# 18.024 Calculus with Theory II

### Spring 2003

#### 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 sets, recitation 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.

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.*