18.024 Calculus with Theory II

As taught in: Spring 2003

An illustration of a squirrel holding a bagel.  The saddle points are highlighted in red.

How many saddle points can you find on a squirrel? And if he is eating a bagel? (Image concept by Dr. Lachowska.)




Prof. James Munkres

Dr. Anna Lachowska

Course Features

Course Highlights

This is the second 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, Vols. I and II, 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

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.

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