Differential Calculus in Several Variables (Prof. Sudipta Dutta, IIT Kanpur) | Mathematics

Differential Calculus in Several Variables

Differential Calculus in Several Variables. Instructor: Prof. Sudipta Dutta, Department of Mathematics and Statistics, IIT Kanpur. This course provides an introduction to a differential calculus of several variables. Functions of several variables and examples; Continuity; Matrix of linear transformation; How to define differentiable functions; Chain rule; Mean value theorem; Higher order derivatives; Taylor's formula; Maximum and minimum for real valued functions; Implicit function theorem and applications. (from nptel.ac.in)

Introduction to Several Variables

Differential Calculus in Several Variables

Lecture 01 - Introduction to Several Variables and Notion of Distance in Rn

Lecture 02 - Continuity and Compactness

Lecture 03 - Continuity and Connectedness

Lecture 04 - Derivatives: Possible Definition

Lecture 05 - Matrix of Linear Transformation

Directional Derivatives, Chain Rule

Lecture 06 - Examples for Differentiable Function

Lecture 07 - Sufficient Condition of Differentiability

Lecture 08 - Chain Rule

Lecture 09 - Mean Value Theorem

Lecture 10 - Higher Order Derivatives

Taylor's Formula and Maximum/Minimum for Real Valued Functions

Lecture 11 - Taylor's Formula

Lecture 12 - Maximum and Minimum

Lecture 13 - Second Derivative Test for Maximum, Minimum and Saddle Point

Lecture 14 - Practical Test based on Hessian Matrix

Lecture 15 - Specialization to Functions of Two Variables

Implicit Function Theorem and Applications

Lecture 16 - Implicit Function Theorem

Lecture 17 - Implicit Function Theorem (cont.)

Lecture 18 - Application of IFT: Lagrange's Multipliers Method

Lecture 19 - Application of IFT: Lagrange's Multipliers Method 2

Lecture 20 - Application of IFT: Lagrange's Multipliers Method 3

Lecture 21 - Application of IFT: Inverse Function Theorem

References

Differential Calculus in Several Variables
Instructor: Prof. Sudipta Dutta, Department of Mathematics and Statistics, IIT Kanpur. This course provides an introduction to a differential calculus of several variables.