Lectures related to Continuous Functions: Integrability and Examples

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Advanced Analysis: Differential Equations Overview

Provides an overview of differential equations, their properties, and methods for finding solutions through various examples and graphical representations.

Taylor Polynomial: Order 2

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

Local Extrema of Functions

Discusses local extrema of functions in two variables around the point (0,0).

Application to Recurrence Defined Sequences

Covers the application of functions defined by recurrence to sequences and the theorem of the fixed point.

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Optimization Methods: Lagrange Multipliers

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.