NOC:Differential Calculus in Several Variables (USB)

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Sudipta Dutta

NPTEL Co-ordinating Institute : IIT Kanpur

NPTEL Lecture Count : 21

NPTEL Course Size : 1.5 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

Lecture 1 - Introduction to Several Variables and Notion Of distance in Rn
Lecture 2 - Countinuity And Compactness
Lecture 3 - Countinuity And Connectdness
Lecture 4 - Derivatives: Possible Definition
Lecture 5 - Matrix Of Linear Transformation
Lecture 6 - Examples for Differentiable function
Lecture 7 - Sufficient condition of differentiability
Lecture 8 - Chain Rule
Lecture 9 - Mean Value Theorem
Lecture 10 - Higher Order Derivatives
Lecture 11 - Taylor's Formula
Lecture 12 - Maximum And Minimum
Lecture 13 - Second derivative test for maximum, minimum and saddle point
Lecture 14 - We formalise the second derivative test discussed in Lecture 2 and do examples
Lecture 15 - Specialisation to functions of two variables
Lecture 16 - Implicit Function Theorem
Lecture 17 - Implicit Function Theorem -a
Lecture 18 - Application of IFT: Lagrange's Multipliers Method
Lecture 19 - Application of IFT: Lagrange's Multipliers Method - b
Lecture 20 - Application of IFT: Lagrange's Multipliers Method - c
Lecture 21 - Application of IFT: Inverse Function Theorem - c