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




Hours as per UGC


  • 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



  • 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



  • Tracing of curves in Cartesian
  • Parametric and polar co-ordinates.
  • Reduction formulae
  • Rectification, intrinsic equation of curve

Nice to know



  • 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


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