Lectures related to Hermite polynomials

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Interlacing Polynomials

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Analyse 2: Rules of Calculation: Addition

Explores the rules of calculation for Taylor polynomials, simplifying derivative computations and showcasing properties of even and odd functions.

Digital Derivation: Evaluation and Formulas

Explores digital derivation, function evaluation, and polynomial approximations for accurate measurements and evaluations.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Complex Plane and Polynomials

Covers the complex plane, operations, transformations, and complex polynomials.

Bezier Curves: Control Points and Regularity

Explores Bezier curves, emphasizing control points and curve regularity.

Interlacing Families and Ramanujan Graphs

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Casting ODEs into Sturm-Liouville form

Explores casting ODEs into self-adjoint form and the role of boundary conditions in ensuring self-adjointness.

Convergence Criteria: Polynomials Limits

Covers convergence criteria for polynomial limits and the theorem of the two gendarmes, emphasizing the importance of indeterminate forms.

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Polynomials: Theory and Applications

Covers the theory of polynomials, including definitions, properties, and applications.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.