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.