Lectures related to Bernstein polynomial

Bezier Curves: Basics and Properties

Covers the basics of Bezier curves and introduces Bernstein polynomials.

Polynomial Functions: Integration and Coefficients

Covers the integration of polynomial functions and determining coefficients using linear algebra.

Quantum Field Theory: Spectral Density

Covers the concept of spectral density in Quantum Field Theory.

Fourier Transform and Residue Calculus

Explores Fourier transform calculation and residue calculus in mathematical analysis.

Bezier Curves II

Covers Bezier curves, de Casteljau Algorithm, properties, derivatives, splines, and end-points.

Polynomial, Exponential, Logarithmic Functions

Covers polynomial, exponential, and logarithmic functions, differentiability, compositions, and limits.

Polynomial Division: Terms and Factors

Covers polynomial division, terms, factors, and integration methods.

Interpolation de degré 2 par intervalles

Explores constructing a piecewise continuous function using degree 2 interpolation by intervals.

Integration of Entire Series

Covers the integration of entire series term by term, demonstrating the convergence radius and providing examples.

Monodromy Conjecture

Explores the Monodromy Conjecture, discussing its origins, implications, and conditions for convergence in mathematical contexts.

Splines: Least-Squares Method

Explores splines, emphasizing the least-squares method for interpolating splines and demonstrating its application using MATLAB.

Important Examples: Operations and Multiplication

Covers important examples related to operations and multiplication in real vector spaces.

Theorem 1.1: Interpolation and Equidistant Points

Covers the concept of interpolation using equidistant points and Theorem 1.1.

Mathematics: Basics and Applications

Covers the basics of mathematics and its applications in architecture.

Polynomial Equations

Covers the topic of polynomial equations and methods to solve them.

Bezier Curves: Fundamentals and Applications

Explores the fundamentals and applications of Bezier curves, focusing on their construction, properties, and practical uses in design and modeling.

System Equivalence

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Complexity: Approximation-Estimation Trade-off

Explores the control of complexity in hypothesis spaces and the trade-off between approximation and estimation in risk decomposition.

Quadrature: Digital Integration

Explains quadrature formulas for digital integration and achieving accurate results.

Quadratic Approximation: Example

Covers finding the best quadratic approximation for a given function in a continuous space.