The material presented here is a combination of the general and the specific. During the academic year 1996-7, Math 151-2 was coordinated by R. Goodman, who prepared material for all sections of the course, building on what was done the previous year and including some contributions from other members of the instructional staff. The course format resembled last year's. Following the material uniformly provided to all sections of the course is some course material specific to sections 9, 10, and 11, taught by S. Greenfield, the previous year's course coordinator. This includes several exams with solutions. A detailed discussion appears below.

** Workshops ** Here are workshop
problems as presented in section 75 (with an exception noted
below). Section 75 was a small class with students receiving 5 credits
for four meetings each week (three 80 minute periods plus one 55
minute period). Most students were enrolled in a 4 credit version of
the course, meeting for 80 minute lectures twice each week and once a
week for an 80 minute workshop/recitation. The material presented
below for sections 9, 10, and 11 was prepared for such a class.

The
workshop problems presented last year represented an effort to
provide a selection of alternatives for instructors. The problems presented here reflect one
version of what might actually be used in the classroom. More
particularly, they usually begin with a "warm-up" problem which almost
all students should be able to do. Beginning with a relatively
accessible problem may be a good way to get students started. Here is
a list of the workshop topics:

- Week 1: review of integration by substitution and the Fundamental Theorem of Calculus.
- Week 2: area, volume, more use of the Fundamental Theorem of Calculus.
- Week 3: substitution, integration by parts, average value of a function.
- Week 4: substitution, integration using partial fractions, integration with rationalizing substitutions.
- Week 5: improper integrals, numerical approximation of integrals using Simpson's Rule and the Trapezoid Rule. TI-82 programs for these numerical techniques were presented in a handout similar to last year's.
- Week 7: calculators and sequences. This workshop begins the core of the course. Many students in the course have seen much of the earlier material in Math 151-2, but most of the students have not previously seen any systematic development of sequences and series. This workshop attempts to use a graphing calculator to help students develop "intuition" about sequences.
- Week 8: calculators and series. Again, this workshop tries to develop "intuition" about series using a graphing calculator. Also: geometric series and the integral test.
- Week 9: the comparison test and alternating series.
- Week 10: power series, the ratio test, and geometric series revisited.
- Week 11: radius of convergence and interval of convergence, the ratio test and root test, and manipulation of power series.
- Week 13: generating functions, graphing parametric curves and tangent lines to parametric curves. As shown here, this workshop was not given in class.

** Review problems** Sets of review
problems were provided before each of the two in-class exams and
the final exam. Novel aspects of the syllabus are reflected in some of
the review problems.

**The Final Exam** Here is one
version of the final exam. Note again that there are some types of
problems new to this course.

** Workshops ** Here (with one exception noted below) are the workshops actually used in sections 9,
10, and 11. They also built upon
last year's workshops and sometimes borrowed ideas from the workshops of the course coordinator
(discussed above). A number of the workshop problems are new,
however. Here is a list of topics:

- Week 1: substitution, volume and area.
- Week 1+: a problem
*not*given, using a geometric approach to investigate substitution. - Week 2: average value of a function, integration by parts.
- Week 3: partial fractions, rationalizing substitutions, trig substitutions.
- Week 4: Riemann sums as numerical approximations, the Trapezoid Rule, improper integrals.
- Week 6: calculators and sequences. This workshop begins the core of the course. Many students in the course have seen much of the earlier material in Math 151-2, but most of the students have not previously seen any systematic development of sequences and series. This workshop attempts to use a graphing calculator to help students develop "intuition" about sequences.
- Week 8: sequences, geometric series, the comparison test and approximation of a sum using a partial sum.
- Week 9: sums and partial sums of series, the comparison test and an "amazing coincidence".
- Week 10: the ratio test, absolute convergence, alternating series, and manipulating geometric series.
- Week 11: power series, the ratio test, and geometric series revisited.
- Week 13: generating functions, manipulating power series.
- Week 14: parametric curves looked at geometrically.

** Review problems** The standard review problems were provided before each
of the two in-class exams and the final exam. Novel aspects of the
syllabus are reflected in some of the review problems.

** Review sessions** Almost every instructor of Math 152 scheduled
exam review sessions. Final exam review sessions were listed on a web
page which students were encouraged to consult. They did, and many
attended several review sessions or attended review sessions held by
instructors other than their own which might have been scheduled more
conveniently. Sometimes additional material was
prepared for such a session (in this case, for the session scheduled
for sections 9, 10, and 11).

** Exams ** Here are questions and answers to one version each of
the first and second in-class exams given to sections
9, 10, and 11 of Math 152. The final
exam was the same for all sections. And again, there are some
types of problems new to this course.

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