Just like the aim of elementary linear algebra is to understand the relations of linear maps and to convert mappings (matrices) into Jordon canonical forms to simplify their relations to understand them better (at least this is my understanding of the subject), from what I've been learning, mathematical analysis is studied in order to rigorously establish the fundamentals of calculus.
However, while I may (or may not...) understand the objective of the discipline, I am finding significant trouble being able to solve any question (especially evident given my midterms this week), unless they are very basic. I believe this is due to my lack of 1) identifying the methodology to solve the given question, and 2) laying out a proof utilizing said methodology that is mathematically sound and sufficiently rigorous.
Unfortunately, the problem ultimately seems to reside with my lack of understanding. The book I am currently using for my course is Baby Rudin. The included proofs are extremely succinct, leaving a lot to fill between the lines, not helping my case at all.
Are there any supplementary books that I could be looking into to help me study analysis better? What would be some tips for approaching the subject matter, and tackling questions in analysis courses?
Thank you in advance.