This is the first course in a two-part sequence on Calculus with Theory, 18.014 and 18.024. The course is taught using the textbook by T. Apostol, "Calculus" Vol. I Second Edition (1967) and the additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus.
18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.
Breiner, Christine. 18.014 Calculus with Theory, Fall 2010. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-014-calculus-with-theory-fall-2010 (Accessed). License: Creative Commons BY-NC-SA