I really enjoy mathematical analysis, particularly the type that involves extensive estimates and calculations, often referred to as "hard" analysis in contrast to "soft" analysis .
I am wondering if there are any books that have a comprehensive collection of materials in this area, especially those focusing on classical (or "hard") analysis methods. For example, books that include techniques for evaluating limits, estimating sums and integrals, and applying various useful inequalities. It would also be great if they cover theorems such as the Silverman–Toeplitz theorem, the Hardy–Littlewood Tauberian theorem, or Watson's Lemma, as these topics are rarely found in standard mathematical analysis texts (at least the ones I am familiar with).
These theorems and techniques usually involve only basic mathematical analysis concepts and avoid delving into overly deep or abstract ideas. However, they are quite useful for estimates and computation, even in more advanced areas of study like Harmonic Analysis or PDEs
Thus, I would like to know if there are any books that cover these less commonly discussed but highly practical "hard" analysis topics. Thank you very much!