Lectures related to Cauchy Problem: Existence and Uniqueness

Ordinary Differential Equations: Introduction

Introduces ordinary differential equations, discussing definitions, examples, solutions, and the transition from implicit to explicit forms.

Cauchy Problem: General Solution

Covers the general solution of Cauchy problems in first-order differential equations.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

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 validity.

Differential Equations: Initial Conditions and Solutions

Discusses ordinary differential equations, focusing on initial conditions and methods for finding solutions.

Separable Differential Equations

Explores the theorem of existence and uniqueness for differential equations and the method to find the general solution.

Separation of Variables: Spatial Problems

Explores the method of separation of variables for solving spatial problems with second-order ODEs, emphasizing the significance of boundary conditions.

Differential Equations: Existence and Uniqueness Theorems

Covers the existence and uniqueness of solutions for differential equations.

Differential Equations: Existence and Uniqueness

Covers differential equations with separated variables, existence and uniqueness of a solution with a given initial condition.

Fluid Friction Forces

Explores fluid friction forces, including laminar and turbulent flow, viscosity, and terminal velocity calculation.

Ordinary Differential Equations: Definitions and Examples

Covers ordinary differential equations, including orders, solutions, and separable equations, with a focus on examples and general solutions.

General Solutions of Differential Equations

Covers finding general solutions for differential equations using various methods and concepts, including explicit and implicit forms, integration constants, and intermediate hypotheses.

Solving Separable Equations

Covers the method for solving separable equations and linear homogeneous equations, as well as a simple population growth model.

Evolution of Partial Differential Equations

Explores the evolution of PDEs, focusing on heat and wave equations in 1D, uniqueness of solutions, and the d'Alembert formula.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Differential Equations: Initial Conditions and Solutions

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

Canonical Transforms: Hamilton-Jacobi Equation

Explores canonical transforms and the Hamilton-Jacobi equation, emphasizing explicit solutions and initial conditions.

Analysis IV: Laplace Equation Solutions

Explores Laplace equation solutions through separation of variables and general solution writing for complex problems.

Linear Differential Equations: Homogeneous and Separable

Covers linear differential equations of order 1, focusing on homogeneous and separable equations.

Advanced Analysis II: Resonant Cases and Variable Coefficients

Covers resonant cases, variable coefficients, and methods for solving differential equations.