Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.
Explores embedding in function spaces, including elliptic equations, Hölder inequality, Lorentz space, and Hardy-Young inequality.
Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.
Explores interpolation of regular functions, error analysis, convergence, and Chebyshev polynomials.
Explores convection-diffusion equations, focusing on Poincare constant, interpolation error, singular perturbations, and boundary conditions.
