Introduction to subject: Advanced Calculus I

Introduction to Function of Several variables

Spherical Neighborhood & Rectangular Neighborhood

Limit of functions of Several Variables

Part-I

Limit of functions of Several Variables

Part-II

Limit of functions of Several Variables

Part-III

Continuity of function of two variables

Partial Derivatives and its Geometrical interpretation

Partial derivatives and its examples

Partial derivatives and continuity

Differentiability for functions of two variables

Sufficient condition for differentiability

Inequality of Mixed Partials

Schwartz's theorem for Mixed Partials

Young's Theorem for equality of mixed Partials

Directional derivative & It's Geometrical interpretation

Differential for Two variables

Chain Rules for Derivatives

Chain Rules for Partial Derivatives

Examples on Chain Rules for Derivatives

Implicit Differentiation

Jacobian

Which variables treated as constant

Homogeneous function

Euler's Theorem on Homogeneous function

Euler's theorem on homogeneous function for n variables

Corollary on Euler’s Theorem for homogeneous function

Corollary based on Euler Theorem for homogeneous function (Part-II)

Examples based on Euler's Theorem for Homogeneous function

Maxima and Minima of Functions of Two variables

Example of Locate all relative extrema and saddle points-I

Example on maxima and minima of the function-II

Example of Maxima and Minima of the function-III