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Basic Calculus for Engineers, Scientists and Economists

Basic Calculus for Engineers, Scientists and Economists. Instructor: Dr. Joydeep Dutta, Department of Humanities and Social Sciences, IIT Kanpur. This course in basic calculus intends to equip the engineering and science with the mathematical tools that they would primarily require for their studies. The emphasis is on understanding the concepts through examples and exercises. There will be on detailed proof of results unless it is very simple. (from nptel.ac.in)

Lecture 04 - Sequences 2

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Numbers, Functions, Sequences, and Limits of Functions

Lecture 01 - Numbers

Lecture 02 - Functions

Lecture 03 - Sequences 1

Lecture 04 - Sequences 2

Lecture 05 - Limits and Continuity 1

Lecture 06 - Limits and Continuity 2

Continuity, Derivative, Maxima and Minima, and Taylor's Expansion

Lecture 07 - Limits and Continuity 3

Lecture 08 - Derivative 1

Lecture 09 - Derivative 2

Lecture 10 - Maxima and Minima

Lecture 11 - Mean-Value Theorem and Taylor's Expansion 1

Lecture 12 - Mean-Value Theorem and Taylor's Expansion 2

Integration of Real Functions

Lecture 13 - Integration 1

Lecture 14 - Integration 2

Lecture 15 - Integration by Parts

Lecture 16 - Definite Integral

Lecture 17 - Riemann Integration 1

Lecture 18 - Riemann Integration 2

Function of Two Variables, Continuity and Differentiability, Lagrange Multiplier Rule

Lecture 19 - Functions of Two or More Variables

Lecture 20 - Limits and Continuity of Functions of Two Variables

Lecture 21 - Differentiation of Functions of Two Variables 1

Lecture 22 - Differentiation of Functions of Two Variables 2

Lecture 23 - Unconstrained Minimization of Functions of Two Variables

Lecture 24 - Constrained Minimization and Lagrange Multiplier Rules

Infinite Series and Multiple Integrals

Lecture 25 - Infinite Series 1

Lecture 26 - Infinite Series 2

Lecture 27 - Infinite Series 3

Lecture 28 - Multiple Integrals 1

Lecture 29 - Multiple Integrals 2

Lecture 30 - Multiple Integrals 3