# InfoCoBuild

## 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.