DEPARTMENT OF MATHEMATICS FACULTY OF ENGINEERING & TECHNOLOGY SRM UNIVERSITY

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1 DEPARTMENT OF MATHEMATICS FACULTY OF ENGINEERING & TECHNOLOGY SRM UNIVERSITY MA 0142 MATHEMATICS-II Semester: II Academic Year: Lecture Scheme / Plan The objective is to impart the students of Engineering & Technology, the concepts of differential calculus, Integral calculus and three dimensional geometry for solving real world problems. 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. Topics Learning Outcomes Cumulative UNIT -1 FUNCTION OF SEVERAL VARIABLES L1.1 Introduction to function of several variables L1.2 Partial Derivatives Definition and Examples Chain rule for function of several variables L1.3 Total Derivatives Differentiation of implicit functions L1.4 Homogeneous functions Euler s Theorem L1.5 Taylor s Expansion for function of two variables L1.6 Finding extreme values of the function of two variables Understanding the concepts of Functions of several variables, solving problems on Taylor s Expansion, Maxima and Minima of functions of two and three variables and Jacobians and able to apply the same for solving practical problems Hours L1.7 Method of Lagrangian multipliers 7 L1.8 Jacobians 8 L1.9 Properties of Jacobian 9 L1.10 Tutorial Page 1 of 5

2 UNIT 2 DIFFERENTIAL EQUATIONS L2.1 First order non-linear differential equations solvable for p L2.2 First order non-linear differential equations solvable for x L2.3 First order non-linear differential equations solvable for y L2.4 Clairaut s equations 14 L2.5 Ordinary Differential Equations Introduction Degree and Order of a differential Equation L2.6 To find complementary function for Homogeneous differential Equations depending on the nature of the auxiliary equation roots Understanding the concept of differential equations and able to apply the same to solve problems in engineering L2.7 Finding the particular integral equation Type-1 Type-2 17 L2.8 Finding the particular integral equation Type-3 Type-4 18 L2.9 Finding the particular integral equation Type-5 Type-6 19 L2.10 Solving Linear differential Equations variable coefficients- Euler s Type 20 L2.11 Solving Linear differential Equations variable coefficients- Lagrange s Type 21 L2.12 Method of variation of parameters 22 L2.13 Tutorial 23 Page 2 of 5

3 UNIT 3 MULTIPLE INTEGRALS L3.1 Introduction, Double Integration in Cartesian 24 L3.2 Double Integration in Cartesian L3.3 Problems in Cartesian Solving problems related to engineering using the concepts of Multiple Integrals L3.4 Double Integration in Polar 27 Describe applications of L Multiple Integrals to L3.6 Change of order of integration practical problems 29 L L3.8 Area as a double integral L3.9 Area as a double integral Triple integration in Cartesian coordinates L3.10 Triple integration in Cartesian coordinates L3.11 Tutorial 34 UNIT 4 VECTOR CALCULUS L4.1 Gradient, divergence, curl 35 L4.2 Solenoidal & irrotational field 36 L4.3 Vector Identities 37 L4.4 Directional derivatives Expected to understand 38 applications of Vector L4.5 Line Integrals 39 calculus in the field of L4.6 surface Integrals engineering. 40 L4.7 Volume Integrals 41 L4.8 Green s theorem and its applications L4.9 Gauss Divergence theorem and its applications L4.10 Stokes theorem and its applications L4.11 Tutorial 45 Page 3 of 5

4 UNIT-5 THREE DIMENSIONAL ANALYTIC GEOMETRY L5.1 Introduction to three dimensional analytical goemetry L5.2 Direction Cosines of a straight line L5.3 L5.4 L5.5 Direction ratios of a straight line Angle between two lines Projection of a line segment Applying concepts of 48 Analytical Geometry of three Dimensions to solve 49 practical problems 50 L5.6 Equation of a plane 51 L5.7 Equation of a plane through the line of intersection of two given planes 52 L5.8 Equation of a straight line 53 L5.9 Coplanar lines 54 L5.10 Skew lines and shortest distance between them 55 L5.11 Tutorial 56 REFERENCE BOOKS: 1. Dr. K. Ganesan, Dr. Sundarammal Kesavan, Prof. K. S. Ganapathy Subramaniyan and Dr. V. Srinivasan, Engineering Mathematics II, Gamma Publication, Revised Edition Grewal B.S, Higher Engg Maths, Khanna Publications, 38 th Edition. 3. Veerajan, T., Engineering Mathematics, Tata McGraw Hill Publishing Co., New Delhi, Dr.V.Ramamurthy & Dr. Sundarammal Kesavan, Engineering Mathematics Vol I&II Anuradha Publications, Revised Edition Kreyszig.E, Advanced Engineering Mathematics, 8 th edition, John Wiley & Sons. 6. Singapore, Kandasamy P etal. Engineering Mathematics, Vol.I & II (4 th revised edition), S.Chand &Co., New Delhi, Narayanan S., Manicavachagom Pillay T.K., Ramanaiah G., Advanced Mathematics for Engineering students, Volume I & II (2 nd edition), S. Viswanathan Printers and Publishers, Page 4 of 5

5 9. Venkataraman M.K., Engineering Mathematics Vol. III (13 th edition), National Publishing Co., Chennai,1998. Web Resources: ` Cycle test 1 scheduled on: Cycle test 2 scheduled on: Model Exam scheduled on: Last working day: Internal Marks Total: 50 Split up: Cycle Test 1: 10 Marks Model Exam: 20 Marks Cycle Test 2: 10 Marks ` Surprise Test: 5 Marks Attendance: 5 Marks Prepared by: Mr. M. Balaganesan Assistant Professor (O.G) balaganesan.m@ktr.srmuniv.ac.in Mr. J.Sasikumar Assistant Professor (S.G) Course coordinator (MA0142) sasikumar.j@ktr.srmuniv.ac.in Prof. K. Ganesan, Ph. D., Professor& Head ganesan.k@ktr.srmuniv.ac.in hod.ma@ktr.srmuniv.ac.in Page 5 of 5

DEPARTMENT OF MATHEMATICS FACULTY OF ENGINERING AND TECHNOLOGY SRM UNIVERSITY

DEPARTMENT OF MATHEMATICS FACULTY OF ENGINERING AND TECHNOLOGY SRM UNIVERSITY MA1001- CALCULUS AND SOLID GEOMETRY SEMESTER I ACADEMIC YEAR: 2014-2015 LECTURE SCHEME / PLAN The objective is to equip the