Stage 1 Introductory Calculus

Introductory Calculus:
As you may have seen, calculus is crucial. It is not only important in advanced mathematics but also can be applied to many other fields. If you learn first year calculus in a college, your suggested text is probably J. Stewart's Calculus. This is a standard modern text, it is colorful and quite detailed. If you prefer it, that's fine. This book is thick, you would like to leave a few section, say vector calculus, double, triple, line and surface integrals, to the next stage. I would suggest a few non-standard texts and notes.

The first thing we need to fix up is the definition of limit, learn the epsilon and delta proof. Other key concepts are the mean value theorem, fundamental theorem of calculus, logarithm and exponential functions, inverse trigonometric functions, hyperbolic functions, basic differential equations, limit of sequences, indeterminate form, infinite series, basic idea of several variables.