Week 1. The objectives of the first week include learning how to use the Macintosh to accomplish the following:

1. Make your own folder inside the Physics 125/225 directory and edit and print the WriteNow, ClarisWorks, or TeX file questionnaire. Sign your completed questionnaire before you leave the first laboratory.

2. Open a file; copy a file; change the name of a file; delete a file.

3. Edit and run a True BASIC program. Learn how to correct your typos, move lines, find words, etc. Start reading the True BASIC tutorial.

4. Read Chapters 1 and 2 in Gould and Tobochnik.

5. Begin Problems 2.1 and 2.2. The main computational objectives during the first two weeks are to understand how to convert a first-order differential equation to a simple difference equation, and to understand how True BASIC handles variables.

6. Use Netscape to reach the course web site and explore the contents of the site and the associated text.

Week 2

1. Write a paragraph or two briefly summarizing the important points of Chapter 1 as you understand them at this time. In what ways are computer simulations like laboratory experiments? In what ways are they different? What is the difference between a computer simulation and a numerical computation? Due Thursday, January 22, 1998.

2. Do Exercises 2.1 and 2.2, pages 18-19 and show one of the instructors your solutions before you leave the lab on Tuesday, January 20. Also explain to one of the instructors the difference between closing a file and quitting an application and the difference between save and save as.

3. Do several of the problems in Chapter 2, especially Problem 2.2. Note that although we are not doing a simulation, it still is possible to ask some simple "what if" questions. You might find it useful to download the empirical data in Table 2.2. Graphs can be made with KaleidaGraph (recommended) or CricketGraph (easier). A report on some aspect of Chapter 2 is due by Monday, January 26. A question for physics students, explain the difference in the effective values of r for black coffee and coffee with cream.

4. Peruse Chapters 3 and 4 to gain some idea of the similarities in approach to Chapter 2.

5. A good summary of how to program is available. Read the article by Jeff Templon on the relative merits of Fortran, C/C++, and Python and the article by Paul DuBois on the strengths and weaknesses of Java. The moral of the story is that there is no universal purpose language.

6. Please see the instructor at any time if you desire alternate assignments.

January 26

1. Discuss the difference between a local and a passed variable and the difference between an integer and a real variable. Due Thursday, January 29.

2. Chapters 3 and 4 of Gould & Tobochnik introduce the use of numerical methods to obtain numerical solutions of Newton's laws of motion. These chapters also make use of elementary graphics. Ideally, the chapters should be read together and you should choose what is interesting. Also the True BASIC tutorial is more or less finished. Your comments would be greatly appreciated.

3. Do Problem 3.1, especially parts (a) and (b). Don't worry if you do not yet understand the Euler-Richardson algorithm since we do not have to use it until Chapter 4.

4. Download styrofoam data. If you are short of time or are confused by derivatives, skip part (a).

5. Problem 3.3 is more interesting than 3.4.

6. Graduate students and more advanced undergraduates should consider doing Problem 3.6.

7. Second laboratory report due on Thursday, February 5.

8. Check out Physics Academic Software and choose one or two software titles to review. After you send me your choices, I will request that the titles be sent to us. On Friday, April 3 I will ask you to demonstrate the software at the New England section meeting of the APS/AAPT/SPS at Clark. Due Tuesday, February 3.

February 2

1. Finish your laboratory report due on Thursday, February 5. You are welcome to show your draft to one of the instructors.

2. Generalize the discussion given in class on the forest fire model to a model for the spread of epidemics. Due Thursday, February 5.

3. Read Appendix 3A about the use of libraries in True BASIC. What is the analog of a library in C?

4. Read Appendix 3B or the tutorial to learn how to use data files in True BASIC. Is there any reason to take written notes while you are in the lab?

5. Read Appendix 3C to learn about strong typing and public and private variables.

6. Remember to quit all applications before you leave the laboratory. What is the difference between Quit and Close?

7. Arrays are introduced on pg. 65 in Chapter 4. Study Program vector carefully if you have not used arrays before. Make sure you understand how arrays are passed in True BASIC. Read the Appendices to see how arrays are used in Fortran and C/C++. If you have a chance, compare how the positions, velocities, and accelerations are treated as arrays in Program planet and in Program planet2, pg. 80.

