Lectures related to Taylor Polynomials: Order 1

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

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

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

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

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

Covers linear approximations up to order 2 and the Hessian matrix.

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.

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

Explores derivatives, Hessians, and Taylor approximations for differentiable functions.

Explores Taylor polynomials, including order, development, limits, and algebraic operations.

Covers the definition of a scalar product on a real vector space and provides examples.