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- To accommodate the diverse backgrounds of our entering students, single and multivariable calculus courses have multiple entry points. In all, there are four (core) calculus courses (Math 1, 3, 8, 13) spanning single and multivariable calculus, and two more hybrid courses (9 and 11) which offer variations to the core sequence.
- We shall describe in words and in more detail the content of the aforementioned courses and for whom they are appropriate, but the following diagram will perhaps allow you to focus more quickly on what exactly you want to read:

- For those with no previous calculus
experience:

Math 1: Introduction to Calculus

**Links:**Catalog description Sample Syllabus - For those with
strong precalculus skills or who have seen some
calculus, but not enough to place out of Math 3 (AB
calculus):

Math 3: Calculus

**Links:**Catalog description Detailed Syllabus and videos - For those who have
passed an AB calculus course (e.g., Math 3), but not
a BC calculus course:

Math 8: Calculus of functions of one and several variables

**Links:**Catalog description Detailed Syllabus and videos - For those who have
taken Math 8 at Dartmouth:

Math 13: Calculus of vector-valued Functions

**Links:**Catalog description Detailed Syllabus and videos - For those who have passed both AB and BC calculus and are ready
for multivariable calculus:

Math 9 or 11 or 13: (see Variations on the core sequence below)

Students who have placement credit for both Math 3 and Math 8 via either the Advanced Placement BC exam, or by having passed the department's Math 8 credit exam, have several options to consider if they wish to continue along the calculus track to multivariable calculus.

**The Issue**: A typical AB/BC syllabus is covered (at
Dartmouth) by taking Math 3 and the first half of Math 8. The second
half of Math 8 investigates differential multivariable calculus
— loosely speaking, the general themes of AB calculus, but for
functions of several variables.

**The Options**: The option you choose depends solely
on your interests and your level of confidence in your command of
the material covered in previous calculus courses. Let's repeat that
point: **The choice is entirely yours.**

**Option 1** (Math 11): If you are very confident in
your knowledge of material on the BC syllabus, and are up for a
briskly paced course, then Math 11 (Calculus for students with two
terms of advanced placement credit) would be a good choice for you
(a
typical Math 11 syllabus) . This course covers the material from
the second half of Math 8 on the differential aspects of
multivariable calculus, while also covering the integration theory
of Math 13. At the end of this course, you will have the equivalent
of Math 13, and can take any course for which Math 13 is listed as a
prerequisite. Your next step is most likely a 20's level course,
perhaps linear algebra or differential equations.

**Option 2** (Math 9): A second option is for those who are
confident in their knowledge of the BC syllabus material so do not
want to repeat it, yet want to move forward at a less brisk pace
than offered by Math 11. The course Math 9 (Multivariable
Differential Calculus with Linear Algebra) offers the material from
the second half of Math 8, but enhanced with a brief introduction to
linear algebra so as to better explain how derivatives of functions
of several variables are linear approximations to functions
(a
sample Math 9 syllabus). Following Math 9, the next course in
the calculus sequence would be Math 13.

**Option 3** (Math 13): If you have obtained credit
for Math 3 and 8, and have taken some multivariable calculus in high
school (in particular the topics covered in Dartmouth's Math 8
(check recent Math 8 syllabi )), you will likely
be fine taking Math 13 instead of Math 11. You should confirm this
with the adviser to first-year students.

**Option 4** (Math 8): On the other hand, if you are
tentative about your skills on the later parts of the BC syllabus,
e.g., techniques of integration and infinite series, you could
(even though you officially have credit for it), opt to retake
Math 8 (Calculus of Functions of One and Several Variables). This
is a seldom chosen option, but if you do choose this, the Math 8 AP
credit on your transcript will be replaced by your eventual grade
in the Math 8 course you take here. This option offers a chance to
strengthen areas from the BC syllabus in the first half of the
course, while then advancing to introduce the differential
multivariable calculus (check recent Math 8
syllabi ). Following Math 8, the next course in the
calculus sequence would be Math 13.

Back to the Main Placement Info Page.