Homework Policy and Suggestions
It's essential that you try to do as many problems as possible, because
Some of the problems assigned each day are routine "drill" exercises. There are certain basic techniques in calcuus that should become complely mechanical procedures for you: procedures you can do "with your spine" rather than your brain. Other problems require more thought. Sometimes you'll think that you can do a problem but get stuck if you actually try to write down the details. It's important to write out neat careful solutions for yourself, even in sections where homework is not collected. It's good to organize these in a separate notebook or file folder. You'll appreciate having them in one place when you want to review, especially if you can read them easily and don't have to work to decipher later what you did a few weeks earlier.
- Math is not a "spectator sport", and you can't learn calculus just by watching your instructor or TA solve problems.
- Doing problems is the best way to test whether you understand the material and to find areas where you need more work.
- Some (not all) quiz questions and exam questions will be very similar to assigned homework problems and textbook examples. Not understanding these problems simply guarantees that you'll throw away quiz and exam points.
After you finish and write up a solution, go back and talk to yourself (or others) about the problem. For example, ask "What are the main ideas involved?", "What's involved with this problem that puts it in this section of the book?", "Why couldn't I have done this problem last week?", "Is there some other way to solve the same problem?" You can learn much more by solving the same problem in a different way, if possible, than by solving several problems all in more or less the same way.
In the same vein: if a problem seems hard, don't give up and turn immediately to the solutions manual. You can often learn a lot more by spending hours (perhaps not all at once!) grappling with a hard problem than by working many simpler problems in the same amount of time.
The "Principles for Problem Solving" in the text (pp. 87 ff.) may be helpful. They're not magic, but they can help you organize your thoughts. At the end of each chapter, the section "Focus on Problem Solving" illustrates how to apply these principles to some harder problems.
The answers to odd-numbered problems are in the back of the textbook. The Student Solutions Manual, containing more complete solutions to odd-numbered problems, is available in the bookstore. If you're interested, consider sharing a manual with one or more friends to save money. We actually recommend against more than a casual use of the Solutions Manual: students become too dependent on it and don't develop confidence in their own work. You and your friends should usually be able to confirm solutions by comparing your work. Moreover, convincing friends that your solution is correct, or becoming convinced by their alternative solution, helps teach the skills of communicating mathematical arguments.
A schedule of Daily Reading and Homework Problems is part of the syllabus. We will try to follow it fairly closely. You will probably find the lectures more valuable if you read the assigned material and attempt some of the problems before coming to class. There may be modifications to the assignment list as the course moves along, so you might want to print out a new copy of it immediately after each exam.