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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

The Basic Real Analysis certification course has been designed with the aim to cover several basic concepts such as real line, differentiation as well as integration. The course prepares candidates for future courses. The theorems have been well explained so that the basics are clear for the aspirants. Theories and logics have been covered in every module of the basic real analysis course.

The course will also be enhancing the skills of the individuals registering for the course. Discussion forums boosts up the confidence level, by offering rigorous learning during the learning phase of course. Assignments, reading sessions, video lectures and quizzes have been designed which ensures that the participants are having smooth learning.

Aspirants registering for the Basic Real Analysis online course will be able to solve the problems easily after the learning they acquire. Different terminologies such as limit superior and limit inferior have been included in the course.

The Highlights

Undergraduate level
12 weeks course duration
100% Free course
Certified program by IIT Bombay
Certification of completion by Swayam

Programme Offerings

Reading Materials
video lectures
Online discussion forums
Self-assessments
quizzes

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	IIT Bombay

For free the participants can register in the Basic Real Analysis certification syllabus.
The candidates taking the exam for the certification, must pay Rs. 1000 as exam fees.

Basic Real Analysis fees detail

Fees Category	Amount in Rs.
Certification fees	Free

Eligibility Criteria

Education

The candidates registering for the Basic Real Analysis certification course must have basic calculus exposure for better understanding.

Certification Qualifying Details

The candidates must take the end term exam for receiving certification. The score will be calculated as the average of the best 8 assignments out of the total 12 must be 25%. The score of the exam must be 75% out of the total marks i.e. 100.

The candidates become eligible for the Basic Real Analysis certification benefits only if they have their average assignment score>=10/25 and the score of the exam is >=30/75. If the candidates fail to meet any of the criteria they will not be given the certificate for the course even if their final score is >=100

What you will learn

Mathematical skill

The candidates will acquire learning in the following areas after registering for the Basic Real Analysis training.

The candidates will learn about the basics of set theory in a simplified way.
During the Basic Real Analysis certification, the aspirants will learn about the differential equations to a rigorous analysis.
The aspirants will learn about the foundation of real analysis in a theoretical manner.
The participants will acquire learning on number theory and mathematical logic.
The course also covers the crucial way of developing thinking skills within oneself.
The candidates will gain insights on the new ways for computing things.
Participants enrolling on the course will be taught about the different levels of analysis.
The participants will be exposed to the mean value theorem and its application during the Basic Real Analysis program.
Continuity and uniform continuity have been covered well in the syllabus easing out the learning for the candidates.
The aspirants will also learn about the functions of various variables such as directional derivative, partial derivative and total derivative.

Who it is for

The following candidates listed below can take Basic Real Analysis training.

The participants who want to explore the real analysis and learn more about the theorems.
Candidates who have proper exposure to calculus and are seeking certification in this domain.

Admission Details

For registering successfully in the Basic Real Analysis certification, the candidates must practice the points mentioned below.

Step 1: The candidates must select the entire link and open it in the browser. https://onlinecourses.nptel.ac.in/noc21_ma04/preview

Step 2: Towards the right of the screen, the candidates will find the option of “JOIN”.

Step 3: The candidates must sign in or register themselves in the next step.

Step 4:For all the new users to the Swayam platform, make your account via google account, Microsoft account or Facebook.

Step 5: After this, the users will have a page where they need to fill all the required details.

Step 6: Once the above steps are followed, the candidates have successfully taken the Basic Real Analysis online course and can start their learning.

The Syllabus

Review of sequences and series of real numbers

Tests for convergence of Series
Limit superior and limit inferior

Cauchy sequences and completeness of R.

Basic notions of Metric Spaces with emphasis on Rn
Connectedness
Compactness
Heine Borel Theorem

Continuity
Uniform continuity

Monotone functions
Functions of bounded variation

Derivatives
Mean Value Theorem and applications

Riemann Stieltjes integral
Riemann`s Criterion for integrability
Improper integrals
The Gamma function

Sequences and series of functions
Uniform convergence

Functions of several variables
Directional derivative
Partial derivative
Total derivative

Mean Value Theorem
Taylor`s Theorem and applications to Maxima/Minima and convexity.

Double and triple integrals
Statement of Fubini's Theorem
Change of variable formula (without proofs) with illustrations

Instructors

IIT Bombay Frequently Asked Questions (FAQ's)

1: When is the last date to apply for the Basic Real Analysis by Swayam course?

The last date to apply for the course has been mentioned in the course details on the website.

2: What is the fee structure?

The course is free of cost. Candidates registering for the end term exam need to pay the examination Basic Real Analysis fees.

3: Can the candidates get the pdf form of the book?

The candidates can download it from the browser. The learning material for Basic Real Analysis certification syllabus does not have the pdf of the books.

4: Who is responsible for conducting the exam?

The exam will be conducted by Swayam as the certification is given by them.

5: What is the minimum qualification needed to register for the course?

There are no qualifications required to register for the course.

6: Are there any financial aids for the candidates?

There are no financial aids involved in the course.

7: When will the sessions for Basic Real Analysis certification benefits be conducted?

The candidates can take the course anytime, depending upon their availability.

8: What is the passing criteria for the exam?

The candidates must score well in order to receive certification. More details regarding the same has been added on the website.

9: For how many weeks will the course continue?

The course will continue for 12 weeks where the candidates will have extensive learning.