Lectures related to Advanced Analysis: Differential Equations Overview

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Bernoulli Differential Equations: Historical Insights and Solutions

Discusses Bernoulli differential equations, their historical context, and methods for solving them, emphasizing the importance of linear algebra concepts in understanding these equations.

Advanced Analysis II: Cauchy Problem Resolution

Covers the numerical resolution of a Cauchy problem using separation of variables and discusses the conditions for the solution's definition interval.

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.