I Expansion of Cosnφ. Sinnφ , Cosnφ. Sinnφ – Hyperbolic functions – seperation of real
and imaginary parts of Sin(α+iβ), Cos(α+iβ), tan(α+iβ), Sinh(α+iβ), Cosh (α+iβ), tan(α+iβ),
tanh(α+iβ). Logarithm of a complex number –summation of trigonometric series.
II Scalar and vector point functions –differentiation of vectors - differential operators –
directional derivative – gradient, divergence, curl. Integration for vectors- line,surface and
volume integrals – Theorems of Gauss, Green, Stokes (Statements only) –Verifications.
III Fourier series –definition – finding Fourier coefficients for a given periodic function
with period 2π- odd and even functions – half range series – change of interval.
Analytical geometry of two dimensions – polar coordinates-equation of a conic –
directrix- chord- tangent –normal-simple problems.
IV Analytical geometry of three dimension- staight lines – coplanarity of straight lines –
shortest distance and equation of shortest distance of between two lines – simple problems.
Anx.18 D - B.Sc Maths (SDE) 2007-08 Page 4 of 26
Sphere – standard equation – results based on the properties of a sphere- tangent plane to a
sphere – equation of a circle.
V Cone and cylinder – cone whose vertex is at the origin – enveloping cone of a sphere
– right circular cone – equation of a cylinder – right circular cylinder.
Conicoids – nature of a conicoid – standard equation of a central conicoid –
enveloping cone – tangent plane – conditions for tangency – director sphere and director plane.