Calculus has practical applications, such as understanding the true meaning of the infinitesimals. (Image concept by Dr. Lachowska.)
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 sets, recitation assignments, and course notes.
» Download the complete contents of this course.
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.