University of Pune Board Of Studies

[Harsh Pandit]

Hi buddy here I have come to get Syllabus of Pune University Board of Studies in Mathematics , if you have then plz provide me here ??

As you are asking I am providing Syllabus of Pune University Board of Studies in Mathematics

AMG-3: Real Analysis and Lebesgue Integration
First Term: Real Analysis
1. Sequences of real numbers : Definition of sequence and subsequence, Limit of
a sequence, convergent sequences, Limit superior and Limit inferior, Cauchy
sequences.
[10 Lectures]
2. Series of Real numbers : Convergence and divergence of series of real num-
bers, alternating series, Conditional and absolute convergence of series, test
of absolute convergence (Ratio test and Root test), series whose terms form a
non-increasing sequence.
[10 Lectures]
3. Riemann integral : Sets of measure zero, Definition and existence of a Riemann
integral, properties of Riemann integral, Fundamental theorem of integral cal-
culus, Mean value theorems of integral calculus.
[14 Lectures]
4. Sequence and series of functions : Pointwise and uniform convergence, sequence
of functions, consequences of uniform convergence, convergence and uniform
convergence of series of functions, integration and differentiation of series of
functions.