This course is intended to be a simultaneous continuation of multivariable/vector calculus and linear algebra. One of the fundamental concepts from calculus is the local approximation of complicated relationships with linear objects (e.g. tangent lines and tangent planes). In higher dimensions or multivariable settings (which are common in real-world applications), this produces a rich interplay between ideas from multivariable/vector calculus and linear algebra. We will revisit some familiar ideas from vector calculus and linear algebra from a unified perspective of these subjects–a perspective that will also allow us to explore new concepts related to differential geometry. Topics of study may include (but are not limited to) the geometry of Euclidean space and manifolds; limits, continuity, derivatives, Taylor polynomials, and integrals in a multivariable setting; vectors, matrices, linear transformations, vector spaces, eigenvectors, and eigenvalues; differential forms and vector calculus.