Ensure you understand transformations and basis vectors.

Linear and nonlinear functional analysis form complementary pillars of modern analysis. Linear theory provides precise structural and spectral tools; nonlinear theory supplies flexible topological and variational methods for complex phenomena. Together they underpin much of contemporary PDE theory, applied mathematics, and mathematical physics.

If you are looking for open-source lecture notes or broader series on this topic, these are excellent alternatives:

The study of is a journey into the heart of modern mathematics. Whether you are looking for a PDF to supplement your graduate studies or to solve a specific engineering problem, understanding these functional spaces and operators opens doors to the most advanced tools in science.