Differential Calculus in Several Variables

This is part of a standard course contents in Several Variable Calculus. The idea of the course is to provide students with different backgrounds a common platform to take up further topics in Mathematics, Physics and Engineering.

Introduction to Several Variables and Notion Of distance in Rn.
Countinuity And Compactness.
Countinuity And Connectdness.
Derivatives: Possible Definition.
Matrix Of Linear Transformation.
Examples for Differentiable function.
Sufficient Conditon of differentiability.
Chain rule.
Mean value theorem.
Higher Order Derivatives.
Taylor's Formula.
Maximum and Minimum.
Second derivative test for maximum, minimum and saddle point.
We formalise the second derivative test discussed in Lecture 2 and do examples..
Specialisation to functions of two variables.
Implicit Function Theorem.
Implicit Function Theorem a.
Application of IFT: Lagrange's Multipliers Method.
Application of IFT: Lagrange's Multipliers Method - b.
Application of IFT: Lagrange's Multipliers Method - c.
Application of IFT: Inverse Function Theorem - c.