REAL ANALYSIS NOTES IN PDF | REAL ANALYSIS NOTES IN PDF-CSIR NET / GATE MATHS / IIT JAM MATHS

  REAL ANALYSIS PDF NOTES  | 

REAL ANALYSIS NOTES IN PDF-CSIR NET / GATE MATHS / IIT JAM MATHS 

Thanks For Watching In this video lecture we are discussed basic concept of Convergence & Divergence of infinite series This video helpful to Engineering Students and also helpful to MSc/BSc/CSIR NET / GATE/IIT JAM students. #ammathstutorials #infiniteseriesinhindi #convergenceoinfiniteseries #divergenceinfiniteseries #aktumaths #studentTtest #csirnet_mathematics #gate_mathematics #iitjam_mathematics #polytechnic_mathematics #gbtutorials VISIT MY WEB PAGE FOR PDF NOTES: https://www.ammathstutorials.in Download pdf notes: https://www.ammathstutorials.in/2022/02/real-analysis-notes-in-pdf-rela.html 1.My web Page (for pdf notes) https://www.ammathstutorials.in 2. Facebook Page https://www.facebook.com/ammathstutorials 3.Twitter https://www.twitter.com/ammathstutorial/ 4.Whatsapp channel https://www.whatsapp.com/channel/0029Va9nWBXEVccBCvqCk72t *how to check Infinite series is convergent , divergent and oscillatory without any method? *convergence of infinite series *diveregnce of infinite series *oscillatory series *sum of infinite series *convergence and divergence of geometric series *how to check geometric series is convergent or divergent *basic problem of infinite series *Convergence and diveregnt of infinite series for CSIR NET *Convergence and diveregnt of infinite series for GATE MATHS *Convergence and diveregnt of infinite series FOR IIT JAM *Convergence and diveregnt of infinite series FOR B.SC. MATHS *Convergence and diveregnt of infinite series for AKTU MATHS *Convergence and diveregnt of infinite series for Engginering Maths

In this article i have discussed notes of Real Analysis is which is also helpful to Engineering students , B.Sc. and M.Sc. students.

this article is also helpful to csir net / gate maths /iit jam maths /other under graduate students.

Real Analysis is most important topic form competitive examination for science students. Every examination asked more question related to Real Analysis

in this article i will provided following type notes related to real analysis:

CSIR NET MATHS - REAL ANALYSIS 

1)Elementary set theory, finite, countable and uncountable sets, Real number system

     as a complete ordered field, Archimedean property, supremum, infimum. 

2)Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem,

     Heine Borel theorem.

 3)Continuity, uniform continuity, differentiability, mean value theorem. Sequences and

      series of functions, uniform convergence.

 4)Riemann sums and Riemann integral, Improper Integrals. 

5)Monotonic functions, types of discontinuity, functions of bounded variation,

6)Lebesgue measure, Lebesgue integral. 

7)Functions of several variables, directional derivative, partial derivative, derivative as

   a linear transformation, inverse and implicit function theorems. 

8)Metric spaces, compactness, connectedness. 

9)Normed linear Spaces. Spaces of continuous functions

GATE MATHS - REAL ANALYSIS 

Real Analysis:

Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem; Weierstrass approximation theorem; contraction mapping principle, Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.

Calculus: 

Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem

IIT JAM MATHS -REALANALYSIS 

Sequences and Series of Real Numbers: Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series.

Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima and minima.

Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability, maxima and minima.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor’s series, radius and interval of convergence, term-wise differentiation and integration of power series

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