Multivariable Calculus with Theory
A rigorous continuation of MIT's Calculus with Theory sequence, covering the same territory as standard Multivariable Calculus but built around careful proofs rather than computation alone. Topics include vector algebra and geometry, partial derivatives, multiple integrals, and vector integral calculus, with substantial attention given to linear algebra as the framework underlying the subject. Students work through theorems on differentiability, the inverse and implicit function theorems, Green's, Stokes', and the divergence theorem, developing the reasoning behind each result rather than just applying formulas. Materials on MIT OpenCourseWare include lecture notes, problem sets with solutions, and exams, drawn from an undergraduate course intended for students who already have a proof-based background from Calculus with Theory. There is no instructor interaction or certificate; the course is offered freely for self-study through MIT's OpenCourseWare platform.