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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

CREDITS -
04

**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

**Module-4**

**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

**Module-5**

**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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