UNIT I           

COMPLEX NUMBERS

12

Demoivre`s theorem and its applications - Expansion of Sin n  Cos n   in terms of Sin  and Cos - Expansion of Sinⁿ , Cosⁿ in terms of sines and cosines of multiples of  , hyperbolic functions. Inverse hyperbolic functions.

UNIT II

MATRICES

12

Rank of matrix - consistency and inconsistency of a system of linear equations - Eigen values and Eigen vectors - Properties  - Cayley Hamilton theorem - Reduction of Quadratic form to Canonical form by Orthogonal reduction.

UNIT III

DEFINITE INTEGRALS

12

Reduction formula for integral of sinⁿ x , cosⁿ x , tanⁿ x - Definite integrals - Properties - Area of Cartesian Curves - Volumes of Revolution.

UNIT IV

ORDINARY DIFFERENTIAL EQUATIONS

12

Solution of second order with constant coefficients and Variable coefficients - Complimentary function - Particular integrals - Simultaneous linear equations with constant coefficients of first order.

UNIT V

APPLICATIONS OF DIFFERENTIATION

12

Curvature of a curve - Radius of a curvature in Cartesian form -  Centre of curvature - Circle of curvature - Evolutes and Envelopes.

TOTAL: 45 + 15

TEXT BOOKS:

Sl.No.

Author(s)

Title of the Book

Publisher

Year of Publication

1.

Veerarajan T

Engineering Mathematics

Tata McGraw Hill Publishing Company.

1999

2.

Narayanan  S, Manicavachagom Pillay T K and Ramanaiah G

Advanced Mathematics for Engineering students

S Viswanathan Printers and Publishers

1992

REFERENCE BOOKS:

SlNo.

Author(s)

Title of the Book

Publisher

Year of Publication

1.

Kreyszig E

Advanced Engineering Mathematics

John Wiley and Sons, Singapore

2001

2.

Grewal B S

Higher Engineering Mathematics

Khanna Publishers.

2004

3.

Venkataraman M K

Engineering Mathematics

National Publishing Co., Chennai

2000

WEB URLs:

•  mathworld.wolfram.com.

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

• www.intmath.com/Matrices-determinants

• www.mathworks.com/moler/odes