IGNOU BMTC 133 REAL ANALYSIS
Vigyan Academy
12 modules
HINGLISH
Access for 180 days
"Unlock the beauty of mathematical analysis with IGNOU BMTC 133 Real Analysis - your key to mastering the fundamentals and exploring the limitless depths of this fascinating subject!"
Overview
The course "IGNOU BMTC 133 REAL ANALYSIS" offered by Indira Gandhi National Open University (IGNOU) covers the fundamental concepts of real analysis. Real analysis is a branch of mathematics that deals with the rigorous study of real numbers and real-valued functions. This course delves into topics such as sequences, series, limits, continuity, differentiability, and integration of real-valued functions. Students taking this course will have the opportunity to deepen their understanding of the foundational principles that underlie calculus and mathematical analysis. They will learn how to construct and analyze mathematical proofs, develop critical thinking skills, and enhance their problem-solving abilities. Through a combination of theoretical concepts and practical applications, students will explore the properties of real numbers, delve into the intricacies of mathematical proofs, and understand the importance of precision and clarity in mathematical arguments. By the end of the course, students will have a solid foundation in real analysis and be able to apply their knowledge to solve complex mathematical problems. Overall, "IGNOU BMTC 133 REAL ANALYSIS" is designed to provide students with a comprehensive introduction to the principles of real analysis and equip them with the skills necessary to succeed in advanced mathematics and related fields.
Modules
Communicating Mathematics
5 attachments • 3 hrs
L1.1 INTRODUCTION TO STATEMENT
L1.2 LOGICAL CONNECTIVES
L1.3 DE MORGAN'S LAW, NEGATION
L1.4 CONDITIONAL CONNECTIVES
L1.5 LOGICAL QUANTIFIERS
Mathematical Reasoning
6 attachments • 4 hrs
L2.1 WHAT IS PROOF AND DISPROOF?
L2.2 DIRECT METHOD OF PROOF
L2.3 INDIRECT METHODS OF PROOF
L2.4 DISPROVE BY COUNTER EXAMPLE
L2.5 PRINCIPLE OF MATHEMATICAL INDUCTION PART1
L2.6 PRINCIPLE OF MATHEMATICAL INDUCTION STRONG FORM
Algebraic Structure of R
9 attachments • 8 hrs
L3.1 THE REAL NUMBER LINE
L3.2 R as field
L3.3 R as ordered field
L3.4 Order Completeness Property of R Part 1
L3.5 Order Completeness important proof and problems Part 2
L3.6 ARCHIMEDIAN PROPERTY AND IMPORTANT THEOREM FOR EXAMmp4
L3.7 ABSOLUTE VALUE AND INEQUALITIES
L3.8 COUNTABLE AND UNCOUNTABLE SET PART 1
L3.9 COUNTABLE AND UNCOUNTABLE SET PART 2
Topological Structure of R
11 attachments • 7 hrs
L4.1 INTRODUCTION TO INTERVALS
L4.2 Neighbourhood Points
L4.3 LIMIT POINTS
L4.4 THEOREM 3 AND PROBLEMS
RAL4.5
L4.6 Problems related to Bolzano Weiestrass theorem
L4.7 CLOSED SET
L4.8 THEOREMS RELATED TO CLOSED SETS
L4.9 PROBLEMS RELATED TO CLOSED SETS
L4.10 INTRODUCTION TO OPEN SETS AND ALL THEOREMS
L4.11 PROBLEMS OF OPEN SETS
Sequence and Convergence
10 attachments • 7 hrs
L5.1 INTRODUCTION TO SEQUENCE
L5.2 ALGEBRA AND GEOMETRICAL REPRESENTATION OF SEQUENCE
L5.3 BOUNDED SEQUENCE
L5.4 MONOTONE SEQUENCE PART 1
L5.5 MONOTONE PROBLEMS
L5.8 CONVERGENT SEQ.
L5.9 CONVERGENT SEQ.
L5.10 CAUCHY SEQ.
L5.11 CAUCHY PROBLEMS
L5.12 ALGEBRA 1
Limits of Sequences
8 attachments • 5 hrs
RAL6.1 ORDER AND LIMIT
L6.2 PROBLEMS
L6.3 MONOTONE CONV. THEOREM
L6.4 PROBLEMS OF CONV SEQ
L6.5 PROBLEMS 2
L6.6 PROBLEMS OF CAUCHY FIRST
L6.7 PROBLEMS OF CAUCHY FIRST THEOREM
L6.8 CAUCHY SECOND THEOREM OF LIMITS
Convergence of series
5 attachments • 3 hrs
L7.1 INTRODUCTION TO INFINTE SERIES
L7.2 PARTIAL SUM OF SERIES
L7.3 CONVERGENCE OF INFINTE SERIES
L7.4 PROBLEMS OF CONVERGENCE
L7.5 ALGEBRA OF CONVERGENT SERIES
Tests for convergence(V.IMP)
5 attachments • 2 hrs
L8.1 COMPARISION TEST
L8.2 PROBLEMS OF COMPARISION THEOREM
L8.3 RATIO TEST
L8.4 CAUCHY ROOT TEST
L8.5 RAABE'S AND GAUSSES TEST
Alternating series
2 attachments • 1 hrs
L9.1 Introduction to alternating series
L9.2 Rearrangment of terms
Continuity
8 attachments • 6 hrs
L10.1 INTRODUCTION TO LIMIT
L10.2 Intro to limit cont.
L10.3 EPSILON DELTA PROB.
L10.4 ONE SIDED LIMIT
L10.5 ONE SIDED LIMIT
L10.6 CONTINITUITY INTRO
L10.7 PROBLEMS OF CONTINUITY
L10.8 UNIFORM CONTINUITY
Differentiability
6 attachments • 2 hrs
L11.1 INTRODUCTION TO DIFFERENTIATION
L11.2 BASIC THEOREMS OF DERIVATIVE 1
L11.3 BASIC THEOREMS 2
L11.4
L11.5 Inverse value theorem
L11.6 IVT PROBLEMS
Higher order derivatives
5 attachments • 3 hrs
L12.1 DARBOUX'S THEOREM
L12.2 ROLLE'S THEOREM
L12.3 C.MVT AND G.MVT
L12.4 LAGRANGES MVT
L12.5 INC. AND DEC. FUNCTION
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