Using VPython to Apply Mathematics to Physics in Mathematical Methods

Using VPython to Apply Mathematics to Physics in Mathematical Methods PowerPoint PPT Presentation


  • 234 Views
  • Uploaded on
  • Presentation posted in: General

The course:. Mathematical Methods for physics at the College of the Holy CrossFirst semester Sophomore physics course, 11 students (9 of which are physics majors)Course contains few examples of applying math to physical situations (due to intense schedule)VPython is new to Holy Cross physics 650

Download Presentation

Using VPython to Apply Mathematics to Physics in Mathematical Methods

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


1. Using VPython to Apply Mathematics to Physics in Mathematical Methods Dedra Demaree, James Eagan, Patrick Finn, Brian Knight, John Singleton, Alfred Therrien The College of the Holy Cross

2. The course: Mathematical Methods for physics at the College of the Holy Cross First semester Sophomore physics course, 11 students (9 of which are physics majors) Course contains few examples of applying math to physical situations (due to intense schedule) VPython is new to Holy Cross physics 650 Course Points: 90 from VPython 110 from homework, 300 from 3 midterms, 150 from final Programming homework worth 45 points, independent final programming project worth 45 points 4 class hours devoted to programming in a lab Only one student claimed to have prior programming experience, though there were indications that more of them may have

3. What we did: pre-written activities Followed activities from pre-written workshop exercises borrowed from the VPython workshop run by Ruth Chabay and Bruce Sherwood Introduction to VPython: Students modeled balls, vectors, and a static planetary system Modeling motion: Students modeled a cart moving on a track Planetary motion: Students modeled orbits and a binary star system Simple Harmonic Motion: oscillating mass on a spring

4. What we did: beyond pre-written activities Pre-written activities guided students with code for learning the programming language, and with specific steps to help students see how to program the physics equations The simple harmonic motion program gave less guidance – it was used as a bridge toward independent programming The last programming homework was to model a simple pendulum, minimal instruction was given Students completed independent final projects in the areas of astronomy, motion of solids, electric and magnetic fields, and oscillations

5. Survey Responses: How did you like using VPython All students stated they liked using VPython Some students commented they felt it helped see links between math and physics, but others commented they liked it but found it irrelevant A few students stated it was a fun alternative to other assignments “Liked it, helpful for understanding both computer programming as well as how physics can be applied to actual phenomena” “Neat being able to program simple systems and see the results of the physics” “Easy enough, didn’t seem relevant” “Very cool”

6. Survey Responses: Did you find it easy or hard to learn? Most students felt that overall it was easy at least when using the packets from the workshop, Some found it easier with practice, others found it harder as assignments got more involved “Easy using guided sheets, but difficult with more vague instructions, still usable and enjoyable” “First programming packet was easy, the difficulty from there skyrocketed” “Learning the language was hard and frustrating at times in the beginning, became easier as we worked more with it” “Relatively easy because directions were clear”

7. Survey Responses: Did you think the program output was worth the time you put into writing it? Most students stated the output was worth the time Some specifying that although they were sometimes frustrated, the output was very interesting and gratifying “Very much so, programs were amazing and interesting once they worked” “Output were pretty cool and didn’t put too much time into it, so yes” “Some seemed not worth the effort, but later exercises built on them so it became more worthwhile” “I think it was worthwhile but didn’t seem to be related to the course

8. Survey Responses: Did you think it was a useful part of this course? Most students thought it was useful to program, but not particularly useful in this course “Yes because it focused on visual physics concepts and not just abstract mathematics” “Related little to course material, but it did show a method for modeling” “Not useful in the course” “Not really useful because physics was unrelated, however it could be good in general physics” “Not sure, but it was interesting”

9. Survey Responses: What would you have liked to have seen done differently with VPython? Students wanted more connection with course material, and more general instructions on the programming language Some wanted a more gradual bridge to independent programming “More connections between class and VPython” “Program a real system like a damped pendulum” “Coordinating lessons with programs, have a manual to help with programming” “Longer introduction with explanation of commands” “More gradual decrease in instructions”

10. Specific Examples: James (Jimmy) Jimmy’s project was to calculate the electric field outside a uniformly charged cube and represent it with field vectors evenly spaced around the cube He was able to represent the field around a point charge, but did not extend that to a spatial integration around a charged object to represent a cube

11. Specific Examples: Patrick (Pat) Pat’s program modeled a mass hanging via two springs in a gravitational field, free to move in three dimensions Pat had extensive programming experience before, and did not need any guidance with his project

12. Specific Examples: Brian Brian’s program modeled two moving masses attached to each other and two walls via springs (with no gravitational field) Brian had difficulty fixing both the endpoints and the lengths of the springs, but his masses moved with the correct physical equations

