Analysis II
This MIT OpenCourseWare course continues from Analysis I into multivariable calculus and global analysis. The first half covers differentiation and integration in several variables, including the inverse and implicit function theorems and change of variables in multiple integrals. The second half develops the theory of differential forms on n-dimensional vector spaces and extends the ideas to manifolds, building toward Stokes' theorem in its general form. Materials include lecture notes, problem sets, and exams with solutions, drawn from MIT's undergraduate mathematics curriculum. The course assumes the rigorous single-variable analysis and proof-writing background built in Analysis I, and it is aimed at students moving from computational calculus toward the abstract structures used in geometry and modern analysis. As with other MIT OCW offerings, the materials are free to use for self-study, with no certificate or instructor interaction attached.