Crash course on linear algebra and multivariate calculus
Real numbers as complete ordered field. Finite dimensional linear spaces over . 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.