**UNIT I**

COMPLEX NUMBERS AND INFINITE SERIES:

De Moivres theorem and roots of complex numbers. Eulers theorem, Logarithmic Functions, Circular, Hyperbolic Functions and their Inverses

Convergence and Divergence of Infinite series, Comparison test dAlemberts ratio test. Higher ratio test, Cauchys root test. Alternating series, Lebnitz test, Absolute and conditioinal convergence.

**UNIT II**

CALCULUS OF ONE VARIABLE:

Successive differentiation. Leibnitz theorem (without proof) McLaurins and Taylors expansion of functions, errors and approximation.

Asymptotes of Cartesian curves.

Curveture of curves in Cartesian, parametric and polar coordinates, Tracing of curves in Cartesian, parametric and polar coordinates (like conics, astroid, hypocycloid, Folium of Descartes, Cycloid, Circle, Cardiode, Lemniscate of Bernoulli, equiangular spiral).

Reduction Formulae for evaluating

Finding area under the curves, Length of the curves, volume and surface of solids of revolution

**UNIT III**

LINEAR ALGEBRA MATERICES:

Rank of matrix, Linear transformations, Hermitian and skeew Hermitian forms, Inverse of matrix by elementary operations. Consistency of linear simultaneous equations, Diagonalisation of a matrix, Eigen values and eigen vectors. Caley Hamilton theorem (without proof).

**UNIT IV**

ORDINARY DIFFERENTIAL EQUATIONS:

First order differential equations exact and reducible to exact form. Linear differential equations of higher order with constant coefficients. Solution of simultaneous differential equations. Variation of parameters, Solution of homogeneous differential equations Canchy and Legendre forms.

**Text books:**

1. Kresyzig, E., Advanced Engineering Mathematics, John Wiley and Sons.

(Latest edition).

2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, Narosa,

2003 (2nd Ed.).

3. Advanced Engineering Mathematics, Dr. A. B. Mathur, V. P. Jaggi (Khanna

publications)

**References books:**

1. Mitin, V. V.; Polis, M. P. and Romanov, D. A., Modern Advanced Mathematics for Engineers, John Wiley and Sons, 2001.

2. Wylie, R., Advanced Engineering Mathematics, McGraw-Hill, 1995.