UNIT  I

DIFFERENTIAL CALCULUS

9

Maxima and minima maxima and minima of two variables, Constrained maxima and minima - Lagrange`s multiplier method

INTEGRAL CALCULUS    

9

Evaluation of multiple integrals, Change the order of integration, Application of multiple integral to find area and volume- Applications to engineering problems.

ORDINARY DIFFERENTIAL EQUATION OF FIRST ORDER 

9

Basic concepts - Geometrical meaning - Separable differential equations. Modeling: Separable equations- Exact differential equations- Integrating factors, Linear differential equation, Bernoulli equations  -  Application to engineering problems.

LINEAR DIFFERENTIAL EQUATIONS OF SECOND AND    HIGHER ORDER EQUATION                                         

9

Homogeneous linear  equation of second and higher order equations with constant coefficients - Euler - Cauchy equation - Method of Variation of parameter  - Solution of specified differential equation s connected with electric circuits, Bending of beams and simple harmonic motion(Differential equations and associated conditions need be given).

UNIT V

VECTOR CALCULUS

9

Differentiation of vectors- Gradient, Divergence, Directional derivative - Line, Surface, Integral,  Statement of Green`s, Gauss divergence and stoke`s theorem, Application to engineering problems.

TOTAL:  45 + 15

TEXT BOOKS:

Sl. No.

Author(s)

Title of the Book

Publisher

Year of Publication

1.

Kandasamy P,

Thilagavathy K and Gunavathy K

Engineering Mathematics

S Chand and Co New Delhi

2007

2.

Veerarajan T

Engineering Mathematics(for first year)

Tata McGraw Hill Publishing Co., New Delhi

2005

3.

Grewal B S

Higher Engineering Mathematics

Khanna Publishers

2004

4.

Ramana B.V.

Higher Engineering Mathematics

Tata McGraw Hill Publishing Co., New Delhi

2008

REFERENCE BOOKS:

Sl. No.

Author(s)

Title of the Book

Publisher

Year of Publication

1.

Kreyszig E

Advanced Engineering Mathematics

John Wiley and  Sons, Singapore

2001

2.

Venkataraman M K

Engineering Mathematics

National Publishing Co., Chennai,

2000

WEB URLs

• www.mathworld.wolfram.com.

• www.answers.com/topic/differential-equation

• www.intmath.com/Matrices-determinants