First part is devoted to
Linear Algebra:
    R³ (vectors, dot product, cross product, scalar triple product, lines and planes, distance formulae (point to a plane?) systems of linear equations, matrices for them solution by row-reduction matrix inversion by row-reduction determinants, det nonzero iff invertible (and other results like this)
Diagonalisation of 3 x 3 symmetric matrices, orthogonal diagonalisation also
Notion of a linear operator on a general vector spaces as an introduction to ODEs

and ODEs:
    1st order linear, Bernoulli eqn (y^n on right, reducible to linear via substitution u = y^{1-n}) 2nd order linear. Idea of particular solution + general solution of the homogeneous equation. Constant coefficient homogeneous cases (real or complex roots, repeated roots). Method of "undertermined coefficients" for finding particular solution.