February 9

1. Minimum goal for Chapter 4: Most of Problem 4.2 with special attention to the importance of conserving the total energy. Problem 4.3, parts (a) and (b) are straightforward extensions. There is some excellent physics to be learned by doing Problems 4.4, 4.6, and 4.7. Advanced students could learn much physics from Sec. 4.11.

2. Arrays are introduced on pg. 65 in Chapter 4. Study Program vector carefully if you have not used arrays before. Make sure you know how arrays are passed in True BASIC. If you have a chance, compare how the positions, velocities, and accelerations are treated as arrays in Program planet and in Program planet2, pg. 80. Also read the tutorial and Appendix B, respectively, to see how arrays are used in Fortran and the C/C++.

3. Report on Chapter 4 or the equivalent due by Monday, February 16.

4. Although we will not do any of the problems in Chapter 5, read Chapter 5, pgs. 96-108 if you have time. If you are physics major, pay particular attention to the notion of phase space discussed in Problem 5.2. Note the use of multiple windows and the passing of channel numbers in Program pendula on pg. 105. Also read Appendix 5A to get an idea of the various algorithms for solving differential equations. Project 5.1 on chemical oscillations gives you an idea of how the algorithms we are learning can be applied in another context.

Week of February 16

1. As of February 14, seven students have not chosen software from Physics Academic Software (PAS). Because this number is too large despite my repeated reminders, I have canceled this assignment. Instead, students may volunteer (for extra credit) to review their selected software title and demonstrate it to attendees of the New England Section of the APS/AAPT/SPS meeting on Friday, April 3 from approximately 3-4 pm. Student volunteers at the meeting will be able to attend the banquet at no charge. Please let me know by Wednesday, February 18 if you wish to volunteer. The most popular software titles from PAS are EM Field, Electric Field Hockey, Graphs and Tracks, and Freebody. So far, nobody has selected any of these titles.

2. Reminder: the first meeting of the extra discussion section for graduate and interested undergraduate students begins on Tuesday, February 17 at 5:30 pm. We will begin discussing molecular dynamics, Chapter 8.

3. Exercise 4.3, page 67. Greg Johnson has pointed out that the insertion sort method is difficult to implement because you must add elements to the middle of an array. Instead of this sorting algorithm, use a variation of the bubble sort algorithm. The idea is to compare every pair of elements in the list and exchange them if they are out of order. This algorithm will require O(n^2) operations. (The number of elements in the list is n.) Take a look at a Java applet demonstration of the bubble sort algorithm. Do this exercise by Tuesday, February 24. Print out your solution and your solutions to Exercises 2.1 and 2.2 by this date.

4. Start Chapter 6. Use the computer to explore the rich dynamical behavior of the logistic map. We will decide in class this Thursday when the next laboratory report is due.

5. Comment on the quote by Robert May on page 128 on the importance of understanding the dynamical behavior of simple nonlinear systems. Write a one to two paragraph statement agreeing or disagreeing with my claim that such an understanding should be an essential part of a liberal arts education. This statement is due Thursday, February 26.

Week of February 23

1. Check here to find out how to save a snapshot of all or part of the screen.

2. Remember the assignments due on February 24 and February 26.

3. Suggested problems in Chapter 6: 6.1-6.4, 6.6, and 6.9. Then reread the chapter to obtain a better perspective of how the ideas we have learned in the context of the logistic map can be applied to more complex systems. Due date for next laboratory report: Tuesday, March 3.

4. Does the Euler-Cromer or the Euler-Richardson algorithm do a better job conserving the total energy when calculating orbits? The answer might surprise you. Some results are given here.

Week of March 2

1. Reminder: Due date for next laboratory report: Tuesday, March 3.

2. David Joyce will speak to the class on Thursday, March 5, on object oriented programming. Useful reading: Primer on Object-Oriented Programming Concepts.

3. Chapter 7 is a simple introduction to Monte Carlo methods. Suggested problems are 7.1, 7.2, 7.6a-d, and one of the problems in Sec. 7.4. Also see Problem 12.1. Read Sec. 7.5 on the method of least squares and do Problem 7.14a. Start reading Chapter 11 which also will serve as an introduction to Monte Carlo methods.

4. So far we have considered more or less traditional topics - topics that existed before computers. During the break peruse the text, especially Chapters 11-17, to get an idea of the nature of some newer topics that have been very much influenced by computers. Also take a look at http://physics.clarku.edu/sip/projects.html to get some ideas for projects that are not in the text.

