Pittaa21/dispensaAnalisi1 ? reverse-engineered prompt

Build me a clean LaTeX study handout for Analisi 1, in Italian, starting from the existing main.tex. I want it to look like a polished university notes document, with a clear title, sections, subsections, definitions, theorems, proofs, formulas, and worked examples where useful.

Please make the layout easy to read and print, with consistent formatting for equations and a nice table of contents. If there are any obvious compile issues or messy parts in the source, fix them so the PDF builds cleanly. Keep the content focused on the main topics of a first analysis course, and make the document feel organized and complete rather than like rough lecture notes.

If you need to check current LaTeX package advice or best practices, look them up online.