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Title- Advance Calculus (Code-09010301)

S.N Unit Content Domain Time                         (Hrs)
1 ONE 1.      Continuity, Sequential Continuity,

2.      Properties of continuous functions, Uniform continuity,

3.      Differentiability,

4.      Chain rule of differentiability,

5.      Rolle’s Theorem and Lagrange’s mean value theorem and their geometrical interpretations.

6.      Taylor’s Theorem with various forms of remainders,

7.      Darboux Theorem (Intermediate value theorem) for derivatives,

8.      Indeterminate forms.

Must know

Nice to know

2 TWO 1.       Limit and continuity of real valued functions of two variables.

2.       Partial differentiation. Total Differentials; Composite functions & implicit functions.

3.       Change of variables.

4.       Homogenous functions & Euler’s theorem on homogeneous functions.

5.       Taylor’s theorem for functions of two variables.

Must know 14
3 THREE 1.      Differentiability of real valued functions of two variables.

2.      Schwarz and Young’s theorem. Implicit function theorem.

3.      Maxima, Minima and saddle points of two variables.

4.      Lagrange’s method of multipliers.

5.      Involutes and evolutes, Bertrand Curves.

6.      Surfaces: Tangent planes, one parameter family of surfaces, Envelopes.

Must know

Nice to know


Books Recommended:

  1. Goldberg, R.R. Real Analysis. New Delhi : Oxford & IBH, 1970.
  2. Gorakh Prasad, Differential Calculus. Allahabad : Pothishala.
  3. Malik, S.C. Mathematical Analysis. New Delhi: Wiley Eastern.
  4. Shanti Narayan. A Course in Mathematical Analysis. New Delhi: S.Chand.
  5. Spiegel, Murray, R. Theory and Problems of Advanced Calculus. New York: Schaum Publishing.