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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kharagpur |
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
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