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Default Sathyabama Institute of Science and Technology M.Tech - Medical Instrumentation SMTA5101 Advanced Mathematics Syllabus

Sathyabama Institute of Science and Technology M.Tech - Medical Instrumentation SMTA5101 Advanced Mathematics Syllabus


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

SMTA5101
ADVANCED MATHEMATICS
(Common to all M.E Branches and M.Tech
Med-Instrumentation)
L T P Credits Total Marks
3 * 0 3 100

UNIT 1 MATRIX THEORY 9 Hrs.
QR decomposition –Eigen values using shifted QR algorithm – Singular Value Decomposition –Pseudo inverse –Least
square approximations

UNIT 2 CALCULUS OF VARIATIONS 9 Hrs.
Concept to Functionals – Euler’s equation–functional dependent on first and higher order derivatives–Functionals on several
dependent variables –Isoperimetric problems –Variational problems with moving boundaries

UNIT 3 TRANSFORM METHODS 9 Hrs.
Laplace transform methods for one dimensional wave equation–Displacements in a string–Longitudinal vibration of a elastic
bar–Fourier transform methods for one dimensional heat conduction problems in infinite and semi infinite rod.

UNIT 4 ELLIPTIC EQUATIONS 9 Hrs.
Laplace equation – Properties of harmonic functions – Fourier transform methods for Laplace equations – Solution for
Poisson equation by Fourier transforms method.

UNIT 5 LINEAR ANDNON-LINEAR PROGRAMMING 9 Hrs.
Simplex Algorithm –Two Phase and Big M techniques – Duality theory –Dual Simplex method –Non Linear Programming–
Constrained extremal problems –Lagranges multiplier method–Kuhn–Tucker conditions and solutions.
Max.45 Hrs.

COURSE OUTCOMES
On completion of the course, the student will be able to
CO1 - Understanding the concepts of Matrix theory.
CO2 - Learning the concepts of calculus of variations and its applications.
CO3 - Understanding the concept of transform methods and elliptic equations.
CO4 - Evaluation of the linear and Non linear programming and its applications.
CO5 - Applying transform methods in one dimensional heat conduction problems

TEXT / REFERENCE BOOKS
1. Bronson, Schaum’s Outline Matrix Operations, McGraw-Hill, 2011.
2. Venkataraman MK, Higher Engineering Mathematics, National Pub. Co, 2003.
3. Elsgolts, L., Differential Equations and Calculus of Variations University Press of the Pacific, 2003.
4. Sneddon I.N., Elements of Partial differential equations, Dover Publications, 2006.
5. Sankara Rao, K., Introduction to partial differential equations. Prentice HallofIndia, 2011.
6. Taha HA, “Operations research-An introduction, McMilan Publishing Co, 2010.

END SEMESTER EXAMINATION QUESTION PAPER PATTERN
Max. Marks: 100 Exam Duration: 3 Hrs.
PART A: 5 Questions of 6 marks each - No choice 30 Marks
PART B: 2 Questions from each unit with internal choice, each carrying 14 marks 70 Marks
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