Mathematics 14

Honors Vector Calculus

Disclaimer Textbook Lectures Instructor Honor Principle
Description Exams Homework Grades Special Needs


Some of the information on this page is tentative and is subject to change. Contact the instructor if you have questions regarding the course or the contents of this page.

More information on the course can be found on the course's Blackboard page.


Mathematics 14 is a course in vector calculus. Prerequisites are Mathematics 9 or equivalent. The course assumes knowledge of representations of lines in two and three space, representations of planes in three space, dot and cross products, partial derivatives, directional derivatives and the chain rule. These concepts will be reviewed briefly as they arise.

We will begin the course with a discussion of the geometry of n-dimensional space and an elementary introduction to linear transformations and matrices. Then we will take up limits, continuity, and differentiability of functions from m-dimensional space to n-dimensional space. We will cover the general chain rule and its applications.

Armed with these concepts we will begin the study of vector fields and curves in space. We will introduce line integrals which are intimately connected with the physical concept of work. This will naturally lead us to the concept of a conservative field and path independence for line integrals.

We will then take up multiple integrals, change of variable in multiple integrals and coordinate systems such as spherical and cylindrical coordinates. We will relate these integrals to various concepts such as volume, mass, charge and probability.

We will close the course with a discussion of surfaces in space. We will discuss surface integrals and their relationship to multiple integrals, including the beautiful theorems of Stokes and Gauss and their applications.


Vector Calculus (fifth edition) by Jerrold Marsden and Anthony Tromba


Period 11
Monday, Wednesday, Friday 11:15 - 12:20
X-Hour Tuesday 12:00 - 12:50
Room: Bradley 103

We may use the Tuesday X-hour on special occasions. Please keep the time available.


François G. Dorais
Office 1R Bradley Hall (in the basement)
Office hours Tuesday an Thursdsay 1pm to 2pm
Personal Home Page


There will be two midterm examinations and a final examination. The exams are tentatively scheduled as follows:

Midterm Exam 1 Date:
Tuesday, January 31
12:00 to 12:50
Bradley 103
Midterm Exam 2 Date:
Tuesday, February 28
12:00 to 12:50
Bradley 103
Final Exam Date:
Saturday, March 11
8:00 to 11:00
Bradley 103

Exams must be taken at the scheduled time. If you have a conflict with one of the two midterms exam, contact the instructor as soon as possible (no later than two weeks before the scheduled exam time) to make alternate arrangements. The final exam will only be given at the scheduled time.



The course grade will be based upon the scores on the two midterm exams, weekly homework, and the final exam as follows:

Midterm Exam 1 100 points
Midterm Exam 2 100 points
Homework 50 points
Final Exam 150 points
Total 400 points

Honor Principle

Special Needs

Students with special needs who plan on taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see their instructor as soon as possible. Also, they should contact the Academic Skills Center for additional services.

Last updated on March 9, 2006 by Francois G. Dorais