Rationale for workshop problems, fall 2006
Why the problems in workshop #2?
- and 2. and 3. All of these problems are simple examples of
geometric/physical modeling situations. Such situations will arise
repeatedly in Math 151. Successful modeling will
strengthen skills which most Math 151 students need in other courses
and will need professionally.
Why the problems in workshop #1?
- This exploration using a "fairy tale" is intended to show students
that limits and function values can be distinct.
- Students entering a calculus course should have verbal, algebraic,
geometric and logical skills. Neglecting deficiencies in these areas
makes the course much more difficult. These problems are an attempt to
detect such deficiencies. The writeups should be evidence that
students can communicate technical material clearly and carefully.
- Students should be able to handle graphical information. They
should be able to transform the graphs in response to simple algebraic
queries, and also answer simple algebra questions about functions
- Polynomials are among the simplest building blocks of functions in
calculus and in many other subjects. This problem seeks to determine
if students can create polynomials with prescribed roots, degrees, and
- Students should be able to "model" and understand simple physical
and geometric problems using the tools of calculus. Here's a rather
simple problem, which additionally requests that students use a
calculator to understand some of the model.
- Absolute value is a mystery to many students. In this course and
elsewhere absolute value is used to compare quantities. Again,
algebraic and logical skill is needed to complete this problem and to
be sure that the results agree with the graphical information. This
interaction is important. Piecewise linear functions occur in the tax
code (as mentioned during the lecture) and also are important enough
so that massive amounts of computer time are devoted to maximizing and
minimizing such functions (a major portion of industrial engineering
and operations research).
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