Vibrating Strings: Mathematical Analysis and Fourier Series

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Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

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

Covers the resolution of a Cauchy problem using the method of variation of constants in differential equations.

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Explores the application of PDEs in viscoelastic materials and materials science.

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

Covers the properties and applications of the Laplace transform in solving differential equations.

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

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.