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Title-Calculus (Code-09010102)

S.N Unit Content Domain Hours as per UGC
1 one 1.    Definition of the limit of a function. Basic properties of limits

2.    Continuous function and classification of discontinuities,

3.    Differentiability, Successive differentiation. Leibnitz theorem

4.    Maclaurin and Taylor series expansions.

5.    Jacobians

Must Know 15
2 Two 6.    Asymptotes in Cartesian coordinates, intersection of curve and its asymptotes

7.    Asymptotes  in polar coordinates

8.    Curvature, radius of curvature for Cartesian Curves, Parametric curves, polar curves

9.    Newton’s method. Radius of Curvature for pedal curves. Tangential polar equation

10.   Center of curvature. Circle of curvature. Chord of curvature, evolutes

11.   Test for concavity and convexity

12.   Points of inflexion. Multiple points ,Cusps, nodes & conjugate points, types of cusps

13.   Tracing of curves in Cartesian, Parametric and polar co-ordinates

Must know 15
3 Three 1.       Reduction formulae.,

2.      Beta and Gama functions,

3.      Double and Triple integrals

4.      Dirichlets integrals,

5.      Change of order of integration in double integrals.

6.      Rectification, intrinsic equation of curves

7.      Quardrature( area ) Sectorial area, Area bounded by closed curves

8.      Volumes and surfaces of solids through revolution.

Must know


Nice to know


Books recommended:

  1. Shanti Narayan: Differential and Integral Calculus.
  2. Murray R.Speigel: Theory and Problems of Advanced Calculus, Schaum’s Outline series, Schaum Publishing Co., New York.
  3. Piskunov: Differential and Integral Calculus, Peace Publishers, Moscow.
  4. Gorakh Prasad: Differential Calculus, Pothishasla Pvt. Ltd. Allahabad.
  5. Gorakh Prasad: Integral Calculus, Pothishasla Pvt. Ltd. Allahabad.