Theoretical Study of Elliptic Partial Differential Equations

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Page 3 of 4

Covers harmonic functions, Laplacian operator, Dirichlet and Robin problems, and sub-harmonic functions in Partial Differential Equations.

Explores elliptic PDEs, weak solutions, regularity, and strong solutions, with a focus on classical solutions and proof techniques.

Introduces the concept of transfer function in dynamic systems analysis.

Covers the basics of Partial Differential Equations, including well-posedness, operators, and classification of physical PDEs.

Explores integration by parts in Sobolev spaces and the Poincaré inequality in

W^{1,p}_0

with applications in PDEs.

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

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Explores characteristic curves and solutions in partial differential equations, emphasizing uniqueness and existence in various scenarios.

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Explores the evolution of PDEs, focusing on heat and wave equations in 1D, uniqueness of solutions, and the d'Alembert formula.