Math 13: Multivariable Calculus

Spring 2011

Turbulence on a Polar Beta-plane (image due to Y. D. Afanasyev & J. Wells)

Look here for more pictures and brief explanations



Solutions to midterms 1 and 2 can be found below.

  Section 01 Section 02
Instructor Craig Sutton Andrew Yang
Lectures MWF 12:30-1:35 (105 Kemeny) MWF 12:30-1:35 (108 Kemeny)
X-Hour Th 1-1:50 (105 Kemeny) Th 1-1:50 (108 Kemeny)
Office Hours Mon 2:30-3:30, Th. 9:30-11:00 (also by appointment) MWF 3:30-4:30 (also by appointment)
Office 321 Kemeny Hall 316 Kemeny Hall
E-mail Craig.J.Sutton AT You Know Where Andrew.Yang AT You Know Where
Phone 603-646-1059 603-646-2960
Syllabus, Announcements, etc.





Tutorials (with Zebediah Engberg) Sun., Tues. & Thurs. 7-9PM (105 Kemeny Hall) Sun., Tues. & Thur. 7-9PM (105 Kemeny Hall)


Course Description: In this sequel to Math 8 we will see how ideas from single-variable calculus can be extended to functions of several variables. As the course progresses we will see that many of the ideas in this course have interesting physical and geometric interpretations.

Topics will include some of the following

  • Review of Concepts from Math 8
  • Double & Triple Integrals (in Euclidean Space)
  • Line Integrals
  • Surface Integrals
  • Vector Fields
  • The Theorems of Gauss, Green and Stokes
  • Vector spaces over arbitrary fields

Prerequisites: Math 8 plus a strong interest in mathematical ideas and their applications.

Textbook: Calculus (Sixth Edition), James Stewart, Thompson 2008. (available at Wheelock Books).

Tentative Syllabus: This syllabus is subject to change, but it should give you a rough idea of the topics we will cover this term. Check blackboard for up-to-date information if you are in Sutton's section and here if you are in Yang's section.



Brief Description

Week 1

14 & 15

Review of concepts from math 8; Introduction to Double Integrals

Week 2


Review of concepts from math 8; Introduction to double integrals


Week 3

16.2 - 16.4

Iterated Double Integrals; Double Integrals over General Regions; Double Integrals in Polar Coordinates


Week 4

16.5 - 16.7

Applications of Double Integrals; Triple Integrals; Triple Integrals in Cylindircal Coordinates


Week 5

16.8 - 17.2

Triple Integrals in Spherical Coordinates; Change of Variables; Vector Fields; Line Integrals

Week 6

17.2 - 17.4

Line integrals; Fundamental Theorem of Line Integrals; Green's Theorem


Week 7

17.4 - 17.7

Green's Theorem; Divergence & Curl; Parametric Surfaces & Surface area; Surface Integrals

Week 8

17.6- 17.9

Parametric Surfaces & Surface Area; Surface Integrals; Stokes' Theorem; The Divergence Theorem

Week 9
17.8- 17.9
Stokes' Theorem; The Divergence Theorem
Week 10
17.8- 17.9
Stokes' Theorem; The Divergence Theorem; Review

Deliverables & (tentative) Grading Guide: The following will comprise the written assignments for this term.

Note: Solutions are not guaranteed to be error-free.

Your course grade will probably be computed as follows.

Written HW
Exam 1
Exam 2
Final Exam


Students with disabilities: If you have a disability and require disability related accomodations please speak to me and Ward Newmeyer, Director of Student Accessibility Services, as soon as possible so we can find a remedy.


Last Updated 30 May, 2011