Lectures related to Analysis I: Derivatives and Limits

Explores algebraic operations for derivatives, including addition, multiplication, and composition of functions on an interval.

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.

Introduces Taylor polynomials for function approximation, starting with linear and quadratic forms and then generalizing to higher orders.

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Explores derivability and function composition with examples.

Explores differentiability in two variables and the chain rule for compositions.