Section 3 Navigating the Course (a short how-to guide)
Doing well in calculus doesn’t require any special talent. It mostly requires good organization, a bit of perserverance, and knowing when to ask for help. (See Section 4 for ways to get help.)
We try to keep the workload fairly consistent throughout the semester, which may be unlike other courses that tend to ramp up toward a midterm or big assignment. Figure out what needs to be done each week, set aside time to get it done, and stick to your schedule.
Online homework.
Online homework is assigned every week. Your answers are graded automatically by the computer, you get immediate feedback on whether or not your answer is correct, and you usually get unlimited attempts to get a question right if you make a mistake on your first try. (Multiple choice questions are a notable exeception to this policy.)
One of the best things you can do is to start the online homework right away. The exercises will be more useful to you if you work on them at the same time that you are seeing similar problems in class, and/or in the textbook.
Doing the problems early gives you plenty of time to ask for help on the ones you get stuck on, and doing a few each night is much less stressful than leaving them all for an hour before the homework is due.
Class meetings.
Our meetings will involve a lot of hands-on work and discussion. You’ll be working in groups to solve problems, while I move through the room to answer questions.
How you prepare for these classes probably depends on your personality. Some will find it useful to use class as a way to determine what topics need further study after class. Some will want to prepare before class, because they don’t want to be stumped in front of their peers.
Using the textbook.
Reading a textbook (especially for a technical subject like mathematics) is a skill you have to learn and practice. A math book can’t be read like a novel. It requires some effort and interaction.
Some general suggestions:
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On your first pass through a section, just scan. Skip the explanatory text. Make a note of the significant parts, like definitions and theorems. (You may even want to keep a notebook where you record all the definitions and theorems for yourself.)
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Next, read the content of the definitions and theorems. Do you understand what they’re saying? (On first glance, it’s quite likely that you don’t.) Now you can read the surrounding explanatory text, to see if it sheds any light.
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Next, move on to the examples. At this point you might know what the definitions and examples say, but this doesn’t mean you know how they are used. The examples will help illustrate this.In the HTML version of the book, the solutions to each example are initially hidden. Write down the problem in the example, and see if you can solve it yourself. Don’t worry if you get stuck. Just make a reasonable attempt. Now you’re ready to look at the solution, and see how it compares to your attempt. If your results differ from the results in the solution, stop and think. See if you can see where you went wrong.Note that many examples have two types of solution: written, and video. You can pick whichever format works better for you.
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Finally, try some of the exercises. If you find that you’re getting most problems in an exercise group correct, it’s probably safe to skip ahead to the next exercise group.If you find that you’re getting them wrong, go back into the section and look for a similar example.You can also look for similar problems in the online homework.
