Vector Calculus in 3DCovers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.
Scalar Product and Euclidean SpacesCovers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.
Curves in the Oriented PlaneExplores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Signal RepresentationsCovers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.
Normed SpacesCovers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
