Interpolation Theory: Embedding and Completeness

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Related lectures (30)

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Interpolation of a Continuous Function

Explores the interpolation of a continuous function by a polynomial.

Finite Element Interpolation: Clément Operator

Explores finite element interpolation using the Clément operator for non-continuous functions and discusses error estimation.

Lagrange Interpolation

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Interpolation of Degree 1 by Intervals

Explains constructing a continuous interpolating function coinciding with the original function at equidistant points.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Function Approximations

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.