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Differential Calculus and Co-ordinate Geometry

3 Credit Hour Course
Intended For Level 1 Term 1 Students

Prerequisite: None

Differential Calculus: Limits, continuity and differentiability; Successive differentiation of various types of functions; Leibniz’s Theorem; Rolle’s Theorem; Mean value Theorem in finite and infinite forms; Lagrange’s form of remainders; Cauchy’s form of remainder; Expansion of functions; Evaluation of indeterminate forms by L’Hospital’s rule; Partial differentiation; Euler’s Theorem; Tangent and Normal, Subtangent and subnormal in cartesian and polar co-ordinates; Maximum and minimum values of functions of single variable; Points of inflexion; Curvature, radius of curvature, center of curvature; Asymptotes, curve tracing.
Co-ordinate Geometry: Transformation of co-ordinates axes and its uses; Equation of conics and its reduction to standard forms; Pair of straight lines; Homogeneous equations of 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 co-ordinates; Diameters; Conjugate diameters and their properties; Director circles and asymptotes.

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