Lectures related to Vibrating Strings: Mathematical Analysis and Fourier Series

Laplace Transform: Solving Differential Equations

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.

Poisson Problem: Fourier Transform Approach

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

Green's Function: Theory and Applications

Covers the theory and applications of Green's function in solving differential equations.

Fourier Transform: Derivatives and Laplace Transform

Explores the Fourier transform properties with derivatives and introduces the Laplace transform for signal transformation and solving differential equations.

Vibratory Mechanics: Continuous Systems

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

Fourier Transform and Differential Equations

Discusses the Fourier transform and its application to solving differential equations, focusing on the wave equation and its transformations.

Cauchy Problem: Differential Equations and Initial Conditions

Covers the Cauchy problem, focusing on differential equations and the role of initial conditions in determining unique solutions.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Fourier and Laplace Transforms: Concepts and Applications

Provides an overview of Fourier and Laplace transforms, their properties, and applications in signal analysis.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Structural Mechanics: Beam Bending and Boundary Conditions

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

Numerical Analysis: Stability in ODEs

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

Advanced Analysis II: Cauchy Problem Resolution

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

Finite Differences and Finite Elements: Variational Formulation

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

Transformations and Inversions: Laplace and Fourier

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

Partial Differential Equations: Viscoelastic Materials

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

Analysis IV: Laplace Equation Solutions

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

Laplace Transform: Properties and Applications

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

Quantum Mechanics: Power Series Solutions

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

Finite Element Analysis: Advanced Mechanisms in Engineering

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