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Sathyabama Institute of Science and Technology B.E.  Civil Engineering SMTA1301 Engineering Mathematics Syllabus SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF BUILDING AND ENVIRONMENT SMTA1301 ENGINEERING MATHEMATICS  III (COMMON TO ALL BRANCHES EXCEPT BIO GROUPS, CSE & IT) L T P Credits Total Marks 3 0 0 3 100 UNIT 1 COMPLEX VARIABLES 9 Hrs. Analytic functions – Cauchy  Riemann equations in Cartesian and polar form – Harmonic functions – Properties of analytic functions – Construction of analytic functions using Milne – Thompson method – Some Standard Transformations – Translation, Magnification and Rotation, Inversion and Reflection and simple problems based on the above  Bilinear transformation. UNIT 2 COMPLEX INTEGRATION 9 Hrs. Cauchy’s integral theorem – Cauchy’s integral formula – problems – Taylor’s and Laurent’s series – Singularities – Poles and Residues – Cauchy’s residue theorem and problems – Contour Integration (Integration around the Unit circle). UNIT 3 Z TRANSFORMATION AND DIFFERENCE EQUATIONS 9 Hrs. Z –Transform – Elementary properties – Inverse Z – Transform – Partial Fraction method, Convolution method, Residue method – Formation of difference equations – Solution of difference equations using ZTransform. UNIT 4 PARTIAL DIFFERENTIAL EQUATIONS 9 Hrs. Formation of equations by elimination of arbitrary constants and arbitrary functions – Solutions of First order Linear PDE – Lagrange’s linear equation – Solution of Linear Homogeneous PDE of higher order with constant coefficients. UNIT 5 THEORY OF SAMPLING AND TESTING OF HYPOTHESIS 9 Hrs. Test of Hypothesis – Large samples – Z test – Single proportion – Difference of proportions – Single mean – Difference of means – Small samples – Student‘s t test – Single mean – Difference of means –Test of variance – Fisher’s test – Chi square test: Goodness of fit, Independence of attributes. Max. 45 Hrs. COURSE OUTCOMES On completion of the course, student will be able to CO1  Define analytic functions, theorems on complex integration, Singularities. List Fourier transform of standard functions and Parseval’s identity. Form partial differential equation. CO2  Explain the properties of analytic functions and Fourier transform. Understand the concept of Taylor’s and Laurent’s series Understanding the concepts of Z transformation and its applications and solving it. CO3  Apply bilinear transformation, Taylor’s and Laurent’s series. Solve problems on Fourier transform. CO4  Classify partial differential equation and test of hypothesis. CO5  Evaluate problems on complex integration and Appraise sampling theory using different tests. CO6  Construct an analytic function, produce the solution of linear partial differential equations. TEXT / REFERENCE BOOKS 1. Erwin Kreyszig, "Advanced Engineering Mathematics", 8th Edition, John Wiley and Sons Asia Pvt. Ltd., Singapore, 2001. 2. Grewal B.S., "Higher Engineering Mathematics", 41st Edition, Khanna Publications, Delhi, 2011. 3. Kandasamy P., Thilagavathy K. & Gunavathy K., "Engineering Mathematics", 4th Revised Edition,S.Chand & Co., New Delhi, 2001. 4. Veerarajan T., "Engineering Mathematics" Tata McGraw Hill Publishing Co., New Delhi, 1999. 5. J.W. Brown and R.V. Churchill, Complex Variables and Applications, 7th Edition, McGraw Hill, 2004. 6. Gupta S.C., Kapoor V.K., "Fundamentals of Mathematical Statistics", S. Chand & Company, 2012. 7. Bali N.P and Manish Goyal, "A Text book of Engineering Mathematics", 8th Edition, Laxmi Publications Pvt. Ltd., 2011. 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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