Lectures related to Ordinary Differential Equations: Definitions and Solutions

Equations: Degree and Solutions

Explores polynomial equations, their degree, solutions, and domain definition.

Definitions and Notations

Covers the definitions and notations related to functions.

Linear Algebra: Surjections

Explores surjections in linear algebra, demonstrating their importance in mapping elements between sets.

Quadrature: Digital Integration

Explains quadrature formulas for digital integration and achieving accurate results.

Development Limit: Order 1 and 2

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

General Manifolds: A First Look

Introduces d-dimensional charts on manifolds and the concept of an atlas.

Integral Closures: Eisenstein Primes

Covers integral closures, focusing on Eisenstein primes and their properties.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Quadratic Approximation: Example

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

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Linear Algebra: Abstract Concepts

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

Mechanics of Rotational Motion

Covers the mechanics of rotational motion, including moments of inertia and energy conservation.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Interpolation de degré 2 par intervalles

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

Minimal Polynomials: Uniqueness and Division

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Properties of Functions

Covers the properties of functions, including symmetry, continuity, and limits.

Algebraic Geometry

Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.