First Course in Calculus Book

This was an excellent text for self-studying the beginnings of calculus. It makes proofs accessible, and even taught me how to prove concepts that seemed obvious but were easy to forget when not used for a while. Learning how to derive and prove concepts like this is essential for someone who wants to study physics, which is the case for me.

I have reservations for recommending this book for Calculus II and beyond. Seeing second- and third-semester calculus topics listed in the table of contents raised my hopes for learning Calc II and III from Lang. Beginning with Taylor polynomials, however, Lang's calculus skipped explanations, became unnecessarily abstract when explaining relatively simple ideas, and yet did not cover the operations I needed in enough depth. This text was not sufficient for learning the calculus of vectors and volume integration.

If you understand pre-calculus and trigonometry, go with this text to learn derivative and integral calculus. Go elsewhere for series, vectors, and multivariable functions.