Details of MA2202 (Spring 2015)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA2202 Analysis II Asok Kumar Nanda

Syllabus

  • Differentiation: Definition and basic properties, higher order derivatives, Leibnitz's theorem on successive differentiation.
  • Mean Value Theorems: Rolle's theorem, Lagrange's and Cauchy's mean value theorems, Taylor's theorem, computation of Taylor's series.

  • Maxima and minima: Maxima and minima of a function of one variable, saddle points, applications.

  • Integration: Riemann integral viewed as an area, partitions, upper and lower integrals, Riemann integrability of a function, basic properties of Riemann integrals, mean value theorems for Riemann integrals, fundamental theorem of calculus, change of variable formula and integration by parts, improper Riemann integral. Beta and Gamma functions.
  • Sequence of functions Uniform convergence, convergence and continuity. Weierstrass approximation theorem.

References

  1. T. M. Apostol, Calculus I (2nd Edition), Narosa Publishers, 1996.

  2. J. M. Howie, Real Analysis, Springer Ungergraduate Mathematics Series, Springer-Verlag, 2008.

  3. C. B. Morrey and M. H. Protter, A First Course in Real Analysis, Springer Ungergraduate Mathematics Series, Springer-Verlag, 2004
  4. W. Rudin, Principles of Mathematical Analysis, (3rd Edition) International Series in Pure and Applied Mathematics, McGraw-Hill, 1976.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Not Allowed
3 MR 2 Not Allowed
4 MR 4 Not Allowed
5 MS 4 Core
6 RS 1 Not Allowed
7 RS 2 Not Allowed