Advanced Calculus II

This is where single-variable calculus gets rebuilt rigorously in n dimensions: you stop computing partial derivatives mechanically and start asking what differentiability actually means when the domain is R^n, why the inverse and implicit function theorems hold, and how integration extends to Jordan regions. Expect weekly problem sets and quizzes built around proofs, plus midterms and a final that lean heavily on written arguments rather than computation. It's the analysis counterpart to MATH 224, and the foundation you'll need before tackling differential geometry, measure theory, or any serious PDE work — Green, Gauss, and Stokes here are the same theorems that resurface throughout the rest of the math major.