Daily Homework, Math 131, Fall 2016
General Suggestions
The Daily Assignments Page of the syllabus gives you recommended problems correseponding to each lecture. These may be adjusted as the course moves along, so you should revisit the page each week. Your solutions are not collected and it is your responsibility to keep up with these to help you master the material. Most of the suggested problems are odd-numbered and the answers are in the back of the text, and more complete solutions are available in the Student Solutions Manual (an optional feature in the course, available for purchase online for those who want a copy (perhaps several friends could share a copy?)
The Daily Assignments Page also contains links to a few online graphing tools and calculators that you might find useful while working on problems.
The textbook has lots of problems to provide practice. I tried to select a reasonable number of problems that show you some of the standard ways the material in each section might be used in calculations or applications. If you know how to do some of the problems assigned in a section, there might be others that are new to you.
You'll probably find the lectures more valuable if you read the assigned material and attempt some of the problems before coming to class.
It's essential that you try to do as many problems as possible, becauseSome of the problems suggested each day are just routine "drill" exercises. There are certain basic techniques in calculus that should become completely mechanical procedures for you -- things you can "do with your spine rather than your brain." Other problems require more thought.
- Math is not a "spectator sport." 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
- Sometimes, quiz and exam questions are very similar to assigned homework problems and textbook examples. Not understanding these problems is a way to needlessly throw away some quiz and exam points.
Sometimes you'll think that you can do a problem but then get stuck when you actually try to write down the details. It's important to write out neat careful solutions for yourself, even though these problems that are 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 waste time trying to figure out what you casually wrote a few weeks earlier.After you finish and write up your 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?" (or, "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.
If a problem seems hard, don't just give up and turn 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 over the same amount of time.
Personally, I actually recommend against constantly running to the Solutions Manual: students become too dependent on it and don't develop confidence in their own work. Usually, you and your friends should be able to confirm solutions by comparing your work. Moreover, convincing a friend that your solution is correct and theirs is wrong (or vice-versa) helps teach the skill of communicating about mathematics.
The Principles for Problem Solving in the text (pp. 71 ff. in your textbook) might be helpful. They're not magic, but they can help you organize your thoughts. At the end of each chapter, there's a section called Problems Plus that illustrates how to apply these principles to some harder problems.