18.014 Calculus with Theory I

As taught in: Fall 2002

A cartoon that demonstrates the importance of understanding the infinitestimals.

Calculus has practical applications, such as understanding the true meaning of the infinitesimals. (Image concept by Dr. Lachowska.)

Level:

Undergraduate

Instructors:

Prof. James Munkres

Dr. Anna Lachowska

Course Features

Course Highlights

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. The website features problem setsrecitation assignments, and course notes.

Course Description

18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.

Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions.

Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site.