SYLLABUS

UNIT-1 Series — Infinite series and Convergent .series. Tests for convergence ofa series —
Comparison test, D’Alembert’s ratio test, Cauchy's n-th root test, Raabe's test,
De-Morgan-Bertrand’s test, Cauchy's condensation test, Gauss's test, (Derivation of tests
is not required). Alternating series. Absolute convergence. Taylor's theorem. Maclaurin's
theorem. Power series expansion ofa function. Powerseries expansion of sinx, cosx, e‘,
log(1+x), (i+x
)n

UNIT-2 Derivative of the length of an arc. Pedal equations. Curvature — Various
fprmulae, Centre of curvature and Chord of curvature. Partial differentiation. Euler's
"theorem for homogeneous functions. Chain rule of partial differentiation. Total
differentiation, Differentiation of implicit functions.

UNIT-3 Envelopes and evolutes, Maxima andMinima offunctions of two variables.
Lagrange's method of undetermined multipliers. Asymptotes. Multiple points. Curve
tracing of standard curves (Cartesian and Polar curves).

UNIT-4 Beta and Gamma functions, Reduction formulae (simple standard formulae),
Double integrals in Cartesian and Polar Coordinates, Change of order of integration.
Triple integrals. Dirichlet's integral.

UNIT-5 Areas, Rectification, VolumesandSurfaces of solids of revolution.