Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Introductory Course In Real Analysis certification is a foundational program crucial for pure and applied Mathematics and Statistics, serving as a cornerstone in science and engineering. Tailored for undergraduate and postgraduate students, the 12-week curriculum strikes a balance between basic concepts and advanced theory, incorporating real-world examples.
The Introductory Course In Real Analysis certification by Swayam offers application-oriented problems to enhance practical understanding. With widespread support from universities, engineering colleges, IITs, and IISER, the course offers a comprehensive overview, ensuring students develop a robust understanding of Real Analysis for diverse applications in their academic and professional pursuits.
The Highlights
- Core Online Course
- 12 Weeks Duration
- Offered by IIT Kharagpur
Programme Offerings
- Certificate of completion
- Practical Learning
- Hands-on Experience
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kharagpur |
The Introductory Course In Real Analysis certification fees is free. However, if you want a certificate, you must register and take the proctored exam at designated centres, which is optional and comes with a fee of Rs 1000.
Introductory Course In Real Analysis Certification Fee Structure
Particulars | Total Fees |
Introductory Course In Real Analysis (exam) | Rs 1000/- |
Eligibility Criteria
Certification Qualifying Details
To receive the Introductory Course In Real Analysis certification by Swayam, you need a minimum average assignment score of 10/25 and an exam score of 30/75.
What you will learn
After completing the Introductory Course In Real Analysis certification syllabus, you will acquire a comprehensive understanding of fundamental concepts that form the backbone of pure and applied Mathematics and Statistics. You will also gain a strong foundation in the principles of Real Analysis.
Upon completion of the Introductory Course In Real Analysis training, you will gain a solid grasp of Real Analysis, empowering you to confidently apply your knowledge to both theoretical and practical scenarios in your academic and professional journey. You will also develop practical skills that are applicable across various scientific and engineering disciplines.
Who it is for
The Introductory Course In Real Analysis is suitable for individuals seeking a foundational understanding of Real Analysis. This course is also beneficial for:
Admission Details
Follow these steps to join the Introductory Course In Real Analysis classes:
Step 1: Browse the URL below:
https://onlinecourses.nptel.ac.in/noc23_ma85/preview
Step 2: Click on the “Sign-in/ Register” button
Step 3: Fill out the necessary details and submit the form
The Syllabus
- Countable & uncountable sets
- Concepts of Metric Space
- Open ball, closed ball, limit point of a set
- Some theorems on Open & closed set
- Ordered set, least upper bound, greatest lower bound
- Compact set & some properties of Compact set
- Heine Borel Theorem
- Weierstrass Theorem, connected set
- Cantor Set & its properties
- Dense set & derived set
- Limit of sequences of real numbers & Monotone sequence
- Some important limits of sequences
- Ratio tests, Cauchy theorems on limits of sequence of real numbers
- Fundamental theorems on limit
- Some results on limit & Bolzano-Weierstrass Theorem
- Criteria for convergent sequence
- Criteria for Divergent sequence
- Cauchy sequence
- Cauchy convergence criteria for sequences
- Infinite series of Real numbers
- Convergence Criteria for series of positive real no.
- Comparison test for series
- Absolutely and Conditional convergent series and Tests
- Ratio & Integral Tests for convergence of series
- Raabe’s test for convergence of series
- Limit of functions & cluster point
- Divergence criteria for limit
- Various properties of limit of functions
- Left & Right hand limits for functions
- Limit of functions at infinity
- Continuity functions (Cauchy‘s definition)
- Continuity functions (Heine‘s definition)
- Properties of continuous functions
- Boundedness Theorem and Max-Min theorem
- Location of root and Bolzano’s theorem
- Uniform continuity & related theorems
- Absolute continuity& related theorems
- Types of discontinuities & Continuity in a Metric Space
- Types of discontinuities & Continuity in a Metric Space
- Relation between continuity & compact sets
- Differentiability of real valued functions
- Local Max. – Min. Cauchy’s and Lagrange’s Mean value theorem
- Rolle’s Mean value theorems & Applications
- Applications of Derivatives
- Application of MVT & Darboux’s theorem
- L’Hospital Rule (1 lecture)
- Taylor’s Theorem
- Riemann/Riemann Steiltjes Integral
- Riemann/Riemann Steiltjes Integral
- Existence of Riemann Stieltjes Integral
- Riemann Stieltjes Integrable functions
- Properties of Riemann Stieltjes Integral
- Various results of Riemann Stieltjes Integral using step function
- Some more Results on Riemann Stieltjes Integral
Evaluation process
The Introductory Course In Real Analysis certification offers an optional exam. Your final score is determined by averaging the best 8 out of 12 assignments (25%) and your proctored exam score (75%).
IIT Kharagpur Frequently Asked Questions (FAQ's)
The course spans 12 weeks, providing a comprehensive overview of Real Analysis concepts over this period.
Yes, the course is designed to cater to the needs of both undergraduate and postgraduate students in science and engineering disciplines.
The course enjoys support from various educational institutions, including universities, engineering colleges, IITs, and IISER, enhancing its industry relevance.
You will acquire foundational knowledge in Real Analysis, covering fundamental concepts, advanced theoretical treatments, and practical problem-solving skills applicable in diverse scientific and engineering contexts.
Upon successful completion, you will earn 3 credit points, contributing to your academic progress and recognition of your proficiency in Real Analysis.