Lectures related to Partial Derivatives: Part 1

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Explores differentiability in functions and the role of gradients in directional derivatives.

Covers the calculation of minimum points and the concept of definite integrals.

Covers the derivative of an integral with parameter-dependent bounds and the gradient.

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Explores higher-order partial derivatives and multi-variables in functions.