Separation of Variables: Spatial Problems

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Explores power series solutions in quantum mechanics for differential equations and energy quantization.

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

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

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

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Explores integrating loads to deform beams, emphasizing boundary conditions and practical applications in stress analysis.

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Covers the numerical resolution of groundwater flows using finite elements and emphasizes the importance of spatial and temporal discretization.

Covers the fixed energy propagator, including its analytic structure and examples of free particle and barrier penetration.