Math 350, Fall 2010

Syllabus and Information

(pdf version here)


Chris Kottke
#303 Kassar-Gould House
ckottke AT

Course website

Office hours

Mon. 11am-12pm, Wed. 1-2pm, Thu. 11am-12pm, or by appointment.


Vector Calculus, 5th Edition by Marsden and Tromba



This class is about calculus in more than one dimension. We'll study functions of several variables, with scalar and vector values; the two main operations of calculus (differentiation and integration) on such functions; and the big theorems which relate these: the Fundamental Theorem of Calculus for Line Integrals, Green's Theorem, The Divergence Theorem and Stokes' Theorem.

Vector calculus is a neat subject, harmoniously combining the analytical tools of calculus with the geometry of curves and surfaces in space. It has numerous applications in economics, engineering, and especially physics, where it is the very language of the theory of electricity and magnetism and fluid dynamics.

This is an honors course, which means the material will be covered in more depth and with a slightly more theoretical foundation than in Math 18 or 20. It also means you will be expected to spend more time studying the material and working on homework assignments. Challenging problems will be fair game on homework and exams!


A solid understanding of single variable calculus, including limits, continuity, differentiation, integration, the Fundamental Theorem of Calculus, etc. We will develop all the necessary linear algebra (vectors, matrices, determinants) as we go along, so no prior exposure to this is required, though those who do have experience in this area will find it helpful. Motivation to work hard is probably also a good prerequisite!


Your final grade will depend on weekly homework scores and exams (2 midterms and 1 final), weighted as follows:


The final will consist of roughly 50% cumulative material, and 50% new material (see the timeline below). Your lowest 2 homework scores will dropped. You are allowed (indeed, encouraged) to work on the homework assignments together, but must write up your answers separately. You will also need to cite your collaborators and any sources consulted on your homework assignments.

Tentative timeline

The course will consist of three units, roughly as follows (we'll pick up bits from Chapter 1 as we need them):

Differentiation. Functions of several variables, partial derivatives, the derivative as a linear approximation, curves and velocity, the gradient and directional derivatives, higher derivatives and Taylor's theorem, maxima and minima with/without constraints and Lagrange multipliers, implicit/inverse function theorems. Ch. 2-39/1-9/29Friday October 1
Integration. Double and triple iterated integrals, integrals over regions bounded by graphs, the change of variables formula and special coordinates (polar, cylindrical, spherical), arc length, vector fields, line integrals and work, the fundamental theorem of calculus for line integrals and conservative vector fields, parametrized surfaces, surface integrals and flux. Ch. 5,6,4.1-4.3, 710/4-11/3Friday November 5
Main Theorems of Vector Calculus. Divergence and curl of vector fields, Green's Theorem in 2D (flux form and work form), the Divergence Theorem in 3D, Stokes' Theorem in 3D, the relationships between these, applications. Ch. 4.4, 811/8-12/3Final Exam December 10

Tips for success