# Sergei Yakovenko's blog: on Math and Teaching

## Crash course on linear algebra and multivariate calculus

Real numbers as complete ordered field. Finite dimensional linear spaces over $\mathbb R$. Linear maps. Linear functionals, the dual space. Linear operators (self-maps of linear space), invertibility via determinant. Affine maps, affine spaces.

Polynomial nonlinear maps and functions, re-expansion as a tool to construct linear (affine) approximation. Differential. Differentiability of maps, smoothness of functions.

Inverse function theorem.

Vector fields, parameterized curves, differential equations.

The first set of notes is available here here.