Send comments or questions to: ldurand@theory2.physics.wisc.edu           

 

FRIENDLY ADVICE: READ OVER THE HOMEWORK INFORMATION SHEET AND THE HOMEWORK STRATEGY SKETCHED BELOW TO SEE WHAT I EXPECT IN THE SOLUTIONS TO THE PROBLEMS, AND WHY: EXPLANATIONS, COMPLETE SOLUTIONS, COMMENTS ON THE RESULTS, ETC.

 
GENERAL STRATEGY FOR HOMEWORK:
 

1. Decide what you think the problem is about, and how you plan to solve it. Many of the problems are longer than you may be used to, and an organized approach is essential if you are to solve them efficiently. It helps to write down for yourself:
    
   • the method to be used,
      
   • the conditions the solution has to satisfy (initial conditions, constraints, etc.),
      
   • and the proposed steps in the solution.
      
   You can revise your approach later, but you should have an initial strategy in mind.
    
2. Work out the solution systematically, writing out each step. You should:
    
   • Add explanatory or interpretive remarks as you go, especially as you start new parts of a calculation or new parts of the problem. We expect to see a logical development, with appropriate explanations. This will also help you when you look over the problems again in preparation for exams!
      
   • Keep track of where you are in your proposed route to a solution. Don't backtrack and start over unless you are convinced your method doesn't work, and have an idea why. You may just have forgotten to use some of the conditions you noted at the beginning (hence the value of outlining your approach before you start). If you do start over, think through a revised approach before plunging in again.
      
   • Impose the constraints and boundary conditions as early as possible to determine or eliminate constants of integration, simplify the calculation, etc.
      
   • If you can't solve explicitly for some quantity (a common occurrence), explain clearly what conditions could be used to determine it numerically.
      
   • Once you have the solution, give some interpretation. Describe what the results mean, what the motion is, what point is illustrated by the problem, etc.
      
   If all goes according to plan, your solution should already be in a suitable form to hand in. But if it's too long or messy, has incorrect steps, etc., and you have to rewrite it, organize the solution as above and include the KEY PARTS of the calculations - don't just refer to calculations on scraps of paper that you threw away!
    
3. Review your results: Look back over your calculations to make sure you really understand what you have done. It should be clear to you why (other than general perverseness) I assigned the problem, what principles and calculational techniques are illustrated in its solution, where they should be useful, and how the specific problem fits into the general problem sequence and the development of the course. Remember that you are trying to develop a coherent body of knowledge and methods with general applicability, not just get answers to particular questions.
    
4. Study groups: Follow the same general strategy when working on the problems together, but organize your efforts:
    
   • It helps for the group to work at the blackboard in outline form. Have one person write down the proposed approach and summarize the key points as you discuss the problem and agree on a method of solution.
   • Make sure that the group follows the agreed upon approach and doesn't get sidetracked.
      
   • It helps to have one person designated as the resident skeptic, with responsibility for insisting that every step is explained to everyone's satisfaction. If you can't explain what you are doing, you probably don't understand it!
      
   Work through the major parts of the problem together. Take individual notes on the approach and main steps, but leave the details to work through independently. The points in working together are to get different points of view on the problems, and to find satisfactory methods of solution without wasting alot of time on false starts. Write up your own solutions independently. You'll really learn what a problem is about when you reconstruct the group solution and interpret the results for yourself! Finally, compare your solutions to make sure that you haven't missed something.
    

SO WORK TOGETHER, AND COME TO ME (PREFERABLY WITH YOUR STUDY PARTNERS) IF YOU NEED A HINT TO GET STARTED, OR WANT TO TALK A PROBLEM THROUGH (WHICH IS HOW I GET YOU STARTED ON A PROBLEM IN ANY CASE). BUT COME PREPARED!

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