Lectures related to Separation of variables

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

Existence and Uniqueness of Solutions in Differential Equations

Explores the existence and uniqueness of solutions in differential equations, including separable equations and open intervals.

Linear Differential Equations: Order 1

Covers linear differential equations of order 1 and their solutions.

Separable Differential Equations

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

Cauchy Problem: Existence and Uniqueness

Explores the Cauchy problem, focusing on the existence and uniqueness of solutions.

Partial Differential Equations: Classification and Solutions

Covers the classification and solutions of partial differential equations, including Laplace transform and separation of variables techniques.

Solving Separable Equations

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

Differential Equations: Applications and Solutions

Discusses applications and solutions of differential equations in circuit analysis and motion problems.

Ordinary Differential Equations: Separable Variables

Covers ordinary differential equations with separable variables and the conditions for unique solutions in EDOs.

Laplace Equation: Decomposition and Solutions

Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.

Solving Differential Equations: Separable Equations

Covers the method of separation of variables to find the general solution of differential equations.

Stokes first problem: hydrodynamic separation of variables

Explores the application of separation of variables in hydrodynamics and the concept of self-similarity.

Vibratory Mechanics: Continuous Systems

Explores vibratory mechanics in continuous systems, covering separation of variables, boundary conditions, and harmonic solutions.

Differential Equations: Initial Conditions and Solutions

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

Wave Equations Stability

Explores resonant shallow water equations, stability analysis, eigenmodes, and clean modes in waves.

Advanced Analysis II: Resonant Cases and Variable Coefficients

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

Unique Solutions in Differential Equations

Explores unique solutions in differential equations, emphasizing the importance of satisfying key conditions for a single solution.

Ordinary Differential Equations: Definitions and Examples

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

Conceptual Questions on Separation of Variables

Discusses separation of variables in differential equations and concepts of impulse and momentum.

Differential Equations: Solutions and Uniqueness

Explores differentiability, continuity, solutions, and uniqueness in differential equations, emphasizing well-posed problems and real-world applications.