# InfoCoBuild

## Introductory Course in Real Analysis

Introductory Course in Real Analysis. Instructor: Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur. This is a basic course in Real Analysis which is a back bone of any course on pure and applied Mathematics and Statistics. This is a very useful course for any branch of science and engineering. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and application oriented problems. (from nptel.ac.in)

 Lecture 61 - Applications of Derivatives

Go to the Course Home or watch other lectures:

 Lecture 01 - Countable and Uncountable Sets Lecture 02 - Properties of Countable and Uncountable Sets Lecture 03 - Examples of Countable and Uncountable Sets Lecture 04 - Concepts of Metric Space Lecture 05 - Open Ball, Closed Ball, Limit Point of a Set Lecture 06 - Tutorial I Lecture 07 - Some Theorems on Open and Closed Sets Lecture 08 - Ordered Set, Least Upper Bound, Greatest Lower Bound of a Set Lecture 09 - Ordered Set, Least Upper Bound, Greatest Lower Bound of a Set (cont.) Lecture 10 - Compact Set Lecture 11 - Properties of Compact Sets Lecture 12 - Tutorial II Lecture 13 - Heine-Borel Theorem Lecture 14 - Weierstrass Theorem Lecture 15 - Cantor Set and its Properties Lecture 16 - Derived Set and Dense Set Lecture 17 - Limit of a Sequence, Monotone Sequence Lecture 18 - Tutorial III Lecture 19 - Some Important Limits of Sequences Lecture 20 - Ratio Test, Cauchy's Theorems on Limits of Sequences of Real Numbers Lecture 21 - Fundamental Theorems on Limits Lecture 22 - Some Results on Limits and Bolzano-Weierstrass Theorem Lecture 23 - Criteria for Convergent Sequences Lecture 24 - Tutorial IV Lecture 25 - Criteria for Divergent Sequence Lecture 26 - Cauchy Sequence Lecture 27 - Cauchy Convergence Criteria for Sequences Lecture 28 - Infinite Series of Real Numbers Lecture 29 - Convergence Criteria for Series of Positive Real Numbers Lecture 30 - Tutorial V Lecture 31 - Comparison Test for Series Lecture 32 - Absolutely and Conditionally Convergent Series Lecture 33 - Rearrangement Theorem and Test for Convergence of Series Lecture 34 - Ratio and Integral Test for Convergence of Series Lecture 35 - Raabe's Test for Convergence of Series Lecture 36 - Tutorial VI Lecture 37 - Limit of Functions and Cluster Point Lecture 38 - Limit of Functions (cont.) Lecture 39 - Divergence Criteria for Limit Lecture 40 - Various Properties of Limit of Functions Lecture 41 - Left and Right Hand Limits for Functions Lecture 42 - Tutorial VII Lecture 43 - Limit of Functions at Infinity Lecture 44 - Continuous Functions (Cauchy's Definition) Lecture 45 - Continuous Functions (Heine's Definition) Lecture 46 - Properties of Continuous Functions Lecture 47 - Properties of Continuous Functions (cont.) Lecture 48 - Tutorial VIII Lecture 49 - Boundedness Theorem and Max-Min Theorem Lecture 50 - Location of Root and Bolzano's Theorem Lecture 51 - Uniform Continuity and Related Theorems Lecture 52 - Absolute Continuity and Related Theorems Lecture 53 - Types of Discontinuities Lecture 54 - Tutorial IX Lecture 55 - Types of Discontinuities (cont.) Lecture 56 - Relation between Continuity and Compact Sets Lecture 57 - Differentiability of Real Valued Functions Lecture 58 - Local Max-Min Cauchy's and Lagrange's Mean Value Theorem Lecture 59 - Rolle's Mean Value Theorems and its Applications Lecture 60 - Tutorial X Lecture 61 - Applications of Derivatives Lecture 62 - Applications of Mean Value Theorem and Darboux's Theorem Lecture 63 - L'Hospital's Rule Lecture 64 - Taylor's Theorem Lecture 65 - Riemann/Riemann-Stieltjes Integral Lecture 66 - Tutorial XI Lecture 67 - Riemann/Riemann-Stieltjes Integral (cont.) Lecture 68 - Existence of Riemann-Stieltjes Integral Lecture 69 - Riemann-Stieltjes Integrable Functions Lecture 70 - Properties of Riemann-Stieltjes Integral Lecture 71 - Various Results of Riemann-Stieltjes Integral using Step Function Lecture 72 - Some More Results on Riemann-Stieltjes Integral Lecture 73 - Tutorial XII