Lectures related to Uniformly Elliptic Operators

Numerical Analysis: Stability in ODEs

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

Green's Function: Theory and Applications

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

Quantum Mechanics: Power Series Solutions

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

Numerical Methods: Runge-Kutta Approximation

Covers the Runge-Kutta method for approximating solutions of differential equations.

Vibratory Mechanics: Continuous Systems

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

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.

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.

Beam Deflection: Integrating Loads to Deformation

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

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.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Parametric Continuation of Invariant Solutions

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

Poisson Equation: Uniqueness and Green Function

Discusses the uniqueness of solutions for the Poisson equation and introduces the concept of Green function.

Vibrating Strings: Mathematical Analysis and Fourier Series

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Finite Difference Method: Approximating Derivatives and Equations

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