Professor Gong Sheng's Concise Calculus: This textbook is the most unique writing structure I have ever seen. After the lecture on limit, we don't discuss derivative, differential and differential properties as in the conventional textbooks, and then discuss indefinite integral ..... but we will talk about definite integral and then differential in the historical development order of calculus and the order that students can accept more easily. What is particularly commendable is that the ε-δ language is specifically described later, and the basic concepts of calculus are strictly logical, which can be used as a higher requirement for engineering students. The book runs through Newton-Leibniz formula, that is, the contradiction transformation relationship and the external differential content in the calculus of multivariate functions, which is the only one in the same textbook in China.
F.M. Fichkingolz's Calculus Course: It is a comprehensive and rich course, and it is the authoritative teaching material and masterpiece of calculus in classical methods.
Introduction to calculus and mathematical analysis by R.Courant: step by step, all-encompassing, with rich examples and applications, but also rigorous. Although this book is easy to get started, the overall depth of this set of books is quite deep.
Zhang Zhusheng's New Theory of Mathematical Analysis: a relatively new textbook of mathematical analysis in China, but it lacks practice.
Lu Ding's Principles of Mathematical Analysis: an authoritative textbook in the world, characterized by clear views and concise words, but not suitable for beginners.
In addition, in recent years, two funny calculus courses, Calculus Slaughter the Dragon and Calculus Sword, have been translated. The former talks about univariate function calculus, while the latter talks about multivariate function calculus. It is quite vivid, popular and humorous. If you have a certain foundation in calculus, it will be easier to read.