B.Tech. (ECE '15), IIT Kharagpur,
AIR 34 in AIEEE - 2011,
Qualified RMO - 2009,
CSE Mains 2017: Essay - 153, Maths - 252

Asim Anand

In this course we shall discuss Real Analysis as per the syllabus prescribed by UPSC. The theory lessons shall be followed by solved examples and solutions to past year's questions. See you there!

Crack UPSC CSE Prelims and Mains Exams. Know how to prepare for UPSC 2019 and 2020, complete syllabus, exam patterns, latest notifications to join IAS, IFS, IPS and other cadres of Civil Services.

UPSC CSE - GS

UPSC - Civil Services Examination (IAS) Preparation

English

Mathematics Optional for UPSC - Real Analysis

Strategy for Mains

Preparation Strategy

Practice & Strategy

UPSC CSE

Ace the toughest competitive and government exams in India 

Test Preparation

Union Public Service Commission Exams (UPSC)

Syllabus

Overview

Natural Numbers, Algebraic Structure and Order Structure [Chapter 1]

Inverse Operations, Integers and Rational Numbers, their Algebraic and Order Structures

Fields of Numbers, Set of Real Numbers as a Complete Ordered Field

Intervals, Supremum and Infimum

Properties of Supremum & Infimum

Greatest (smallest) member of set bounded above (below)

Bounded & Unbounded Sets

Solved Examples

Order Completeness of set of Real Numbers - I

Order Completeness of set of Real Numbers - II

Equivalent descriptions of Order Completeness property.

Equivalent descriptions of Order Completeness property, Dedekind Property

Equivalence of Dedekind Property and the Order Completeness property of R.

Equivalence of Dedekind Property & Order Completeness Property

Set of Real Numbers as a Complete Ordered Field - Summary, Archimedean Property

Archimedean Property (cont'd.)

Archimedean Ordered Field, Denseness Property of R.

Archimedean Ordered Field, Denseness Property of R

Denseness Property of R (cont'd)

Modulus of a Real Number - I

Modulus of a Real Number - II

Principle of Mathematical Induction, Bernoulli's Inequality.

Principle of Mathematical Induction, Bernoulli's Inequality [Chapter 1 conclusion]

Neighbourhood & Deleted Neighbourhood of a Point, Examples [Chapter 2]

Examples cont'd.

Properties of Neighborhoods

Properties of Neighborhoods (cont'd), Limit Point of a Set

Limit Point of a Set (cont'd), Derived Set, Examples

Examples (cont'd)

Bolzano-Weierstrass Theorem

Bolzano-Weierstrass Theorem (cont'd), Theorem II

Theorem III, Theorem IV

Theorem V

Open & Closed Sets

Theorems concerning Families of Open & Closed Sets - I

Theorems concerning Families of Open & Closed Sets - II

Theorems concerning Families of Open & Closed Sets - III

Examples of Open & Closed Sets

Interior, Exterior & Boundary of a Set, Examples

Theorems on Interior of a Set - I

Theorems on Interior of a Set - II

Adherent point and Closure of a Set

Theorems on Closure of a Set - I

Theorems on Closure of a Set - II

Theorems on Closure of a Set - III

Isolated Points, Discrete Sets, Dense Sets.

Isolated Points, Discrete Set, Dense Sets

Illustrations

Cantor Nested Interval Theorem

Cover of a Set

Compact Set

Properties of a Compact Set

Heine - Borel Theorem

Properties of a Compact Set (cont'd.) [Chapter 2 conclusion]

 10 years of teaching experience in UPSC CSE category .Took more than 6k lectures . Cleared UGC NET & JRF , Gave UPSC interview twice. 

Saurabh Pandey

In this course the attempt is made to improve the answer writing skill. On regular basis the lessons will be published . Each lessons will have different themes taken from different subjects based on which the questions will be asked.

(Hindi) UPSC/IAS Mains Answer Writing for IAS Mains 2019 and 2020.

Founder - Anuj Garg Coaching I 9 years of teaching experience | Use my code "AGC10"  to Unlock free content | 

Anuj Garg

In this course I will be dealing with some important previous year questions asked in history optional

(Hindi) Target History Optional-2019/20

In this course I will be discussing some important questions asked in UPSC mains from modern history section

(Hindi) Modern History Previous Year Paper Analysis (2014-2018)

Referral code : LIVEAMIT10 for 10% off on Plus Subscription
4+ Years of Teaching experience for IIT JAM, CSIR NET
Provided Top Rankers like 

Amit Ranjan

In this course we will be focussing on the preparations for UPSC mains for the optional paper Physics.

(Hindi) Mains Optional Physics - UPSC CSE

AFMC MBBS'06 AIR 44, NEET PG MDS AIR 20, Orthodontics, Facial Orthopedician, Qualified UPSC CSE Mains , Anthro Paper1-176, Adventure sport 

Mayank Jain

This course will help you to score high marks in interview by not repeating the mistakes which I did during my interview. It will cover the basics of interview, review of the board members, expected questions from economy , IR and social issue

(Hindi) UPSC Interview- Learn from my Mistakes

Kapil Sharma

(Hindi) l important Previous Years Question for UPPCS,RAS,MPPSC.UGC NET, SSC.CGL examination

Lessons

51 lessons • 5h 27m

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Overview

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Natural Numbers, Algebraic Structure and Order Structure [Chapter 1]

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Inverse Operations, Integers and Rational Numbers, their Algebraic and Order Structures

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Fields of Numbers, Set of Real Numbers as a Complete Ordered Field

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Intervals, Supremum and Infimum

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Properties of Supremum & Infimum

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Greatest (smallest) member of set bounded above (below)

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Bounded & Unbounded Sets

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Solved Examples

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Order Completeness of set of Real Numbers - I

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