The only way to learn this kind of mathematics is by doing it. The homework is very important and is assigned each time we meet, with the expectation that you will do it by the next class meeting, although it will not be collected. This means that you have the responsibility for your own learning.
I try to select representative problems without overburdening you, but you must budget your time to work on most of these even when you have other deadlines to meet. (When under excessive time pressure at least do some key problems when they are assigned. Finish the rest as soon as you can.) Typically we begin each class looking at a few of the assigned problems, either at your request or mine to you. This is your opportunity to get questions answered. (But watching me do the problems and copying down what you can will not substitute for your doing the same problems from scratch on your own. Like two people driving in a car, the one in the driver's seat has much more probability of remembering how to repeat a trip than the person in the passenger's seat. Think about it from your own experience.)
Keep a notebook or looseleaf binder or something in which to record your worked homework problems. Homework will not usually be collected. [Its goal is for you to learn by doing, not deliver a product by a deadline.] Bring your notebook/binder/something to office hour when seeking help. Not doing homework will have a snowball effect in derailing your understanding in the course.
Certain textbook homework problems will be marked for MAPLE calculation by an asterisk, usually with instructions and a template file if needed. Common MAPLE assignments will be collected as single worksheets at the end of each chapter done in groups of 2 or 3 and will count as 10 percent of your grade (and graded 0: unsatisfactory, 1: mostly okay but incomplete, 2: acceptable). Save your worksheet frequently, and at the end of a session save it to a memory stick if you are not working on your own computer and keep a separate backup copy (your partners can serve this function if everyone keeps a copy of their joint work: email it to them as an attachment). Only 1 worksheet per group should be turned in as an email attachment when requested, using exactly the subject header requested, and CCing it to all other partners so everyone has a copy of the submitted worksheet. These are not usually difficult, and I am always ready to help you overcome any difficulties that you have with the MAPLE software. It is easy to get full credit on these assignments, since you may get help from me on any problem that you have trouble doing. Don't wait until they are due to attempt them or they will not help you with the concept digestion as we are learning new concepts.
Before doing the homework, read the corresponding section of the textbook carefully. Some assigned homework problems may refer to examples or material for which there is not enough class time to discuss. Reading will also reinforce what you have heard and perhaps clarify some of the things that may not have been clear to you in class. Then only by actually working problems, referring back to your notes or the text interactively, will you know if you are acquiring control of the ideas. Learning mathematics is a digestive process that does not happen just by a single exposure to new material.
It is also a good idea to form partnerships in the class for doing homework together. The Math Learning and Resource Center (MLRC), even without tutors on duty, is a good place to meet to work together, or CEER rooms for this purpose. [MLRC: M-Th 2:30-5:00, S-Th 6:30-9:00, tel:610-519-5193]
Absences: Notify me in advance (if possible) in person or by phone/voice-/e-mail. If not possible to anticipate an absence, call/e-mail the same day if possible and explain in person at the next available occasion. No valid excuse means 0 (zero). If your excuse is valid a makeup test will be arranged.
Freshman note mandatory class attendence rule [excuse note required from VPAA office]. All students: excessive absence coupled with poor performance will result in a grade penalty. All students are held responsible for all class material, including handouts that are distributed.
A short almost weekly quiz will monitor your understanding of the homework and class material. Only textbook sections for which the homework has been discussed in class (since the previous quiz) will appear on a given quiz. Lowest quiz grade dropped. No quiz during a test week.
3 hour tests plus final exam. Lowest of first two test grades dropped only if the subsequent test grade is higher (rewarding improvement).
A formula like
.10 (quiz avg) + .05 (Maple hw avg) + .20 (hw avg) + .65 (test,finalexam avg)
will be used to compute your raw number grade which has only a relative significance. Letter grades will be assigned in as intelligent a fashion as possible, based on an impression of absolute and relative performance. Individual student progress (and decline!) is also weighed by hand.
[You can check out a sample of my Excel gradespreadsheet and compute your own grade at any time during the semester with udogrades.xls, which has internal instructions.]
Try to be conservative in taking notes so that you are able to think about the discussion as you are writing and not just be obsessed with copying everything down. Try to understand roughly what I say as I say it, and ask a question or slow me up if you are confused. Communicate with me, during class and after class. Tell me what is unclear. My lecture on new material is a get acquainted look: you cannot expect to absorb it just from sitting in class. It must be backed up by reading the text and interacting with the text as you do the homework problems.
Remember: mechanical calculations can be done by machines; you need to learn the ideas to think for the machines in applying them.
When you are working a problem, whether for yourself on homework or on a quiz or test, it is important to always use the proper mathematical symbol for an expression you write down by using an equation whose lefthand side is the symbol and whose right hand side is the expression. If you manipulate this expression without changing its value, you may continue on the next line with an aligned equal sign and so on, starting a new such equation if you do something to change the value of the expression, as in:
f(x) = x (x+2)
= x2 + 2 x
f '(x) = 2 x + 2
Do not put equal signs at the end of the line, but at the beginning of the next line, and align them vertically. This is part of good organization.
Almost all calculations in calculus involve algebra either before, during, or after calculus operations, so it is very important to show all steps one step at a time to make sure no mental errors are made and no incorrect rules of algebra are used.
Good organization of your work helps you understand better what you are doing while you are doing it, and is good practice for technical communication, which you may need to do if you succeed in getting a job in a technical field later in life where may have to work in a group and will certainly have to justify your calculations to other people.
For routine calculations, palette entry in Maple with right margin context sensitive menus makes it easy to check any derivative or integral without knowing Maple syntax. There is no excuse for getting such steps wrong in this course.