I'm in a Second Course in Linear Algebra this semester, and we've just been introduced to the idea of a dual space, dual vectors and briefly to a double dual space. I completely understand how all of these things work and how they're defined, but I don't understand why we care.
I've been...
This is a ridiculously easy question, so I apologize for bugging you all with it, but google has been less than helpful.
Consistently when I watch videos of rocket launches I hear operators talking about propellant utilization being active (usually with individual stages singled out). What does...
I just got back a test and I received 0 for the following problem. I am (somewhat) comfortable with the idea that my justification isn't good enough, but I'm a little unsure where my error is so I would love to have someone illuminate that for me.
The problem was to show that the gcd(a,b) =...
Hi all,
I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out on some larger matrices, but I don't really want to go through the hassle of row reducing a couple of 10x10 matrices to double check my program.
Does anyone happen to know of...
Hello all,
I'm not really a programmer at all, but I learned c++ for a while so I can do basic stuff. Having just finished my linear algebra class I suddenly had an urge to write myself a simple matrix solver. I knew it wouldn't be easy (especially because of my lack of skill) but I was...
I just had my last Linear Algebra class, and I didn't get a chance to ask the one question that has been bugging me ever since we started in earnest with matrices.
Why aren't there cube matrices? I mean, mathematical entities where numbers are 'laid out' in 3d not in 2d (not quite...
Hey all,
I haven't been alive for that long, so I guess my data probably isn't as good as it should be, but in my experience there have been far more noteworthy comets appearing only to the southern hemisphere, and not to the northern one. In fact, I haven't ever seen a comet (since I was a...
Hello,
I am just not satisfied with the following theorem (I don't know it's name):
Let T:R^n -> R^m be a linear transformation. Then T is one-to-one if and only if the equation T(x) = 0 has only the trivial solution.
The "proof" involves saying that if T is not one-to-one, then there...
For a long time I've wondered how you derive the equations of orbital motion from the law of universal gravitation. Recently I've been feeling like my mathematics knowledge has caught up to the point where I can attempt to do this myself, but I keep getting stuck at the same point and I was...
I recently received Why Does the World Exist by Jim Holt. I haven't gotten around to reading anything but the first chapter, but the book opens with a rather interesting paragraph:
The book then starts on a completely different note, and from my skimming it doesn't seem to treat this...
I have been wondering:
Given an arbitrary geometric shape is there a sequence of tests I can perform on individual parts of the shape to determine whether or not it is achiral?
I was hoping for something a little less trivial that simply seeing if the mirror image could be adjusted to...
Hey all,
I was working through some problems in my spare time when I realized that I wasn't so satisfied with my understanding of how to use Greens theorem with holes. Can someone refresh my memory?
More specifically:
Lets say I want to take the line integral in some vector field of a curve C...
We all know the ##\vec{i}##,##\vec{j}##,##\vec{k}## unit vectors for Cartesian space. But I've never been shown basis unit vectors in other coordinate systems.
Do basis vectors exist in other coordinate systems? And if so what are they?
Homework Statement
The problem is to prove the work-energy theorem: Work is change in kinetic energy.
Homework Equations
Line integral stuff, basic physics stuff.
The Attempt at a Solution
I'm given the normal definitions for acceleration, velocity and I'm given Newton's second law. I'm...
I feel really ridiculous asking for help online like this, but I don't have anyone to ask whose position is impartial, and so I'm turning to you guys.
I've been in a solid relationship for a little bit over a year now; I love my girlfriend, and she loves me. But over the last several months...
Hello all.
I'm doing a small presentation on Chirality in my Chemistry class. As the teacher knows I'm really more of a physics/math kid, he said it was okay if I did my presentation on chirality in physics instead of the molecular stuff most people are doing. I knew a bunch before, and I've...
I have become aware of a scandal that has developed in the last couple days regarding a particular costume in the Victoria's Secret fashion show (which happened this week I think), and I was hoping some people could help me understand parts of it. I'll link to pictures of the costume in question...
Homework Statement
Show (using the epsilon-delta method) that the ##\lim_{\substack{x\rightarrow a\\y\rightarrow b}} y = b ##
Homework Equations
Epsilon-Delta Definition
##\lim_{\substack{x\rightarrow a\\y\rightarrow b}} f(x,y) = L ##
means that for every ##\epsilon## > 0, there...
In the thread concerning the second Presidential Debate Russ_Watters just posted advocating tax cuts vs stimulus (edit: no longer there).
I want to see if I can start a debate on this, but I didn't want to sidetrack the original thread. So I'd like to ask this question here, hopefully some...
Hey,
Over the past month or so I've been teaching myself Latin in Rosetta Stone. It's been going steadily, and I hope to have the first level done by the end of the month.
By pure luck, I came across the notebook I kept in 6th grade when I took Latin for a semester (I had forgotten I had...
Hello all,
Cosmic Variance just had a great post up about Black Holes, wherein they were talking about something called the firewall, located at the horizon. I gathered it was a result of the Unruh Effect + Hawking Radiation, and CV seemed to say that this would cause anyone passing the...
http://postimage.org/image/urnvnzkhz/ [Broken]
I was watching a tv show (the astute watcher will recognize it as How I Met Your Mother), when I saw one of the characters holding this thing (the curved plastic measuring-thing).
My dad used to have one of those on his work bench, and I used...
I am trying to understand what generalized coordinates are but I'm having some trouble. After reading up on them a bit my best understanding of the idea of generalized coordinates is the following:
Because choice of coordinate system is arbitrary when solving physical systems (or anything for...
Hello all.
I'm teaching myself C++ (my first programming language), and as an exploration I decided to see if I could make a simple four-function calculator. The thing is I'm having trouble. I managed to successfully write a program that would input two integers and return all four functions...
For starters, I have no idea where to post this question but I think this is a good place.
Earlier today I bought a compressed can of moisture-less duster to clean my computer fans with. That is all good, but when I was done I wasn't sure where to dispose of the can.
Normally it would be...
Hello all.
I have a fairly rudimentary knowledge of matrices and broader linear algebra. This gets me in a lot of trouble when I'm following along the math of something fine and then I run into some matrix stuff and get stumped, like this. I'm a little bit confused on taking the inner product...
Is it fair to call the lorentz factor the derivative of measured time relative to proper time? I've seen the lorentz factor equated twice now to \frac{dt}{d\tau} and I wanted to know whether that was a legitimate way to look at it.
Thank you
In one of the early chapters of Gravity by Hartle, he is developing the line element on a sphere in preparation for developing the concept of a spacetime interval. Whilst finishing up the proof Hartle sort of implicitly says that if two lines are orthogonal the line element connecting two points...
Basically: I jump forwards, exerting an amount of energy enough to push me forward with some velocity.
But in my reference frame, I exert the same force, except the entire universe moves backwards with that same velocity, where did that energy come from?
I sort of know this has to do with...
Hello all,
I am looking for a good calculus-based textbook to self-teach Physics 1 from. I have Halliday but I find it slow-going and too tedious for me, not in depth but in repetition. I have already taken a Physics 1 class at my school, but my school's physics department is rather dreadful...