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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.