DEPARTMENT OF MATHEMATICS FACULTY OF ENGINERING AND TECHNOLOGY SRM UNIVERSITY MA0211- MATHEMATICS III SEMESTER III ACADEMIC YEAR: 2011 2012 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 them for solving real world. 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 56 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. Lect. No Lesson schedule Learning outcomes Cumulative hours UNIT I: FOURIER SERIES L 1.1 Introduction of Fourier series, Dirichlet s conditions 1 L1.2 General Fourier series 2 L1.3 Fourier series of odd and Even 3 functions in (-, ) L1.4 Fourier series of odd and Even 4 functions in (-, ) L1.5 Tutorial 5 Students have good L1.6 Half Range sine and Cosine series 6 knowledge in Fourier in (0, ) series L1.7 Half Range sine and Cosine series 7 in (0, ) L1.8 Parseval s Identity 8 L1.9 Harmonic Analysis 9 L1.10 Harmonic Analysis - problem 10 L1.11 Tutorial 11 Commencement of Cycle Test I 03.08.2011 Page 1 of 5
UNIT II: PARTIAL DIFFERENTIAL EQUATION L2.1 Introduction to Partial Differential Equations, Formation of PDE by elimination of arbitrary constants - 12 L2.2 Formation of PDE by elimination of arbitrary functions L2.3 Solutions of standard types of first order equations in ordinary cases L2.4 Methods to solve the first order Type-1, Type-2 The students will be able to use partial differential equations in the study of fluid mechanics, heat transfer, electromagnetic theory and quantum mechanics. L2.5 Tutorial 16 L2.6 Methods to solve the first order Type-3 L2.7 Methods to solve the first order Type- 4 L2.8 Lagrange s Linear Equations- Method of Grouping L2.9 Lagrange s Linear Equations- Method of Multipliers 20 L2.10 Tutorial 21 L2.11 Linear Homogeneous Partial constant co efficient Type -1 L2.12 Linear Homogeneous Partial constant co efficient Type -2 L2.13 Linear Homogeneous Partial constant co efficient Type -3 L2.14 Linear Homogeneous Partial constant co efficient-type4 They will be able to simulate mathematical models using partial differential equations. 17 13 14 15 18 19 22 23 24 25 Page 2 of 5
L2.15 Classification of second order PDE 26 Commencement of Cycle Test II 14.09.2011 UNIT III: ONE DIMENSIONAL WAVE & HEAT EQUATION L3.1 Introduction to One Dimensional Wave Equation 27 L3.2 Tutorial 28 L3.3 One Dimensional Wave Equation 29 Boundary and initial value Problems with zero velocity L3.4 Boundary and initial value Problems with zero velocity - 30 L3.5 Boundary and initial value 31 Problems with Nonzero velocity L3.6 Boundary and initial value 32 Problems with Nonzero velocity L3.7 One Dimensional Heat Equation with zero boundary values L3.8 Steady state conditions and zero boundary conditions L3.9 Steady state conditions and Non-zero boundary conditions Students can be familiar with one dimensional wave and heat equation L3.10 Tutorial 36 L3.11 Steady and transient states - 37 L3.12 Steady and transient states - 38 Surprise Test UNIT IV: TWO DIMENSIONAL HEAT EQUATION L4.1 Introduction to Two Dimensional Heat Equation 39 L4.2 Steady state heat flow equation 40 L4.3 Laplace equation in Cartesian 41 form L4.4 L4.5 Tutorial Laplace equation in Polar form Students can be 42 familiar with Two 43 L4.6 Laplace equation in Polar form dimensional heat equation 33 34 35 44 Page 3 of 5
L4.7 Heat flow in circular plates including annulus L4.8 Heat flow in semi circular plates 46 L4.9 Heat flow in semi circular plates- 47 L4.10 Tutorial 48 UNIT V: FOURIER TRANSFORMS L5.1 Introduction to Fourier 49 Transforms- statement of Fourier integral theorem L5.2 Fourier Transforms and its inversion formula - 50 L5.3 Fourier Sine Transforms 51 L5.4 Fourier Cosine Transforms 52 L5.5 Tutorial 53 L5.6 Properties of Fourier Students gain good 54 L5.7 Transforms Properties of Fourier sine & cosine Transforms knowledge in the application of Fourier transforms 55 L5.8 Transforms of simple functions 56 L5.9 Tutorial 57 L5.10 Convolution Theorem 58 L5.11 Convolution Theorem - 59 L5.12 Parseval s Identity 60 Commencement of Model Exam: 31.10.2011 Last Working Day 9.11.2011 45 (Duration: 3 Hours) REFERENCES 1. Grewal B.S., "Higher Engineering Mathematics" 36th edition, Khanna Publishers, 2002 2. Kreyszig. E, "Advanced Engineering Mathematics", 8th edition, John Wiley & Sons, Singapore, 2000 3. Kandasamy P etal. "Engineering Mathematics", Vol. II & Vol. III (4th revised edition), S.Chand & Co., New Delhi, 2000 4. Narayanan S., Manicavachagom Pillay T.K., Ramanaiah G., "Advanced Mathematics for Engineering students", Volume II & III (2nd edition), S. Viswanathan Printers and Publishers, 1992 5. Venkataraman M.K., "Engineering Mathematics" - Vol.III - A & B (13th edition), National Publishing Co., Chennai, 1998 Page 4 of 5
WEB RESOURCE: http://engg-maths.com/home Internal marks Total: 50 Internal marks split up: Cycle Test 1: 10 Marks Cycle Test 2: 10 Marks Attendance: 5 marks Dr. V. Srinivasan, Ph. D., Professor/ Mathematics Course Coordinator: MA0211 Email: srinivasanv@ktr.srmuniv.ac.in Model Exam: 20 Marks Surprise Test: 5 marks Prof. K. Ganesan, Ph. D., H.O.D/Mathematics Email: ganesank@ktr.srmuniv.ac.in hod.ma@ktr.srmuniv.ac.in Tel: +91 44 27417000 Ext2701 Page 5 of 5