Engineering Mathematics - I

Calculus of several variables

This 60-lecture NPTEL course from IIT Kharagpur extends single-variable calculus to functions of two variables. It opens with Rolle's theorem and the mean value theorems, then uses them to handle indeterminate forms and Taylor series before reaching multivariable limits.

Where the lectures go

• Limits, evaluation and continuity for functions of two variables.
• Partial derivatives, including higher-order ones.
• Differentiability, worked through in several parts, along with composite and homogeneous functions.

Each step builds on the one before, so the differentiability lectures depend on the limit and continuity material coming earlier.

Who it suits

Engineering students in their first year who need a rigorous treatment of multivariable calculus will find it useful. Anyone reviewing before an exam can use the differentiability lectures as a focused refresher.