FIRST SEMESTER EXAMINATION
(THEORY PAPERS)

Mathematics

UNIT I
COMPLEX NUMBERS AND INFINITE SERIE S: De Moivre’s theorem and roots of complex numbers.
Euler’s theorem, Logarithmic Functions, Circular, Hyperbolic Functions and their Inverses. Convergence
and Divergence of Infinite series, Comparison test d’Alembert’s ratio test. Higher ratio test, Cauchy’s root
test. Alternating series, Lebnitz test, Absolute and conditioinal convergence.
UNIT II
CALCULUS OF ONE VARIABLE: Successive differentiation. Leibnitz theorem (without proof)
McLaurin’s and Taylor’s 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.