Math 156 - Applied Honors Calculus II
Robert Krasny
University of Michigan
Applied Honors Calculus is a sequence of courses
currently being developed
in the Mathematics Department.
The sequence consists of Math 156/255/256
and
is designed for students majoring in science and engineering.
Math 156 is taught in the Fall semester.
The students are entering freshmen with
AP credit for 1st semester calculus.
The prerequisite is a score of 4 or 5 on the AB exam.
Math 156 provides students with
the math background they need for
courses in physics, engineering, etc.,
as well as for 3rd semester calculus
and
more advanced math courses.
The syllabus covers traditional 2nd semester calculus topics:
integration,
differential equations,
and
infinite series.
The text is ``Calculus" by James Stewart,
although as course coordinator I
distribute customized lecture notes to the other instructors.
Math 156 is a balance between application and theory.
The course develops the students' skill in computation and analysis.
Theorems are carefully stated and several are proven.
The proofs are presented in easily understood steps
(based on my experience from prior years).
Many examples are given to illustrate the theory.
At the beginning of the semester,
we review the definition of the integral as a limit of Riemann sums
and
then quickly move on to topics which most students havn't seen before.
This includes
improper integrals
and
applications such as work, center of mass,
arclength, surface area, hydrostatic pressure and force,
and
probability density functions.
We avoid the traditional
chapter on methods of integration for-their-own-sake,
and
instead discuss the methods
as they arise in specific applications.
We avoid the more exotic cases
(e.g. partial fractions in full generality)
in favor of emphasizing the cases that come up
most often in applications.
Infinite series and Taylor approximation are discussed in depth.
The final segment on ordinary differential equations
treats
exponential growth/decay,
Newton's law of heating/cooling,
and
the logistic equation.
enrollment history
1994 - 102 (3 sections)
1995 - 093 (4 sections)
1996 - 175 (6 sections)
1997 - 144 (5 sections)
1998 - 190 (7 sections)
1999 - 151 (6 sections)
2000 - 105 (6 sections)
2001 - 098 (4 sections)
The students are roughly
1/2 Engineering and
1/2 LSA (Literature, Sciences and the Arts) Honors.
The class meets 4 times per week
and each class is 50 minutes long.
There are uniform weekly homework assignments
and uniform exams
(two 90 minute midterms and one 2 hour final exam).
The homework assignments include
problems from the text
and
customized problems.
I try to ensure a close connection between lectures,
homework, and exams.
The instructors write solutions to the homework problems
which made are available to students in the Undergraduate Library.
Additional items:
1. The students receive instruction in MAPLE,
a computer software package.
2. There is exposure to special topics such as
asymptotic expansions,
Bessel function,
complex numbers,
error function,
fractal sets,
Gamma function,
Laplace transform,
polar coordinates.
3. I use
an interactive/Socratic/discovery lecture format,
i.e. asking the students many questions
and
encouraging them to ask me questions.
My aim is for the students to stay involved and participate
in the lecture.
I encourage the other instructors to follow a similar format.
4. There is a small amount of group work in class,
mostly to break the ice at the beginning of the semester.
5. The students are encouraged to work together on homework,
but each student is required to write up and submit
their own individual set of homework solutions.