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

 S.No. Content of the topics Learning Objectives Teaching Guidelines Methodology Time (Hours) 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. Student will be able to study limit, Continuity & differentiability of function Lecture should be effective so that student will be able to grasp the topics easily Assignment/ seminar/ Class tests/ Presentation 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 Student will be able to study of Asymptotes, Curvature and Points of infixion Lecture should be effective so that student will be able to grasp the topics easily Assignment/ seminar/ Class tests/ Presentation 15 3 Tracing of curves in Cartesian Parametric and polar co-ordinates. Reduction formulae Rectification, intrinsic equation of curve Student will be able to trace the curves & study Reduction formulae , Rectification Lecture should be effective so that student will be able to grasp the topics easily Assignment/ seminar/ Class tests/ Presentation 8 4 Quardrature (area) Sectorial area Area bounded by closed curves Volumes and surfaces of solids of revolution. Theorems of Pappu’s and Gulden. Student will be able to find the area and Volumes of curves Lecture should be effective so that student will be able to grasp the topics easily Assignment/ seminar/ Class tests/ Presentation 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.
• Gorakh Prasad: Differential Calculus, Pothishasla Pvt. Ltd. Allahabad.
• Gorakh Prasad: Integral Calculus, Pothishasla Pvt. Ltd. Allahabad.
• G.B. Thomas and R.L. Finney: Calculus, 9th Ed., Pearson Education, Delhi, 2005.
• M.J. Strauss, G.L.Bradley and K.J. Smith: Calculus, 3rd Ed., Dorling Kindersley (India) P.Ltd. (Pearson Education), Delhi, 2007.
• H.Anton, I. Bivens and S. Davis: Calculus, 7th Ed., John Wiley and sons (Asia) P. Ltd. Singapore, 2002.
• R. Courant and F.John, Introduction to Calculus and Analysis (Volume 1 and 2),Springer-Verlag, New York, Inc., 1989