Sathyabama Institute of Science and Technology BE EEE SMTA1101 Engineering Mathematics - I Syllabus

[Arvind Kumar]

Sathyabama Institute of Science and Technology BE EEE SMTA1101 Engineering Mathematics - I Syllabus

SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF ELECTRICAL AND ELECTRONICS ENGINEERING

SMTA1101 ENGINEERING MATHEMATICS I
(COMMON TO ALL BRANCHES EXCEPT BIO GROUPS)
L T P Credits Total Marks
3 0 0 3 100

UNIT 1 MATRICES 9 Hrs.
Characteristic equation of a square matrix – Eigen values and Eigen vectors of a real matrix – Properties of eigen values
and eigen Vectors – Cayley-Hamilton theorem (without proof) – verification, finding inverse and power of a matrix –
Diagonalisation of a matrix using orthogonal transformation – Quadratic forms – Nature of quadratic forms – Reduction of
quadratic form to canonical form by orthogonal transformation.

UNIT 2 GEOMETRICAL APPLICATIONS OF DIFFERENTIAL CALCULUS 9 Hrs.
.Curvature – centre, radius and circle of curvature in Cartesian co-ordinates – Evolutes – Envelope of family of curves with
one and two parameters – Evolute as envelope of normal.

UNIT 3 FUNCTIONS OF SEVERAL VARIABLES 9 Hrs.
Partial derivatives (Definition) – Total derivative – Jacobian – Taylor’s expansion – Maxima and minima of functions of two
variables – Constrained maxima and minima using Lagrange’s multiplier method.

UNIT 4 INTEGRAL CALCULUS I 9 Hrs.
Definite integrals – Properties of definite integrals and problems – Beta and Gamma integrals – Relation between them –
Properties of Beta and Gamma integrals with proofs – Evaluation of definite integrals in terms of Beta and Gamma function.

UNIT 5 INTEGRAL CALCULUS II 9 Hrs.
Double integrals in Cartesian and Polar co-ordinates – Change of order of integration – Change of variables from Cartesian
to Polar coordinates – Area of plane curves using double integrals – Triple integrals – Volume using triple integrals in
Cartesian co-ordinates (Simple Applications).
Max. 45 Hrs.

COURSE OUTCOMES
On completion of the course, student will be able to
CO1 - Define eigen values and eigen vectors, radius and circle of curvature. Recall properties of definite integrals.
CO2 - Understand the concept of partial derivatives to find Jacobian and Taylors series expansion. Explain change of
order of integration.
CO3 - Uses of Cayley Hamilton theorem and its verification. Solve problems in Area and Volume using integration.
CO4 - Point out the stationary points and categorize maxima and minima. Discuss the problems involving Beta and
Gamma integrals.
CO5 - Produce diagonal matrix by transformation of symmetric matrices.
CO6 - Develop the canonical form of a quadratic form. Construct evolute and envelope of family of curves.

TEXT / REFERENCE BOOKS
1. Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th edition, John Wiley & Sons, Singapore, 2012.
2. Grewal B.S., “Higher Engineering Mathematics”, 41th Edition, Khanna Publications, Delhi, 2011.
3. Veerarajan T., “Engineering Mathematics for First Year”, II Edition, Tata McGraw Hill Publishers, New Delhi, 2008.
4. Kandaswamy P & Co., “Engineering Mathematics for First Year”, IX revised edition, S.Chand& Co Pub., 2010.
5. Venkataraman M.K., “Engineering Mathematics – First Year” (2nd edition), National Publishing Co., 2000.
6. Ramana B.V., “Higher Engineering Mathematics”, Tata McGraw Hill, New Delhi, 11th Reprint , 2010.
7. Bali and Manish Goyal, “A Text book of Engineering Mathematics”, Laxmi publications, Reprint 2008.

END SEMESTER EXAMINATION QUESTION PAPER PATTERN
Max. Marks: 100 Exam Duration: 3 Hrs.
PART A: 10 Questions of 2 marks each - No choice 20 Marks
PART B: 2 Questions from each unit of internal choice; each carrying 16 marks 80 Marks