In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions.[1] Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability.

Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions.

Sequence and series is a content from Real Analysis which mugs up the Basic concept of sequences and series , Subsequences , Cauchy Sequence with expected theorems like Bolzano Weierstrass Theorem , Riemann Theorem , Concept of Upper and Lower Limit of a sequence , Rearrangement of series of Real and Complex numbers .

An Interesting and Expected Theorems on :

• Continuity

• Continuous Functions

• Uniform Continuity

• Continuity and Compactness

Various ideas from real analysis can be generalized from the real line to broader or more abstract contexts. These generalizations link real analysis to other disciplines and subdisciplines. For instance, generalization of ideas like continuous functions and compactness from real analysis to metric spaces and topological spaces connects real analysis to the field of general topology, while generalization of finite-dimensional Euclidean spaces to infinite-dimensional analogs led to the concepts of Banach spaces and Hilbert spaces and, more generally to functional analysis.

The student will support for their queries from the instructor and get a certificate of completion in the end of the course which can also be tracked via unique link.