13. Specific Examples: John (Jack) Jack is the only student who took the initiative to completely design his own project His program represents the classic e/m experiment with charged particles circling in a magnetic field created by Helmholtz coils His program represents a Tau particle and a Proton He first used a proton and an electron and thought his program had a bug because the proton did not circle – however, this was due to the large difference in e/m values for those two particles He added “particle guns” just for fun

14. Jack:

15. Specific Examples: Alfred (Terry) Terry modeled a ball rolling down the inside of a circle under the force of gravity He had difficulty constraining the motion of the ball without explicitly defining one position coordinate in terms of the other and the radius of the circle

16. Conclusions and Observations: Students enjoyed VPython, and it seemed a good introduction to programming Most students did not realize they were doing basic numeric integration, despite instructions in workshop packets and reviewing this in lecture Mathematics and physics done in VPython were more consistent with the general physics level than with Sophomore level physics However, it seemed many students benefited from applying general physics to programming as a review of concepts Programming could be more integrated into the course material

17. Abstract At the College of the Holy Cross, the sophomore mathematical methods of physics students completed VPython programming projects. This is the first time VPython has been used in a physics course at this college. These projects were aimed at applying some methods learned to actual physical situations. Students first completed worksheets from North Carolina State University to learn the programming environment. They then used VPython to apply the mathematics of vectors and differential equations learned in class to solve physics situations which appear simple but are not easy to solve analytically. For most of these students it was their first programming experience. It was also one of the only chances we had to do actual physics applications during the semester due to the large amount of mathematical content covered. In addition to showcasing the students’ final programs, this poster will share their view of including VPython in this course.

18. Survey Responses: How did you like using VPython All students stated they liked using VPython Some students commented they felt it helped see links between math and physics, but others commented the liked it but found it irrelevant A few students stated it was a fun alternative to other assignments Liked it, helpful for understanding both computer programming as well as how physics can be applied to actual phenomena Easy enough, useful, didn’t seem relevant Liked it very much, put practical use to theory learned in class Fun, nice break from other work At first skeptical, easy to work with, nice change of pace Neat being able to program simple systems and see the results of the physics Beneficial, simple enough, very physical Enjoyed it, first experience in programming, interesting Liked it a lot, great insight into computer modeling and learning how to program “Very cool”

19. Survey Responses: Did you find it easy or hard to learn? Easy using guided sheets, but difficult with more vague instructions, still usable and enjoyable Very easy although help files in VPython weren’t very helpful Basic steps easy to learn with worksheets, frustrating that a little error would cause the program to not run First programming packet was easy, the difficulty from there skyrocketed Easy Learning the language was hard and frustrating at times in the beginning, became easier as we worked more with it Hard, early packets were easy but abruptly changing to no instruction was hard Relatively easy because directions were clear Would have been easier if there was a sheet with a list of commands Hard to learn because wasn’t used to it and didn’t know all of the commands Wasn’t that difficult once I got a pointer as to how to start

20. Survey Responses: Did you think the program output was worth the time you put into writing it? Definitely worth it, though occasionally something small and seemingly unimportant caused the program to run incorrectly taking much more time than necessary Pretty happy with pendulum, other programs seemed tedious Very much so, programs were amazing and interesting once they worked Don’t think I got anything out of it except a break from regular homework Output were pretty cool and didn’t put too much time into it, so yes Some seemed not worth the effort, but later exercises built on them so it became more worthwhile Yes because it gave us computer skills using physics, was both mathematical and physical Yes for the most part, most didn’t take too long Yes, expected it would take some time based on other computer work I like these kinds of things but it could have been difficult and frustrating for anyone who had no experience programming I think it was worthwhile but didn’t seem to be related to the course

21. Survey Responses: Did you think it was a useful part of this course? Yes, very beneficial Not particularly Not sure what was covered in class was used in Vpython, however it introduced something new and interesting Not useful in the course Did not have to do with the physics we were doing that particular semester Not really useful because physics was unrelated, however it could be good in general physics Yes because it focused on visual physics concepts and not just abstract mathematics Not sure, but it was interesting Related little to course material, but it did show a method for modeling Weird doing programs that had little to do with the class More useful for general physics, Maple would be better for this class

22. Survey Responses: What would you have liked to have seen done differently with VPython? Better to have the final project earlier in the semester More connections between class and VPython Coordinating lessons with programs, have a manual to help with programming More time using packets since it is tough to learn More relevant physics problems to program Give explanations about the programming language More gradual decrease in instructions More applications to the class in programs Program a real system like a damped pendulum Longer introduction with explanation of commands Program using math learned in the class instead of simple topics from general physics

  • Login