SparklyUnicorn Posted December 9, 2017 Share Posted December 9, 2017 What is the point? What is this used for? I find the big picture and the "why in heck" to be useful. Instructor spends 100,000 years talking about the proofs and zzzzz....I believe you it works (and I'm not smart enough to argue). But what is it for? Quote Link to comment Share on other sites More sharing options...
regentrude Posted December 9, 2017 Share Posted December 9, 2017 (edited) Taylor series expansion for example. you probably have encountered this in calc. You can approximate any function by a series of polynomials involving the function's derivatives. That's how your calculator calculates functions inside. It also allows to obtain information about very complex functions through approximations in the vicinity of interesting points. There's tons of physics applications. Edited December 9, 2017 by regentrude 2 Quote Link to comment Share on other sites More sharing options...
regentrude Posted December 9, 2017 Share Posted December 9, 2017 btw, this is not a dumb question at all! 1 Quote Link to comment Share on other sites More sharing options...
regentrude Posted December 9, 2017 Share Posted December 9, 2017 Let me give you an example. There is a model for the force between two atoms in a diatomic molecule. It's rather complicated and by looking at it you cannot really see what all it does. But you know that there is one distance for which the atoms are perfectly in equilibrium and neither repel nor attract each other. If you do a Taylor series expansion around this particular point, you find that in the vicinity of this equilibrium the force behaves exactly like an elastic spring that makes the particles oscillate about the equilibrium, and from the parameters of the force you can immediately read off what the period of such an oscillation would be, without doing complicated calculations. This is really useful and cool stuff. 3 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted December 9, 2017 Author Share Posted December 9, 2017 wow, now that's interesting Quote Link to comment Share on other sites More sharing options...
luuknam Posted December 9, 2017 Share Posted December 9, 2017 This site looks interesting: https://plus.maths.org/content/teacher-package-series 1 Quote Link to comment Share on other sites More sharing options...
Caroline Posted December 9, 2017 Share Posted December 9, 2017 (edited) So I’m teaching this right now in my BC class. (Sparkly, you aren’t really a 16 year old girl are you? Just kidding.) It’s not a dumb question, and I love regentrude’s answers. I just taught the integral test for convergence Thursday. Then we got 6 inches of snow yesterday, which in Georgia means we send everyone home from school. Monday, we will be continuing with p-series. I will admit that when I took the college class on sequences and series (beyond what we do in calculus class, the 4000 level one) I decided that I really didn’t need that double major. One of my students whose mom was a math major said his mom said she almost changed majors after that class. I can still picture that book (which I am sure is on a shelf in my basement) by Boyce and DiPrima. Edited December 9, 2017 by Caroline 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted December 9, 2017 Author Share Posted December 9, 2017 So I’m teaching this right now in my BC class. (Sparkly, you aren’t really a 16 year old girl are you? Just kidding.) It’s not a dumb question, and I love regentrude’s answers. I just taught the integral test for convergence Thursday. Then we got 6 inches of snow yesterday, which in Georgia means we send everyone home from school. Monday, we will be continuing with p-series. I will admit that when I took the college class on sequences and series (beyond what we do in calculus class, the 4000 level one) I decided that I really didn’t need that double major. One of my students whose mom was a math major said his mom said she almost changed majors after that class. I can still picture that book (which I am sure is on a shelf in my basement) by Boyce and DiPrima. LOL Just curious, what is a 4000 level course? I'm not familiar with this type of course numbering. I'm a 43 year old girl... :tongue_smilie: 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted December 9, 2017 Author Share Posted December 9, 2017 I found an explanation for 4000 level on-line. I wonder why some schools use thousands and others hundreds. Huh... Quote Link to comment Share on other sites More sharing options...
luuknam Posted December 9, 2017 Share Posted December 9, 2017 (edited) I found an explanation for 4000 level on-line. I wonder why some schools use thousands and others hundreds. Huh... Not sure, other than it gives access to more course numbers. So, if the first digit is for level (freshman, sophomore, etc), and the second digit is for credits, then with 3-digit course numbers you'd have only 10 numbers left, which at a bigger school offering a lot of courses in a topic might be too few. So, at the school I attended, CS1337 for example was a freshman level computer science course which'd get you 3 credit hours. Plus, having 4 digits allowed them to spell out leet. :laugh: https://en.wikipedia.org/wiki/Leet ETA: I think at some (all?) schools using 3-digit course numbers the course number doesn't tell you in any way how many credits the course was. Edited December 9, 2017 by luuknam 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted December 9, 2017 Author Share Posted December 9, 2017 Not sure, other than it gives access to more course numbers. So, if the first digit is for level (freshman, sophomore, etc), and the second digit is for credits, then with 3-digit course numbers you'd have only 10 numbers left, which at a bigger school offering a lot of courses in a topic might be too few. So, at the school I attended, CS1337 for example was a freshman level computer science course which'd get you 3 credit hours. Plus, having 4 digits allowed them to spell out leet. :laugh: https://en.wikipedia.org/wiki/Leet ETA: I think at some (all?) schools using 3-digit course numbers the course number doesn't tell you in any way how many credits the course was. ah I can imagine larger schools probably use the 4 digits? My uni wasn't super small though. Quote Link to comment Share on other sites More sharing options...
regentrude Posted December 9, 2017 Share Posted December 9, 2017 (edited) we recently switched from 3 digit to 4 digit numbers because we ran out of numbers. each department uses some kind of coding for their courses: ends in 9 =lab, ends in 5= for non majors etc. No code for number of credits though. Edited December 9, 2017 by regentrude 3 Quote Link to comment Share on other sites More sharing options...
vonfirmath Posted December 14, 2017 Share Posted December 14, 2017 ah I can imagine larger schools probably use the 4 digits? My uni wasn't super small though. Texas A&M doesn't. http://catalog.tamu.edu/undergraduate/appendices/texas-common-course-numbering-system/ But yes, 3 digit course numbers don't have the number of credits for the course in the course numbering system Quote Link to comment Share on other sites More sharing options...
kiana Posted December 14, 2017 Share Posted December 14, 2017 I still remember when I took DiffEq. It had been several years since my last calculus class (I dropped out) and the series solutions of differential equations absolutely murdered me because I had forgotten absolutely everything about series. Quote Link to comment Share on other sites More sharing options...
Arcadia Posted December 14, 2017 Share Posted December 14, 2017 I used infinite series for engineering though my husband’s field of engineering use it more than mine. I can still picture that book (which I am sure is on a shelf in my basement) by Boyce and DiPrima. Elementary Differential Equations and Boundary Value Problems? We bought an old edition for $3 at Half Price Bookstore. Quote Link to comment Share on other sites More sharing options...
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