Week of March 16

1. Chapter 7 is a simple introduction to Monte Carlo methods. Suggested problems are 7.1, 7.2, 7.6a-d, and one of the problems in Sec. 7.4. Also see Problem 12.1. Read Sec. 7.5 on the method of least squares and do Problem 7.14a. Start reading Chapter 11 which also will serve as an introduction to Monte Carlo methods.

2. David Joyce will discuss Java programming on Thursday, March 19. You might wish to learn Java programming as part of your project.

3. The next laboratory report will be due on Friday, March 27 and will include Chapter 7 and parts of Chapter 11.

Week of March 23

1. The next laboratory report is due on Friday, March 27 and includes Chapter 7 and parts of Chapter 11. If you are working on your project, write a progress report instead.

2. Suggested problems in Chapter 11 include some combination of 11.1 and 11.2a-d and 11.3.

3. Start thinking about your choice of project. I do not expect you to think of one on your own. Look over the text and take a look at http://physics.clarku.edu/sip/projects.html to get some ideas for projects that are not in the text. If you tell me about your interests, I will suggest 2-3 possible projects. Deadline for submitting the title of your project: Tuesday, April 7.

4. The following questions are based on the article, "Repealing the Law of Averages," Ian Stewart, Sci Amer. 278(#4), 102 (1998).

   Toss a fair coin and maintain a running count of the number of heads and tails. Suppose that at some time, there are 100 more heads than tails. Is there any tendency for tails to "catch up" in future tosses? The answer depends on what we mean by catching up. We know that future probabilities of a head or a tail are not changed by what happened in the past. Do a simulation of a coin toss. Suppose that heads corresponds to a step up and tails to a step down, and make a plot of the "height" (the number of heads minus the number of tails) as a function of time. You will probably note that unbalanced behavior can persist for a long time. However, it is possible to show that if you wait long enough, the balance will correct itself with probability one. In this sense things do tend to balance out in the long run. But you don't know how long the long run will be.

   Suppose that you toss a coin a million times and count the number of times that heads or tails is in the lead. What proportion of the time do you expect heads to have the lead? Do the simulation and see.

   Suppose that you toss a coin of 100 times and get 55 heads and 45 tails. If you wait long enough. the balance will correct itself with probability unity. But what if you choose a fixed number of tosses, say a million. What will the number of heads and tails be (given that there was an imbalance after 100 tosses)?

   Let us ask similar questions about rolling a die (with six faces). Count the cumulative numbers of each occurrence of each face. What is the probability that however long you throw the die, the six numbers even out at some stage?

Week of March 30

1. Deadline for submitting the title of your project: Tuesday, April 7.

2. The New England Section meeting of the APS/AAPT/SPS is this Friday and Saturday, April 3 and 4. The talk by Ernest Prabhakar is at 2 pm, and our mini-computer show is from approximately 2:45 - 4 pm. If you are going to participate in the show, please show me a demonstration of the software that you will show.

3. The next laboratory report is due Friday, April 10. The subject is open. Some suggested problems include 11.6, 11.8, 11.3, 12.9, 12.19, and 13.1.

4. If you have done so already, start making a simple Web page for yourself. It is up to you whether you wish to link it or not. A simple example is available. The idea is for you to learn some simple HTML.

Week of April 6 and 13

1. If you have not done so already, please send me email summarizing your project. Some additional suggestions for projects (specifically for Jeremy and Melissa).

2. Read Chapters 13 and 14 so that you become familar with the topics which we will discuss in class.

3. Deadlines: Next laboratory report is due by Friday, April 17 (deadline extended). If you write a progress report on your project in lieu of a regular laboratory report, follow the same format and be sure to write more than one paragraph. I would like to see your preliminary Web page by Tuesday, April 21.

4. There will be no class if the discussion occurs on Spree Day, but the laboratory will be open. I expect you to make up any missed laboratory time.

Week of April 20

1. The mini-poster session has been rescheduled for Tuesday, April 28 at 10 am. Refreshments will be served. We will meet in the usual room.

2. The final project report is due on Thursday, May 7, the last day of finals. I would be happy to look at your draft(s).

Suggestions for lab reports

1997 Assignments

Updated 23 April 1998.