Lectures related to Interpolation Theory: Embedding and Completeness

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.

Interpolation: Lagrange polynomial and error analysis

Covers the interpolation of functions using Lagrange polynomials and error analysis, emphasizing the dependence on the function.

Generalized Integrals: Type 2

Covers the integration of limit expansions and continuous functions by pieces.

Properties of Continuous Functions: Maximum and Minimum

Explores the properties of continuous functions, including maximum and minimum values and intermediate values.

The Intermediate Value Theorem

Explains the Intermediate Value Theorem for continuous functions on closed intervals.

Continuous Functions: Definitions and Criteria

Covers the definition and criteria for continuous functions and explores the intermediate value theorem.

Continuous Functions: Definition

Explains the definition of continuous functions and isolated points.

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Bisection Method: Proposition and Demonstration

Covers the bisection method proposition and its demonstration for finding roots.

Analysis II: Abstract Integration

Explores abstract integration of functions and the need for stronger conditions beyond continuity.

Interpolation in Finite Element Spaces

Covers interpolation in finite element spaces and the regularity of solutions in convex domains.