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| vikash | Sathyabama Institute of Science and Technology B.E. - Automobile Engineering SMTA1101 Engineering Mathematics - I Syllabus Sathyabama Institute of Science and Technology B.E. - Automobile Engineering SMTA1101 Engineering Mathematics - I Syllabus SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF MECHANICAL 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 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 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. N.P. 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 |
