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F.Y.B.A. [Mathematics]
Paper-I


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.             

Paper-II Co-Ordinate Geometry and Experimental

Unit No.     Topics

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.

  1. Drawing curves from their defining properties : circle, ellipse, parabola, cycloid ccardiod.

  2. String construction by curves : concentric circles, parabola, epicycloids.

  3. 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....)

  4. Study of curves with special properties : curves of constant with, quickest descent (cycloid), bell shaped curve. 

  5. Verification of certain geometrical results : pedal line, nine point circle, Michael's point, Fermat's point.

  6. Surfaces : developable and non-developable rules, orient able and non-orient able surfaces (sphere, cylinder, cone paraboloid, ellipsoid, hyperboloid, mobius band) 

  7. Curves on surfaces : plane sections of a sphere, cone cylinder, cube, ellipsoid, paraboloid, hyperboloid, geodesics on certain surfaces (sphere, cone, cylinder, cube)

  8. Regular polyhedra.

  9. Curves and surfaces in nature and in day-to-day life situations.

  10. Geometrical Transformations : reflection, rotation, translation, symmetry transformations.

  11. Traversible curves and Konisberg bridge problem.

  12. Factals.

Unit    5    Experimental Mathematics -2 Arithmetic, Algebra and Calculus          

  1. Curve tracing : tracing of curves, whose cartesian polar or parametric equation are given, using analytic techniques and calculus.

  2. Study of properties of functions through graphs (one-to-one, increasing / decreasing, continuity, differentiability, maxima / minima) 

  3. Geometrical meaning of derivative, geometrical meanings of Roll's theorem and mean value theorem, finding area by counting squares and integration.

  4. Geometrical  verification of algebraic identities and geometrical solution of qudratic equations.

  5. Boolean Algebra : algebra of  0 and 1 and its application to simplification of  circuits.

  6. Introductory coding theory : encoding and decoding with help of matrices.

  7. Games based on binary and ternary representations of  numbers.

  8. Magic squares.

  9. Tower of Brahma.

  10. Short-cut methods for arithmetical calculations.

Note :        All units carry equal marks.

Ref. book
 (1)    Co-ordinate geometry  of three limensions.          Shantinarayan        S. Chand