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.
Differential Calculus in Several Variables
Indian Institute of Technology Kanpur and NPTEL via Swayam
This course may be unavailable.
Overview
Syllabus
Week 1: Functions of several variables and examples; continuity; concept of distances in higher dimension; examples; how to define differentiable functions.
Week 2: Directional derivatives as direct generalization from one variable; drawbacks; definition of differentiable functions of several variable; examples; matrix of a linear transformation; Jacobian matrix; recovering directional derivative from derivative; chain rule.
Week 3: Comparison with one variable calculus: version of MVT, higher derivatives and Taylor’s formula; Sufficient condition for equality of mixed derivatives; extremas for real valued function and special case for functions with two variables.
Week 4: Statement of Implicit Function Theorem and Inverse Function Theorem.; deriving Inverse Function Theorem form Implicit Function Theorem; Illustration of Implicit Function Theorem for function of two variables; examples from solutions of ordinary differential equations; proof of Implicit Function Theorem; Lagrange’s Multipliers.
Taught by
S. Dutta
