23UMATC14 Differential Calculus Syllabus:

23UMATC14 Differential Calculus Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives

  • The basic skills of differentiation, successive differentiation, and their applications.
  • Basic knowledge on the notions of curvature, evolutes, involutes and polar co-ordinates and in solving related problems.

UNIT-I:

Successive Differentiation: Introduction (Review of basic concepts) – The  derivative – Standard results – Fractional expressions – Trigonometrical transformation – Formation of equations involving derivatives – Leibnitz formula for the  derivative of a product

Chapter – III: Section – 1.1 to 1.6 and 2.1 to 2.2

UNIT-II:

Partial Differentiation: Partial derivatives – Successive partial derivatives – Function of a function rule – Total differential coefficient – A special case – Implicit Functions.

Chapter – VIII : Section – 1.1 to 1.5

UNIT-III:

Partial Differentiation (Continued): Partial derivatives of a function of two variables – Maxima and Minima of functions of two variables – Lagrange’s method of undetermined multipliers.

Chapter – VIII : Section –1.7, Section 4, Section 5.

UNIT-IV:

Envelope: Method of finding the envelope – Another definition of envelope – Envelope of family of curves which are quadratic in the parameter.

Chapter – X : Section – 1.1 to 1.3

UNIT-V:

Curvature: Definition of Curvature – Circle, Radius and Centre of Curvature – Evolutes and Involutes – Radius of Curvature in Polar Co-ordinates.

 Chapter – X : Section – 2.1 to 2.6

Recommended Text Book

  • S.Narayanan and T.K.Manicavachagom Pillai, Calculus Volume I, S.Viswanathan (Printers&Publishers) Pvt Limited , 1987.

Reference Books

  • Courant and F. John, Introduction to Calculus and Analysis (Volumes I & II), Springer- Verlag, New York, Inc., 1989.
  • Apostol, Calculus, Volumes I and II.
  • Goldberg, Calculus and mathematical analysis.
  • Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., 2002.
  • B. Thomas and R.L. Finney, Calculus, Pearson Education, 2010.
  • M.J. Strauss, G.L. Bradley and K. J. Smith, Calculus, 3rd Ed., Dorling Kindersley (India) P. Ltd. (Pearson Education), Delhi, 2007