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Default Sathyabama Institute of Science and Technology B.Tech - Chemical Engineering SMTA1101 Engineering Mathematics - I Syllabus

Sathyabama Institute of Science and Technology B.Tech - Chemical Engineering SMTA1101 Engineering Mathematics - I Syllabus

SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF BIO AND CHEMICAL ENGINEERING

SMTA1101
ENGINEERING MATHEMATICS - I
(COMMON TO ALL BRANCHES EXCEPT BIO GROUPS)
L T P Credits Total Marks
3 * 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, 2nd Edition, Tata McGraw Hill Publishers, New Delhi, 2008.
4. Kandaswamy P & Co., Engineering Mathematics for First Year, 9th 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 N.P. 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
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