Unit No. Topics.
Unit 1 Successive derivatives, standard results for nth derivatives Leibnitz's rule, indeterminate forms . L'
Hospital & rule.
Unit 2 Roll's Lagrange's and Cauchy's Mean Value theorems. Taylor's theorem expansion in power series of
sinx, cosx, log (1+X), ex and (1+X)n under proper restrictions if any, Maclauri's series.
Unit 3 Convergence and divergence of infinite series (including absolute convergence and alternating
series), comparison test, ratio test, root test, convergence of power series.
Unit 4 Integration : integral as a limit of the sum reduction formula of x/25 sinmø , dø, ofx/2, sinmø dø,
(m.n, non negative integers), application of definite integrals to.
(1) summation of series, (2) rectification (3) surface and volume revolution
Unit 5 Partial derivatives, differential - their definition and meanings, tangent plane and normal to surface,
Euler's theorem for homogeneous functions. Differential Equations : Exact differential equation of
two variables. order liner and higher degree equation and their application. Linear differential
equation with constant coefficients and those reducible to this equation of
the Xn Yn + Xn-1 Yn-1 ...... + y = p
Note All Units carry equal marks.
Unit 1 Sphere : Plane section of a sphere, intersection of two spheres, intersection of a sphere and line,
power at a point, tangent plane and normal, plane of contact, angle of intersection of two spheres.
condition for orthogonality spheres through a given circle.
Unit 2 Cone and Cylinder : Definition of a cone, vertex, guiding, curve, generations equation of a cone
with a given vertex and a guiding curve, right circular cone with given vertex. axis and semi-vertical
angle. Definition of a cylinder, equation of a cylinder whose generators intersection given conic and
are parallel to a given line, equation of a right circular cylinder.
Unit 3 Conicoids : Standard equation of ellipsoid, hyper-boloid of one and two sheets, Elliptic paraboloid and
hyperboloc paraboloid. Intersection of a line and a coincoid, target plane and normal condition of
tangency. Polar and cartesian coordinate systems and their relations, equations of conics in polar
coordinates, transformations of coordinates in IR2 and IR3
Unit 4 Experimental Mathematics-1 Geometry.
Drawing curves from their defining properties : circle, ellipse, parabola, cycloid ccardiod.
String construction by curves : concentric circles, parabola, epicycloids.
Construction by ruler and compass : equilateral triangle, square, rectangle of a given size, golden ratio, regular pentagon, regular hexagon, regular octagon, triangles with given conditions , line segment of length (n =2,3,4....)
Study of curves with special properties : curves of constant with, quickest descent (cycloid), bell shaped curve.
Verification of certain geometrical results : pedal line, nine point circle, Michael's point, Fermat's point.
Surfaces : developable and non-developable rules, orient able and non-orient able surfaces (sphere, cylinder, cone paraboloid, ellipsoid, hyperboloid, mobius band)
Curves on surfaces : plane sections of a sphere, cone cylinder, cube, ellipsoid, paraboloid, hyperboloid, geodesics on certain surfaces (sphere, cone, cylinder, cube)
Curves and surfaces in nature and in day-to-day life situations.
Geometrical Transformations : reflection, rotation, translation, symmetry transformations.
Traversible curves and Konisberg bridge problem.
Unit 5 Experimental Mathematics -2 Arithmetic, Algebra and Calculus
Curve tracing : tracing of curves, whose cartesian polar or parametric equation are given, using analytic techniques and calculus.
Study of properties of functions through graphs (one-to-one, increasing / decreasing, continuity, differentiability, maxima / minima)
Geometrical meaning of derivative, geometrical meanings of Roll's theorem and mean value theorem, finding area by counting squares and integration.
Geometrical verification of algebraic identities and geometrical solution of qudratic equations.
Boolean Algebra : algebra of 0 and 1 and its application to simplification of circuits.
Introductory coding theory : encoding and decoding with help of matrices.
Games based on binary and ternary representations of numbers.
Tower of Brahma.
Short-cut methods for arithmetical calculations.
units carry equal marks.
(1) Co-ordinate geometry of three limensions. Shantinarayan S. Chand