Math 112 is a difficult course to design because there are so many 
important topics that one might cover, and one cannot cover them all.
The UCC has heard about wide variations in content of Math 112 during the 
last several semesters, and in a meeting of August 11, 2003 we discussed what 
needs to be in Math 112.  Here is our consensus concerning topics that 
have sometimes appeared and sometimes have been skipped in recent Math 
112 courses.

1) Differential equations must appear because this is the only place in
the required curriculum that our students encounter the subject. (At least
slope fields and Euler's method, separable equations, and exponential
growth should be covered;  Sebastian Schreiber will propose a Maple lab on
Euler's method that could be added, even though it will not be part of 
the student lab packet.)

2) Sequences and series (at least up to Taylor's theorem with remainder). 
This is the only required course in which majors in the applied track or
teaching track will see this topic.

3) Approximate integration (Cover at least the trapezoid rule with use of
the error estimate. However, there is some nice geometry that helps
explain the relation between the estimates provided by the trapezoid and
midpoint rules in certain circumstances and, time permitting, that would
justify covering both. Simpson's rule is optional.)

4) As you know, Math 112 is a course that awards GER1 credit.  To do that 
it must include numerical calculations, some explanation of why the 
numerical calculations work, and a discussion of applications that would 
be recognized as such to an educated outsider.  We have no problem in 
meeting the first two of these criteria, but we need to be careful not to 
overlook the third. 

5) What, then, should be covered in Math 112?  The following list is based 
on the fourth edition of Stewart's "Calculus with Early Transcendentals" 
and will need to be updated when we move to the fifth edition.

Review Chapter 5 (Introduction to integration). Students should have
seen some of this material (up to 5.5), but that was three months ago
and they need a review at the start of Math 112.  Integration by
substitution is likely to be an area where they are particularly weak.
The section on logarithms and integrals is optional.

Chapter 6 (Applications): Cover areas between curves, volumes of rotation 
by disks and washers, and work problems. Skip cylindrical shells.

Chapter 7 (Integration techniques): Sections 7.1 to 7.5, plus 7.7 
(approximate integration, including some work with error bounds) and 7.8.

Chapter 8 (More applications): Cover arc length (8.1) and hydrostatic 
pressure (in 8.3); skip surface of revolution and center of mass.

Chapter 9 (Differential equations): Modeling, direction fields and 
Euler's method, separable equations, exponential growth, and logistic 
models.  Systems with two interacting populations would also be nice, but 
might not fit.

Chapter 11 (Sequences and Series): Essentially all of this chapter (11.1 
to 11.10 with 11.11 optional) should be covered.

Chapter 10 (Parametric equations and polar coordinates) should be the 
last material covered in the course and should be the first to be omitted 
under time pressure.  We would be very surprised it you can fit this 
material into Math 112.