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# Calculus (Code 09050102) B.Sc. Mathematics (Hons) 1st semester

#### Calculus (Code-09050102) B.Sc. Mathematics (Hons) – 1st semester

 S.No. Topic Domain Hours as per UGC 1 Definition of the limit of a function. Basic properties of limits, Continuous function and classification of discontinuities, Differentiability, Successive differentiation. Leibnitz theorem Maclaurin and Taylor series expansions. Must know 14 2 Asymptotes in Cartesian coordinates, intersection of curve and its asymptotes Asymptotes in polar coordinates Curvature, radius of curvature for Cartesian Curves Parameterize curves, polar curves Newton’s method. Radius of Curvature for pedal curves. Tangential polar equation. Center of curvature. Circle of curvature. Chord of curvature, evolutes Test for concavity and convexity Point of inflexion. Multiple ,Cusps, nodes & conjugate point Must know 15 3 Tracing of curves in Cartesian Parametric and polar co-ordinates. Reduction formulae Rectification, intrinsic equation of curve Nice to know 8 4 Quardrature (area) Sectorial area Area bounded by closed curves Volumes and surfaces of solids of revolution. Theorems of Pappu’s and Gulden. Nice to know 8

Books recommended:

• Shanti Narayan: Differential and Integral Calculus.
• Murray R.Speigel: Theory and Problems of Advanced Calculus, Schaum’s Outline series , Schaum Publishing Co., New York.
• N. Piskunov: Differential and Integral Calculus, Peace Publishers, Moscow.