Math 12 (Fall 2011): Calculus+

Quick links on this page: News | Introduction | Class coordinates | Instructor information | Exam Schedule | Grading | Homework Policy | Textbook | Course Description | Weekly Schedule

Quick links to other Math 12 webpages: Homework Assignments | Class Notes | Exam review page



Math 12 is a calculus class intended for incoming first-year students who have taken the equivalent of Calculus BC and scored a 5 on the AP exam. We cover the standard curriculum of multivariable calculus; doing this in a trimester versus the usual semester at most universities means the pace of this class will be rather quick.

Math 11 and math 12 more or less cover the same material, but as math 12 is intended for students who would like more of a challenge, certain topics will be covered more in-depth (for example, the intepretation of the derivative as a linear transformation) and homework assignments may be more difficult. All this being said, transferring between the two classes should not be too much of a problem.

Class Coordinates

Room: Kemeny 007
Time: 1:45pm - 2:50pm, Monday, Wednesday, Friday
X-hour: Thursday, 1:00pm - 1:50pm. We may use the X-hour a few times for mandatory classes (if we fall behind schedule or I need to reschedule a class), and some of the X-hour classes will be optional, like review sessions for exams or talks about topics which are related but not essential parts of the course curriculum.

Tutorial room: 312 Silsby
Tutorial times: 7:00pm - 9:00pm, Thursday, Sunday
TA: Sarah Wolff

Instructor information

Name: Andrew Yang
Office: Kemeny 316
Office Hours: Tuesday 2:30pm - 4:00pm, Thursday 1:00pm - 2:20pm.

Examination Schedule

There will be two midterms and a final exam. All exams are closed book and no calculators or computational assistants of any kind.

If you are unable to be at any of these exams, please contact me as soon as possible so we can setup alternate test-taking arrangements.


Your grade in this class will be determined by homework and exams.

There will be two types of homework assignments: Webwork and written assignments. Webwork is an automated computer-based grading system where you get slightly randomized problems, and try to solve them until the computer tells you your answer is correct. We will generally use Webwork for easier questions which are more suited for computer automated grading. These will usually be given out three times a week, and shouldn't take too long to complete (not much more than 60 to 90 minutes, say.)

Written assignments will consist of questions which will usually be more difficult than Webwork assignments. You will need to write down solutions which justify your answers and turn them in.

There will be two midterm exams and a final examination. All exams will be at a specified location and will be closed book.

Each of the above contributes to your final grade in the following fashion:

Your final letter grade is computed using a curve. Exactly what the distribution of letter grades cannot be determined in advance, although it should not stray too far from the way grades were distributed in previous terms.

Homework Policy

Written homework assignments will be posted on this website and will be usually due about a week after they are posted. Late assignments will only be accepted when granted an extension, which must be requested from the instructor several days in advance. In general, extensions will only be granted for health-related reasons or family emergencies. Exceptions may be made for school-related travel.

The homework collaboration policy for this class is more or less in line with other Dartmouth math classes. You are allowed to collaborate with others on homework, but must write your own solutions. A good rule of thumb is that you should never be copying phrases or sentences from anyone else or any source. You may use theorems, lemmas, etc. that we have covered from the textbook, but in general you should not use theorems, lemmas, etc. from sections of the book we have not covered or from external sources. Also, please write down the people you collaborated with and outside sources (namely, anything besides the required textbook) you consulted on your homework assignments.


The required book for this class is Calculus, 7th edition, by James Stewart, ISBN 978-0538497817.

There are many books about calculus. The following are a few books which might be worth consulting:

Course description

Our primary goal in this class is to cover chapter 13 through 16 of the textbook. We begin by quicking thinking about lines and planes in three dimensional space. We then study differential calculus of functions of several variables, which includes topics like vector-valued functions, partial derivatives, directional derivatives, tangent planes, the second derivative test, and Lagrange multipliers. After that we study integral calculus of functions of several variables, which includes topics like multiple integration and coordinate changes. Finally, we apply everything learned earlier to the study of line and surface integrals, and conclude with the three great theorems of the subject, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.

Weekly schedule

This schedule is preliminary and will almost certainly be adjusted over the course of the term.

Week 1: Geometry in \( \mathbb{R}^{3} \)

Week 2: More geometry in \( \mathbb{R}^{3} \), vector-valued functions

Week 3: Vector-valued functions, derivatives of multivariable functions

Week 4: Applications of partial derivatives

Week 5: Lagrange multipliers, the chain rule

Week 6: Double integration

Week 7: Triple integration

Week 8: Line integrals

Week 9: Green's Theorem, curl and divergence, parameteric surfaces

Week 10/11: Surface integrals