CSIR NET REAL ANALYSIS

Expiry :
**200 Days**

**In This Package we have collection of test series of real Analysis. and solution will be updated soon. **

**n every exam there will two part. **

**One part have MCQ (SECTION B) type questions and 2nd part will have MSQ (Section- C) Type questions. **

**Syllabus :**

Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem. Sequences and series of functions, uniform convergence.Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.

**IN CSIR NET ASK QUESTIONS FORM Real Analysis: **

**Section B : 6-9**

** Section C: 7-10**