Free Online Course: Differential Calculus in Several Variables provided by Swayam is a comprehensive online course, which lasts for 4 weeks long, 2-3 hours a week. The course is taught in English and is free of charge. Differential Calculus in Several Variables is taught by S. Dutta.
4 weeks long, 2-3 hours a week
Finished
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.
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.
