NOC:Differential Calculus in Several Variables


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