If you're self-studying or taking a advanced calculus / analysis-heavy multivariable course, you know Apostol Vol. 2 is a beast. The problems are brilliant but brutal – especially the linear algebra chapters and the vector calculus proofs.
✓ Verify your epsilon-delta choices. ✓ Check if your chosen parameterization for a surface integral matches the manual’s (often multiple are correct). ✓ Catch sign errors in curl/divergence calculations.
Worth hunting down a PDF (if out of print for your edition) or borrowing from a math department library. But remember – Apostol designed the book so you struggle productively. The manual is a flashlight, not a bulldozer.