Separation of variables

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Related lectures (27)

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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.