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{excerpt:hidden=true}A broad-brush introduction to this wiki's instructional approach.{excerpt}

Given the many textbooks on Introductory Newtonian Mechanics using Calculus, we would have little intellectual incentive to write another, except that we have important goals that are different from existing texts of either the  "standard" or "reform" variety.  This is the case: we have three important goals

Our three top goals are:
 
* Give our students the strategic knowledge to attack new and unfamiliar problems in Mechanics using a pedagogy that we call Modeling Applied to Problem Solving
* Help our students obtain an overview of the subject, and - by using a Glossary - help them understand the specialized vocabulary of Mechanics
* Explore the advantages of an electronic format to reach these goals, and generally to construct an environment for learning that is superior to a printed textbook.

h3. Modeling Applied to Problem Solving - a Strategic Pedagogical Approach

Our overarching goal is to help you learn to solve mechanics problems. Problems, by definition, do not have an obvious solution once you fully understand the problem.  Hence a problem for you may be an exercise for someone else, and vice versa.

Imagine that you have a problem.  You understand the material in your textbook, and you now understand what's asked in the problem.  But you realize that you don't know how to solve it.  You need to figure out what to do next.  Most textbooks suggest some variant of Polya's (1945) four step process:
# Understand (visualizing the motion is very helpful for mechanics)
# Plan your solution
# Solve the Problem
# Check Over for Reasonableness and Lessons learned.

Unfortunately, they don't indicate how to bridge the gap between 1 and 2 - i.e. how do you plan a solution if you don't see how to solve it?

The Modeling Approach to Problem Solving is designed to give you _strategic knowledge_, how to understand the problem in a way that enables you to decide which of the factual and procedural knowledge that you've learned can profitably be applied to the problem at hand.

{HTMLComment}??MORE Stuff from our approach.  In particular, mention idea of model to collect facts into applicaable chunks, and categories of models keyed by physics of problem. {HTMLComment}

h4. _Problems_ vs _exercises_

Consider this question: 

An ice skater of mass m=55kg experiences a force of 20N when she is at rest due to the wind.  Find her acceleration neglecting friction with the ice.

For most of you, this question is (or soon will be) an _exercise_.  An exercise is defined as "Once you understand the question, the plan of solution is obvious."  Once you understand that this question involves mass, force, and acceleration you will think of F=ma.  The plan of attack is then obvious \-  rearrange this equation to give a=F/m and substitute the given quantities to obtain a = 0.36 m/s.

The following question should be a _problem_ for you (if it's not, you may not get much from reading this WIKItextBook):

An ice skater of mass m=55kg experiences a force of 30N when she is at rest due to the 10 m/s wind.  Find her position vs. time neglecting friction with the ice and assuming that the drag force of the wind is proportional to the square of its relative velocity.

The plan for solving this question involves 
# Find the acceleration of the skater - unfortunately it involves her velocity which is unknown and is hence a differential equation.
# This is the only kind of differential equation you will need to be able to solve in this WIKItextBook - it can be solved by separation of variables
# The resulting v(t) can be integrated to find x(t)

h3. Giving an Overview and a Glossary

A big part of Strategic Knowledge is organizing your knowledge of Mechanics - gaining a perspective on its major categories, what are the characteristics of each, and which categories do each of the facts and procedures you know fit under (maybe more than one).  Not long ago a group of educators reconsidered the textbook [http://serc.carleton.edu/textbook].  Chief among their criticisms was that conventional textbooks do a poor job of imparting strategic knowledge.  They partition the subject into chapters, but don't say how the chapters relate to each other, or how to decide when a problem needs the material taught in a particular chapter.  Often the only overview is provided by the table of contents, and this is not very useful to someone who doesn't understand the many technical words it contains.

The central page of this WIKItextBook offers you several ways to get an overview of mechanics.  Foremost is the organization of the content into four categories, each with its hierarchy of models [hierarchy of Models].  In addition, we provide an expandable table of contents.  This table has a series of Traditional Lessons which present the models that cover the core material in much the usual sequence of topics (rather than the more abstract categories and model hierarchy).  It also has a section on Interactions - very important because they are the key to strategic knowledge in mechanics.

Our [vocabulary glossary] helps you to understand with precision the various technical terms used, a necessity to learn any scientific topic.  This is particularly important in mechanics, because so many of its concepts have become everyday words with broad common usage meanings - like acceleration, momentum and energy. We will try to incorporate the Glossary summary when technical words are introduced, and we will make many of them links to remind you to be sure you understand them.  The Glossary entries expand with a click to help you understand these words more fully and appreciate some of their implications.  

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h3. Exploiting Electronic Format

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?? orthis create an electronic WIKItext that is more conducive to learning than a textbook.

Printed textbooks do a poor job of giving a grand overview of the material due to their serial nature and lack of an easy search mechanism. This eBook can arrange by lectures (as in a regular textbook), but dedicated users can make other sets of lectures to shift the emphasis or change the level of sophistication.