Most students are not interested in mathematics for just for mathematics' sake. They often don't see the importance of studying mathematics, even if their teachers have told them, "When you get to ____ you will need to know this (esoteric) mathematical trick." This sounds like, "When you grow up, you will be glad you factored your polynomials." (Something like eating spinach?) As far as we are concerned, you have grown up now. It is time for us to "put up or shut up" as mathematics teachers. These projects show you why and how calculus is important in a number of deep examples. You cannot answer the questions raised in these projects without calculus and you can answer them with calculus.
The projects explore questions from serious ones like, "Why did we eradicate polio, but not measles?" to fun ones like, "Will the bungee diver rip his leg off or smash his head on the rocks?" There is a wide variety and we hope you will find several that interest you. If you want to know why you should study calculus read through the list of projects, then work one that is on a topic you find interesting.
The projects are an important part of our calculus course. Calculus is a beautifully coherent subject in its own right, but even if you are interested in studying mathematics for its own sake, you should be aware of the fact that calculus has important things to say about science and the world around us. Working a few of these projects over the course of the year will not only show you the power of using calculus to express "how things change," it will also help you understand the mathematics. (The Math Background book on the CD answers all your theory questions.)
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The projects are not easy.
They require a lot of work and time to think.
You don't just plug in a formula from the book, manipulate for 3 minutes, and go home, but you will find the effort worthwhile.
No pain, no gain.
Without exception, students understand the point of these projects once they have worked them.
A few find it "too much work," but almost all are justifiably proud of the effort that goes into a finished project.
At the University of Iowa, students (with majors from music to mechanical engineering) work three large projects in the first year. (Students at other schools have also worked many of these projects.) They choose topics of interest and spend up to 3 weeks on and off working out their complete solution with a partner.
In the large projects, teams submit a first draft for criticism and partial credit after a week, then clarify and refine their work in a final report of about 10 pages.
During the week before the first submission, we do not have lectures; student teams work in the lab.
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The goal of the projects is for you and a partner to write a "technical report" or "term paper" on the subject.
You should not expect to "find THE answer," write it, circle it, and hand it in to an instructor who already knows what it is.
Rather, your final goal is a report.
Imagine sending it to your boss at your new job.
Your boss is no dummy, and she can fire you, but she has been out of school a long time and doesn't remember the details of her calculus course (or the subject of the project). You need to write a clear explanation of the problem, your basic steps in solving it, and your conclusions.
The projects have "exercises" aimed at helping you get started and posing the right questions.
The exercises are not the whole story.
In this edition I called them "hints" because some students treated them like the drill problems in high school math.
They felt that if they just worked the exercises, with nose to the paper, they would be done.
The hints are only intended to help you discover the "big picture." The hints become gradually more vague and sometimes build up to more open-ended "explorations." Some of these projects don't even have single answers, but require you to make choices.
Read the project introduction and work the exercise hints, but remember that the projects require you to develop an overall understanding of the subject.
Organizing your work on the hints and writing a clear explanation of your solutions will help you develop this understanding.
Finally, write the "Introduction" to your report last.
Do NOT begin your project by rewriting my introduction.
Start by working on the hints.
Do NOT write an introduction like, "In our project we are going to
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Our website
contains Mathematica and Maple programs for each project to help you solve the hint exercises in the projects and to help you write your report.
Check it out.
The web is also a rich source of information about the projects.
." But rather something like, "Using calculus, we found a simple mathematical criterion needed to prevent the spread of a disease.
This report derives the condition and gives examples.
In the case of polio, our condition is easily met, 20% of the population can be susceptible, whereas, for measles
" Use your introduction as an advertisement to interest your reader in the rest of the report or, in the case of your busy corporate boss, to give her the basic conclusions clearly and concisely.