Lectures related to Quantum Mechanics: Power Series Solutions

Sturm-Liouville Problem: Legendre Equation

Explores the Sturm-Liouville problem linked to the Legendre equation and its significance in physics.

Quantum Chemistry: Energy Quantization and Eigenvalues

Covers the quantization of energy levels in quantum chemistry.

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

Separation of Variables

Explores the concept of separation of variables in quantum mechanics and its application in solving differential equations.

Fixed Energy Propagator: Density and Examples

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

Poisson Problem: Fourier Transform Approach

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

Heterogeneous Reactions: Transport Effects

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.

Beam Deflection: Integrating Loads to Deformation

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

Separation of Variables: Spatial Problems

Explores the method of separation of variables for solving spatial problems with second-order ODEs, emphasizing the significance of boundary conditions.

Numerical Groundwater Flow Resolution: Finite Elements

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

Law of Hooke Applications: Spring Problems

Explores the application of the law of Hooke to spring problems and solving equations of motion for block-spring systems.

Inverse Monotonicity: Stability and Convergence

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

Finite Difference Method: Approximating Derivatives and Equations

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

Numerical Analysis: Stability in ODEs

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

Boundary Conditions and Basis Decomposition

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

Analysis IV: Laplace Equation Solutions

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

Parametric Continuation of Invariant Solutions

Explores parametric continuation of invariant solutions and influence matrix in differential equations.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Partial Differential Equations: Viscoelastic Materials

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

Diffusion Equations in Spherical Coordinates

Explores solving diffusion equations in steady state conditions for concentric spheres with fixed concentration and flux, emphasizing the importance of linearity and homogeneity.