Rudin Real and Complex Analysis Ch7
This was fun. The 7th chapter of Rudin’s RC Analysis covers differentiation and has many fun and interesting problems. At the core, many of the concepts were similar to the ones I encountered in math 2230-2240, such as the use the Jacobian (defined differently from Hubbard) and various famous theorems like Change of Variables, the definition of the derivative, and the fundamental theorem of calculus. However, the specificity for defining derivatives (using tools such as nicely shrinking sets and absolute continuity) clear up many of the inconsistencies that arise from Lebesgue integrals.
My favorite question was probably question 11 simply because it relied heavily on tools developed in the Hilbert Space chapter. My full solutions can be found below: