DEPARTMENT OF MATHEMATICS FACULTY OF ENGINEERING AND TECHNOLOGY SRM UNIVERSITY SEMESTER II MA1002- ADVANCED CALCULUS AND COMPLEX ANALYSIS ACADEMIC YEAR: 2014-2015 LECTURE SCHEME / PLAN The objective is to equip the students of Engineering and Technology, the knowledge of Mathematics and its applications so as to enable them to apply for solving real world problems. The list of instructions (provided below) may be followed by a faculty relating to his/her own schedule includes warm-up period, controlled/free practice, and the respective feedback of the classes who handle. The lesson plan has been formulated based on high quality learning outcomes and the expected outcomes are as follows Each subject must have a minimum of 60 hours, which in turn, 45 hours for lecture and rest of the hours for tutorials. The faculty has to pay more attention in insisting the students to have ≥ 95 % class attendance. UNIT I: MULTIPLE INTEGRALS Lect. No L 1.1 L.1.2 L.1.3 L.1.4 L.1.5 L.1.6 L.1.7 L.1.8 L.1.9 L.1.10 L.1.11 Lesson schedule Learning outcomes Introduction of Integration Double integration in Cartesian coordinates Double integration in polar coordinates Tutorial Change of order of integration Area as a double integral Tutorial Triple integration in Cartesian coordinates Conversion from Cartesian to polar Volume as a Triple Integral Tutorial Students apply double integrals to compute areas and learn the use of triple integrals in computing volumes. Students understand the use of multiple integrals in vector fields. Cumulative hours 1 3 4 5 6 7 8 9 10 11 12 UNIT II: VECTOR CALCULUS L.3.1 L.3.2 L.3.3 L.3.4 L.3.5 Gradient,divergence,curl Solenoidal and irrotational fields Vector identies(without proof) Directional-derivatives Tutorial CYCLE TEST – I L.3.6 L.3.7 L.3.8 L.3.9 Line,Surface and Volume integrals Tutorial Greens theorem(without proof) and its applications Gauss divergence theorem(without proof) and its applications Students understand the use of vector calculus to solve problems in electromagnetic fields, gravitational fields and fluid flow 13 14 15 16 18 DATE: 09.02.2015 19,20 21 22 24 Page 1 of 3 2. az.4.5 L.5.5.1 L.7 L.4.4 L.2.10 L.11 Stokes theorem(without proof) and its applications(Verification and applications to cubes and parallelepipeds only) Tutorial 25 UNIT III: LAPLACE TRANSFORMS L.5.1 L.unit circle and semi circular contour Tutorial Students are able to calculate complex integrals and real integrals using calculus of residues 51 52 53 54 55 56 57 58 59 60 Page 2 of 3 .3 L.9 recognize Definition of Analytic Function and Cauchy Students Riemann equations fundamental properties of Properties of analytic functions analytic functions such as Determination of harmonic conjugate uniqueness.5.8 L.4.2.2 L.6 L2.4.3.4 L.2 L.2.4.6 L.4.4 L.3 L.5.03.2 L.11 Transforms of simple functions Basic operationalProperties (without proof) Transforms of derivatives and integrals Tutorial Inverse transforms Convolution theorem Periodic functions Tutorial Applications of Laplace transforms for solving linear ordinary differential equations up to second order with constant coefficients only Tutorial CYCLE TEST – II : Students use transforms to solve differential equations Students understand the use of transforms to solve circuit analysis problems 26 27 28 29 30 32 34 36 38 39 DATE: 09.6 L. L.2015 UNIT IV: ANALYTIC FUNCTIONS L.2.5.2. Poles and Residues Cauchy’s residue theorem(with proof)Evaluation of real definite integrals using Cauchy’s residue theorem Contour integration. az+b construct simple Tutorial conformal mappings Bilinear transformation Tutorial SURPRISE TEST 40 42 43 44 45 47 48 49 50 UNIT V: COMPLEX INTERGATION L.9 Cauchy’s integral theorem(without proof) Cauchy’s integral formulae(with proof) Application of Cauchy’s integral formulae Tutorial Taylor’s and Laurent’s expansions (statements only) Tutorial Singularities.4.5.3.2.3 L.7 L.5.1 L.2.4.5.5 L. zeroes and Tutorial poles Milne-Thomson’s method to find Students are able to Conformal mappings: 1/z .9 L.7 L.2.9 L.8 L.5.4.8 L.10 L. Advanced Calculus and Complex Analysis... S. 8th edition.srmuniv. 1998. E. K.. 38th Edition. Ganesan. Dr. New Delhi. 5.com/Math/ http://botw. Chennai. Dr.S Higher Engineering Mathematics. K.Singapore. Narayanan S.New Delhi. S. Kandasamy P et al. Venkataraman M.com/science/Mathematics/ http://en. Veerarajan T. Volume II &III (2nd edition).yahoo. Ninth Ed. Kreyszig.. 2000 Engineering Mathematics.the-science-lab.III-A&B(13th edition).maths@ktr. Advanced Mathematics forEngineering students. 2000 3. Viswanathan Printers and Publishers.. K.srmuniv.in Tel: +91-44-27417000 Ext: 2701 Page 3 of 3 . Advanced Sons.in Tel: +91-44-27417000 Ext: 2702 Dr. Gamma [email protected] (Duration: 3 Hours) LAST WORKING DAY : 30. Sundarammal Kesavan Professor Course Co-ordinator Email: sundarammal. S.ac. 2011. Ganesan Professor & Head Department of Mathematics Email: hod.. K. Chand & Co. WEB RESOURCES: http://www. 4. Dr. K. Engineering Mathematics. Srinivasan. Grewal B. Mathematics –Vol. Engineering Mathematics for first year Tata McGraw Hill Publishing Co.. Engineering NationalPublishing Co. REFERENCES 1. Manicavachagom Pillay T. MODEL EXAM 15.ac.04. Sundarammal Kesavan. 2010.org/top/science/Math/ http://dir. 1992. V. Khanna publications. Ganapathy Subramanian. Ramanaiah G.wikipedia.. Prof. John Wiley & 2.. 2.org Internal marks Total: 50 Internal marks split up: Cycle Test 1: 10 Marks Model Exam: 20 Marks Cycle Test 2: 10 Marks Surprise Test: 5 marks Attendance: 5 marks Dr.2015 TEXT BOOKS 1.
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