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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 – CayleyHamilton 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 coordinates – 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 coordinates – 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 coordinates (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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