| December 4th, 2020 12:32 PM | |
| prince karak | 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 |
