Details of MA2201 (Spring 2020)

Level: 2 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA2201 Analysis II Sushil Gorai

Differentiation: Definition and basic properties, higher order derivatives, Leibnitzs theorem on
successive differentiation.
Mean Value Theorems: Rolles theorem, Lagranges and Cauchys mean value theorems,
Taylors theorem, computation of Taylors series, LHopitals rule
Maxima and Minima: Maxima and minima of a function of one variable, saddle points,
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 integral 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.

Suggested Texts:

1. Al-Gwaiz, M.A. and Elsanousi, S.A., Elements of Real Analysis, CRC Press.
2. Apostol, T.M., Calculus I (2nd edition), Narosa Publishers.
3. Howie, J.M., Real Analysis, Springer-Verlag.
4. Morrey, C.B. and Protter, M.H., A First Course in Real Analysis, Springer-Verlag
5. Rudin, W., Principles of Mathematical Analysis (3rd Edition), McGraw-Hill.

Course Credit Options

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