be displayed on LMS at the end of semester i.e. last week of regular classroom teaching. 5.1.1 CLASS TESTS/QUIZZES TESTS/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. 5.1.2 ASSIGNMENT ASSIGNMENTS S: 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 GENERAL DISCIPLINE: DISCIPLINE: Based on student’s 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.
MID TERM EXAMINATION: WEIGHTAGE – 20% Mid Term examination shall be Two Hours duration and shall be a combination of Short and Long theory Questions. 3
Date of showing Mid Term Examination Answer Sheets: Oct. 26/27, 2010
Sl. No
5.3.
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.
6.0
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.
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
8.0
DETAILED SESSION PLAN
No. of Sessions 9
1.
16 2
10
3
4
7
Pedagogy
Assignments:1 Class –Test /Quiz:1 Assignments:1 Class –Test /Quiz:1 Assignments:1 Class –Test /Quiz:1 Assignments:1 Class –Test /Quiz:1
Detail of References
Ref.1,4,5,6
Ref.3,4,5
Coverage
Pictorial Depiction (if any)
UNIT-1: Matrices
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UNIT-2: Differential Calculus
Ref. 1,2,4,5
UNIT-3: Multiple Integrals
Ref. 1,2,4,6
UNIT-4: Fourier Series
9.0
SUGGESTED READINGS:
9.1
TEXT BOOK:
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1. Jain, R. K., Iyengar, S. R. K., "Advanced Engineering Mathematics", 3e, Narosa Publications, India, 2009 9.2
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 4
10.0
OTHER RESOURCES
10.1
VIDEO RESOURCES:
10.2
WEB RESOURCES: RESOURCES:
11.0
MINOR AND MAJOR PROJECTS (DESIGN (DESIGN ASSIGNMENTS)
11.1
PROJECTS USING SOFTWARES:
11.2
CONVENTIONAL PROJECTS:
5
