Main purpose: For self-learning performance, neither for exam nor degree courses.
Calculus textbook using now[1]: Calculus I, Weinstein&Marsden, UTM, Springer
Question Description: I've been reading book[1] for weeks, 90% of text, 30%-40% of exercises solved. It's not bad, but for the following:
Advantages: (a)Suitably explained for concepts (b)Clear Structure
Disadvantages: (a)Not contain enough theorems (b)Too many exercises in formula-calculation/real application (c)Too little deep/proof exercises (d) Approximately 8000 exercises in total, 300-400/chapter, but 80% is simple-formula-calculation/realistic application.
My Opinion: Will it be more beneficial to start using analysis textbooks now instead of this calculus book ? For 3 reasons:
(1). Most good EU bachelor in maths, they use analysis directly in first semester instead of calculus. (e.g. Bonn University/ETHz)
(2). Since book[1] contains too many exercises of formula-using/real application ones but not deep/proof, if I continue to work with it (solve all exercises/ second time reading), book[1] will still cost several months, I doubt if it's beneficial compared with directly starting analysis.
(3). Will Analysis textbooks(e.g. book[4][5]) also contain needed calculus?(intuition/calculation skills) If it's the case, such analysis books would do both to train modern theory and calculation skills( compute derivatives/integrals which are useful later such as ODE,PDE), then there'd be no need to read calculus any more.
Future Goal: Research in Dynamic System theoretically oriented.
Note: Though [1] is UTM, but it seems engineering-oriented(not theoretical/rigorous-oriented) compared with others within series.
[2]Rose, Elementary Analysis, UTM, Springer.
[3]Serge Lang, A First Course in Calculus/Calculus of Several Variables, UTM, Springer(Even though it's still calculus, but Lang's book is more abstract-oriented)
[4]Zorich, Analysis, Universitext, Springer(As @nbubis said, analysis needs intuition behind, from the content, it seems Zorich's analysis contains many physical problems, will it works for that ?)
[5]Courant, Introduction to Calculus and Analysis I&II, Springer
Desirable answer: Advices, Discussions