(c) copyright Foundation Coalition (S. A. Fulling) 1997

Classes 1.1, 1.M

Introduction to Coalition Calculus and to Maple

Reading assignment for Wednesday, September 3

• This Web page
• CalcLabs 1.1-1.4
• Take note of the Important announcement below about setting up lab accounts.

Reading assignment for Thursday, September 4

• CalcLabs 14.1, 14.3-14.5
  • Warning: The currently available edition of the CalcLabs book discusses the syntax of Maple V, Release 3. Hence there are occasional inconsistencies with Release 4. This is typical of the way the world works these days; you might as well get used to it. (Release 4 has a better user interface than Release 3; lots of the things that used to be problems no longer are.)
• Lab assignment sheet, "Using Maple's On-Line Help"

Definitions. In Mathematics 151 we have three types of regular class meetings:

• "Classes" or "lectures" conducted by a faculty member. For the Coalition these are in Richardson 106 on Monday-Wednesday-Friday.
• "Labs" conducted by graduate teaching assistants. Each Coalition group is divided into 3 sections; each section will meet for one hour on Monday or Wednesday in one of themathematics department's computer labs, equipped with X-terminals and UNIX servers.
• "Recitations" conducted by graduate teaching assistants. Each coalition group will meet for one hour on Thursday afternoon in Rich 106. This is your main opportunity to ask for help with homework, old tests, etc.

There may also be occasional help sessions and review sessions with attendance voluntary.

Important announcement. Some of you will be instructed to report to a lab room before our first class meeting, to set up your accounts on the UNIX system. Please follow those instructions. Because of the disruption of our regular schedule by team training sessions during the first two weeks, the recitation periods during those weeks will be run like labs, the Monday labs will not meet, and the Wednesday labs will be used just for setting up accounts. Starting with Week 3, each Coalition Group will be divided into three lab sections, two of which meet on Monday and one on Wednesday. These permanent lab sections

• have nothing to do with the numbered sections that the university's computer says you are enrolled in;
• have nothing to do with the time you were told to appear to sign up for accounts;
• are subject to change whenever teams are reassigned.

What the computer lab in engineering calculus can do for you

• Equip you with a powerful modern problem-solving tool (Maple), and develop your confidence and judgment in the use of that type of tool.
• Provide high-quality visual representations (graphics) of mathematical objects with aminimum of effort.
• Reduce tedious algebraic manipulations, thereby promoting a sharper focus on thefundamental ideas of calculus and on strategies for formulating and solving problems.
• Enable you to include verbal commentary in your work (and to edit it) with a minimum of effort.
• Provide more opportunities for interactive learning and learning by discovery and experiment.
• Provide experience with a second programming language, with instructive similarities and differences compared with FORTRAN.

What you get out of the lab is up to you. You can can react in three ways:

1. You can blow it off, and accept a low grade in the lab part of the course.
2. You can treat it as a required chore, and do the assigned work mechanically, concentrating on turning it in for a grade.
3. You can approach it with your intelligence and your imagination, both to understand mathematics better and to find ways to use computers in the future when you'll be on your own (and to sense when computers might be dangerous).

Only in the third case will you get any benefit.

So, why do we still need to learn calculus?

• In life, you will not always have access to a computer. (In the exam room, there are not enough computers to go around.)
• You can't use a machine competently unless you understand what it is doing. You can't solve a problem competently by computer until you understand how, at least in principle, to solve it by hand.
• Analytic solutions are more general, and more insightful, than numerical solutions.
• Mathematics is more than grinding out numerical answers. (Often, the purpose of a test question is defeated if a calculator is available.) Routine calculational skills no longer make one employable -- a PC is cheaper and faster than an employee. You need to develop
• a deeper understanding of concepts, not just rules;
• the sense for when to apply concepts and rules in real problems!

How to Learn Calculus

1. Accept the fact that YOU must do 90% of the work. Learning requires time, effort, and patience.
2. Don't expect to understand everything the first time you hear or read it. Don't confuse temporary frustration (which is normal) with failure.
3. Read the book (Web page, etc.) BEFORE the class. Plan your Maple calculation BEFORE you sit down at the keyboard. Try all the homework BEFORE the recitation or help session.
4. Don't hesitate to ask questions. (But choose the time sensibly.)
5. Aim for understanding. Don't just memorize.
• Whenever possible, memorize methods instead of formulas.
• Whenever possible, learn how a method works, why a formula is true, what each symbol means.
• Always make sure you understand when the formula or method should be applied.
• Penalties for memorizing formulas and imitating examples instead of thinking (Click Here) (HTML version)

  
  
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6. The night before a test is for sleeping.

But of a good leader, who talks little,
When his work is done, his aim fulfilled,
They will all say, "We did this ourselves."

_._._._._._._._._._._._._._. Lao-Tzu

Remember that active learning is a cardinal principle of the Coalition. These Web pages and other printed resources take the place of detailed lectures. Again, what you (and your teammates) get out of class will depend on what you (and your teammates) put into it.