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Other Names of this Course / Subject
Mathematics, Math, Calculus, Geometry
Syllabus
(i) Differential Calculus:
Limits, continuity, and differentiability, Successive differentiation of various types of functions; Leibnitz Theorem; Rolle's Theorem; Mean value Theorem in finite and infinite forms; Lagrange form of remainders; Cauchy form of remainder; Expansion of functions; Evaluation of indeterminate forms by L Hospital rule: Partial differentiation; Euler Theorem: Tangent and Normal, Subtangent and subnormal in cartesian and polar co-ordinates; Maximum and minimum values of functions of single variable; Points of inflection; Curvature, the radius of curvature, center of curvature; Asymptotes, Curve tracing.
(ii) Co-ordinate Geometry:
Transformation of co-ordinates axes and their uses; Equation of conics and its reduction to standard forms; Pair of straight lines; Homogeneous equations of the second degree; Angle between a pair of straight lines; Pair of lines joining the origin to the point of intersection of two given curves, circles; System of circles; Orthogonal circles, Radical axis, radical center, properties of radical axes; Coaxial circles and limiting points; Equations of parabola, ellipse, and hyperbola in cartesian and polar co-ordinates; Tangents and normals, pair of tangents; Chord of contact; Chord in terms of its middle points; Pole and polar parametric coordinates; Diameters; Conjugate diameters and their properties; Director circles and asymptotes.
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