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Phy 231
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Reply_to_Qs_in_Query_06_Notes
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I'm writing in response to your Notes (copied/pasted below) in your evaluation of my Response to the last Question in Query 06 (http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_09/levl2_62/02-20-2013_____PHY_231_query_06_submitted_20130219.htm).
-----[start Notes:]-----
Have you had a linear algebra course?
Did you study in precalculus or analysis how to use matrix products and inverses to solve systems of linear equations?
If no to the former I highly recommend it.
If no to the latter I can give you a link to my introduction to and synopsis of this from my Precalculus II course.
-----[end Notes:]-----
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I understand everything about the situation; I just wanted to answer your questions and ask two follow-ups (follows-up?) of my own.
1) I've never taken a linear algebra class, although I've probably encountered at least some of the subject matter in other classes.
2) I've never had an analysis class, at least by that name, and my precalculus class did not discuss matrices. My Algebra II course did introduce us to matrices, although we didn't learn to use their products and/or inverses to solve systems of linear equations. (The only ways to solve linear-equation systems that we learned, or at least the only ones that I can remember, were substitution and addition/subtraction, along with graphing as a visual heuristic to help us know what to look for and/or check the plausibility of the solutions that we'd found.)
-- When my PHY 201 professor mentioned that pressure is a tensor and that tensors are represented by matrices, I started thinking about matrices and realized that the only things that I could remember about them were that a) every matrix has something called a determinant and b) something called Cramer's Rule has something to do with the bottom right corner of the matrix. Seriously, that's ALL that I remembered, and I probably even messed up the part about Cramer's Rule -- that's what I get for spending so many study halls playing chess and/or MUDding.
-- - Of course, after that embarrassment, I consulted some online sources and re-learned (or, more likely, learned for the first time) a few properties and applications of matrices, so I'm somewhat more familiar with them now, although I'd probably still need to go back and check the sources to make sure that I'm doing everything properly.
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1) Although I don't expect to have enough time to take a linear algebra class any time soon, I'd enjoy reviewing a textbook and/or some online materials. Can you recommend any specific ones?
2) Would you please send me the URL (for the introduction and synopsis from your Precalculus II course) that you mentioned?
Thanks!
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The reason for my questions is simply to know what your status is so I can refer you to the relevant pages in my webs.
Interestingly one of my former students, who worked for me during summers while in undergraduate and his first year of graduate school, and has come by regularly since, came by today to confuse me with some of his PhD research (he should finish up his math PhD at UNC next spring). He took my multivariable, differential equations, linear algebra and calc-based physics courses while still in high school, and he's working on some pretty far-out stuff right now. He commented that he and other grad students had concluded that most of they, and most research mathematicians do ends up being to reduce very abstract and involved problems to multivariable calculus, linear algebra and combinatorics.
The Class Notes for my precalculus course are at
http://vhcc2.vhcc.edu/pc2fall9/frames%20pages/class_notes.htm
#'s 17-22 address matrices, along with some extraneous material
#'s 22-26 are largely about combinatorics
If you email me to prompt me to do so while I'm on campus (or if I remember when I'm there), I'll send you a copy of the DVD that contains these lectures. I have your mailing address from the lab form.
The Precalculus II homepage is at
http://vhcc2.vhcc.edu/pc2fall9/frames%20pages/mth_164_homepage_menu_driven.htm
The qa's are on the assignments page and the brief assignments page. #'s 13 - 15 address matrices.
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