Lectures related to Advanced Analysis 2: Linear Differential of Functions

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

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Explores solutions of differential equations and properties of functions.

Covers the calculation of partial derivatives of order 3 and the concept of differentiability in functions.

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

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

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Covers the concept of partial derivatives and their applications in mathematical analysis.

Covers differentiability theorems and methods to check for differentiability in functions.

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

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

Explores solutions of differential equations and their monotonicity properties.

Explores differentiability, matrices, Jacobian matrix, and derivatives calculation.

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.