Unit 2    Roll's, Lagrange's and Cuuchy's Mean Value theorems, Taylor's theorem, expansion in  power series of sinx, cosx, log (1+X), e^x 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 sin^m0 d0, of^x/2 sin^m0 d0, (m, n non negative integers), application test of definite integrals to.  (I) summation of series, (II) rectification, (III) surface and volume revolution.

Unit 5    Partial derivatives, differentials - their definitions and meanings, tangent plane and normal to  surface, Euler's theorem for homogeneous functions.

             Differential Equations :  Exact differential equations of two variables, determination of constants of Integration using boundary conditions, first order linear and higher degree equations and their applications. Linear differential equations with  constant coefficients and those reducible to this, equations of the type XⁿY_n + X^n-1 Y_n-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 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, generators, 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 a given conic and are parallel to a  given line, equation of a right circular cylinder.

Unit    3       Conicoids :    Standard equation of ellipsoid, hyperboloid of one and two sheets, Elliptic paraboloid and hyperboloid paraboloid. Intersection of a line and a coincoid, tangent plane and normal condition of tangency. Polar and cartesian coordinate systems and their relatios, equations of conics in polar coordinates,  trensformations of coordinate in IR² and IR³.

Unit    4       Experimental Mathematics-1 : Geometry

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

              2.    String construction of curves : concentric circle, 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 width, quickest descent (cycloid),

                     bell shaped curve.

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

                     point.

              6.    Surface : developable and non-developable rules, orient able and non-orient able surface (sphere,

                     cykinder, 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 problem.

              12.    Factals.

Unit    5        Experimental Mathematics-2 : Arithmetic, Algebra and Calculus.

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

              2.    Study of properties of function 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 quadratic equations.

              5.    Boolean Algebra : algebra of 0 and 1 and its applications to simplifications of circuits.

              6.    Introductory coding theory : encoding and decoding with  the 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. 

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

                (2)    Vaishalik bhumiti                                        :      G. M. Patel etc.

                (3)    Vaishalik bhumiti                                        :      Suthar Shukla and Shah    Avda

                (4)    Vaishalik bhumiti                                        :       Darshan Singh and  Uni. gra. N. V. Patel  Nirman. Board  Ahmedabad.