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ENGINEERING  MATHEMATICS-II[As per Choice Based Credit System (CBCS) scheme](Effective from the academic year 2015 -2016)SEMESTER - I/II

Subject Code - 15MAT21
IA Marks - 20
Number of Lecture Hours/Week - 04
Exam Marks - 80
Total Number of Lecture Hours - 50
Exam Hours - 03

Course objectives:
To enable students to apply the knowledge of Mathematics in various engineering fields by making them to learn  the following’
• Ordinary differential equations
• Partial differential equations
• Double and triple integration
• Laplace transform

Module – I
Linear differential equations with constant coefficients: Solutions of  second and higher order differential equations - inverse differential operator method, method of  undetermined coefficients and  method of variation of parameters. 10 Hours

Module -2
Differential equations-2:
Linear differential equations with variable coefficients: Solution of Cauchy’s    and Legendre’s linear differential equations.                                                                     Nonlinear differential equations - Equations solvable for p, equations solvable for y, equations solvable for x, general and singular solutions, Clairauit’s equations and equations reducible to Clairauit’s form.  10 Hours

Module – 3
Partial Differential equations:
Formulation of  Partial differential equations by elimination of arbitrary constants/functions, solution of non-homogeneous Partial differential equations by direct integration, solution of homogeneous Partial differential equations involving derivative with respect to one independent variable only. Derivation of one dimensional heat and wave equations and their solutions by variable separable method.  10 Hours

Integral Calculus:
Double and triple integrals: Evaluation of double  and  triple integrals. Evaluation of double   integrals by changing the order of integration and by changing into polar co-ordinates. Application of  double  and  triple integrals to find area and volume. .  Beta and Gamma functions: definitions, Relation between beta and gamma functions  and simple problems. 10 Hours

Laplace Transform 
Definition  and  Laplace transforms of  elementary functions.   Laplace transforms of     (without  proof) ,  periodic functions and unit-step function- problems

Inverse Laplace Transform  Inverse Laplace Transform  - problems, Convolution theorem to find the inverse Laplace transforms(without proof) and problems,
solution of linear differential equations using Laplace Transforms.
10  Hours

Course outcomes:
On completion of this course, students are able to,
• solve differential equations of electrical circuits, forced oscillation of mass spring  and elementary heat transfer. 
• solve partial differential equations  fluid mechanics, electromagnetic theory and
heat transfer. 
• Evaluate double and triple integrals to find area , volume, mass and moment of
inertia of plane and solid region.
• Use curl and divergence of a vector valued functions  in various  applications of electricity, magnetism and fluid flows.
• Use Laplace transforms to determine general or complete solutions to linear ODE Question paper pattern:
• The question paper will have ten questions. 
• Each full Question consisting of 16 marks
• There will be 2 full questions(with a maximum of  four sub questions) from each module. 
• Each full question will have sub questions covering all the topics under a module. 
• The students will have to answer 5 full questions, selecting one full question
from each module.

Text  Books:
• B. S. Grewal," Higher Engineering Mathematics", Khanna publishers, 42nd edition,  2013. 
• Kreyszig,  "Advanced Engineering Mathematics "  -    Wiley,      2013 Reference Books: 
• B.V.Ramana "Higher Engineering M athematics" Tata Mc Graw-Hill, 2006
• N P  Bali  and Manish Goyal, "A text book of  Engineering mathematics" ,
Laxmi publications, latest edition. 
H. K Dass and Er. Rajnish Verma ,"Higher Engineerig Mathematics",           
S. Chand publishing,1st edition, 2011. V



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