Math 39000: Vector Analysis
Supervisor: Sean Cleary
Vector fields, line integrals, and theorems of Green, Stokes, and Gauss.
Prerequisites: grade of C or higher in Math 21300 or placement by the Department. (Part of sequence 20100, 21200, 21300, 39000.) 2 hr./wk.; 2 cr.
No credit for Math 39000 will be given to students who have completed Math 21300 before Fall 2022.
Career: Undergraduate
Category: Regular
Term Offered: Spring
Pre-requisites: C or better in Math 21300 or placement
Hours/Credits: 2 HR/WK; 2 CR
Date Effective: Spring 2026
Course Supervisor: Sean Cleary
Course Description
Vector fields, line integrals, parametric surfaces, surface integrals, and theorems of Green, Stokes, and Gauss.
Syllabus
Text: Calculus Early Transcendentals (9th ed.), Stewart, Clegg, Watson.
Alternative Text: Essential Calculus Early Transcendentals (2nd ed.), Stewart
Topics and Allotted Times
(from Calculus Early Transcendentals (9th ed.), Stewart, Clegg, Watson)
| Section | Topics | Suggested Hours |
|---|---|---|
| 13.1, 12.6 | review of parameterizing curves, examples of surfaces | 1 |
| 16.1, 16.2 | review of vector fields and line integrals | 1 |
| 16.3 , 16.4 | Work Integrals, Conservative Vector Fields, Green's Theorem | 2 |
| 16.5 | Curl and Divergence (vector forms of Green's Theorem) | 2 |
| 16.6 | Surfaces and surface area | 4 |
| 16.7 | Surface integrals | 4 |
| 16.8 | Stokes' Theorem | 4 |
| 16.9 | Divergence Theorem | 4 |
| 16.10 | Unified Theory | 2 |
| 24 |
Course Learning Outcomes
After taking this course, the student should be able to:
- Model spatial problems with curves and surfaces in space. a, b, c
- State and apply Green's theorem. a, b, e1, e2
- Describe surfaces parametrically and find surface areas. a,b,e
- Set up and evaluate surface integrals, including flux integrals a, b, e1, e2
- State and apply Stokes' Theorem. a, b, e1, e2
- State and apply the Divergence Theorem. a, b, e1, e2
Course Assessment Tools
- Term average, based mostly on in-class examinations: 60% of grade.
- Comprehensive written final exam: 40% of grade.
Departmental Learning Outcomes
The mathematics department, in its varied courses, aims to teach students to:
a. Perform numeric and symbolic
computations.
b. Construct and apply symbolic and graphical
representations of functions.
c. Model real-life problems mathematically.
d. Use technology appropriately to analyze mathematical
problems.
e. State (e1) and apply (e2) mathematical definitions and
theorems.
f. Prove fundamental theorems.
g. Construct and present (generally in writing, but
occasionally orally) a rigorous mathematical argument.
Sections
For Spring 2026, the following sections are being offered:
| Letter | Instructor | Time & Place |
|---|---|---|
| 001 | Sean Cleary | Tu 12:15PM-1:55PM in NAC 1/511E |
