Lectures related to Advanced Analysis 2: Linear Differential of Functions

Solutions of Differential Equations

Explores finding solutions of differential equations, emphasizing maximal solutions and general solutions with constants.

Differential Equations: Initial Conditions and Solutions

Covers the solution of differential equations with initial conditions and limit analysis.

Partial Derivatives and Derivability

Explains partial and directional derivatives, and functions' derivability.

Functions and Derivatives

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Theorem of Generalized Mean Value: Study of Functions

Explores the conditions for continuity and differentiability of functions on a closed interval.

Gradient and Taylor Formula

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