Pure Mathematics
Total Marks 150
(i) Trigonmetry
De – Moivre’s Theorem Hyperbolic and inverse Hyperbolic functions. Summations of Trigonometric series. Standard same as for degree examination.
(ii)(a) Analytical Plane geometry—Rectangular and Polar Co-ordinates, the Straight lines. Parallel lines, points at infinity, line at infinity, pair of straight lines, simple case of Harmonic ranges and Pencils. The circle, including, coaxi circle, the elpse, the Hyperbola and the Rectangular Hyperbola, the Parabola, Transformation of co-ordinates, Polar equation of coins, Tracing of conic given by the General Equation of the second degree.
(b) Analytical Solid geometry, the straight line, the plane, the sphere, equations of Cylinder and one of second and of their tangent plane, Standard same as for degree examination.
(iii) Algebra—
(a) Theory of Equations, cubic and quadratic equations.
(b) Determinants of third and fourth order, their development and properties. Standard same as for degree Examination.
(iv) calculus—
(a) Differential calculus—
Function, Limits, Continuity, Definition of Differentional Co-efficient Differentiation of function of one variable, Roll’s Theorem, Mean Value Theorem, Successive differentiation, Taylor’s and Machlauren’s Theorems with Largrangs form of remainder, Partial differentiation, Approximation and Small, errors maxima and Minima Double points curvature, curve Tracing.
(b) Integral Calculus:-
Different methods of Intergration, reduction, Formulae Integration as the limit of sum, Definite integral Retification Quadrature , Volumes and Surface of (Solids) of Revolution. (c) Difference equation of the types—
(i) dy + Py dx Q where P and Q are functions of X
(ii) dy square dy—cy.
(iii) Dx square + dx-F(X)/Mx
Where f (x) is of the form _____________ Sin mx of Cos mx Standard same as for degree examination.