Introduction to scalars and vectors: operations with scalars and vectors, scalar product, vector product, vector equations, indices, Einstein summation convention, kronecker delta, Levi-Civita symbol.

Introduction to functions: types, continuity, limits, derivatives, integrals, integration methods, taylor series, remainder.

Functions with scalar input and vector output: curves, tangent, normal, velocity, acceleration, curvature, torsion. Frenet-Serret basis and kinematics.

Functions with vector input and scalar output: extrema, contours, gradient, directional derivative, tangent space.

Multiple integrals

Functions with vector input and vector output: conservative fields, rotational fields, divergence, curl, line integral, surface integral, Stokes and Gauss

Differential equations: damped harmonic oscillator with driving