Intuition Definition and 276 Threads

Hi, The change of variables theorem states that given a diffeomorphism g:A \rightarrow B between open sets, and a continuous function f:A \rightarrow R, then \int _A f = \int _B f \circ g |Det Dg| given that either one of the integrals exist. I was wondering if anyone here could help explain...

you ever felt like math was more then just something to use or more then what's outside your work experience, and you just want to explore it and see how it all works; connecting it to things. even using it as makeup; everything. And then you go into the class; and you get failing grades...

Intuition check--tiling a 3-sphere with 16 tetrahedra Lately I've been trying to understand/visualize the geometry of a 3-sphere (been hanging out in the cosmology section), and I think I'm getting it, at least to some extent. Intuitively, I think a 3-sphere can be tiled by 16 tetrahedra...

Hi I want to make sure my intuition is correct about the buoyant force. What I am confused by if we take a cube or some sort of object and its submerged at height H1 as in picture I uploaded,then their will be a force of P1 * A; in case of the cube it's it would be d^2. What I don't understand...

Hi, I just want to make sure my intuition is correct for why capacitors add normally when placed in parrallel and add reciprocally when placed in series. In parrallel they add normally for example C = C1 + C2 + C3; Because when placed in parrallel the right hand plate share same...

Homework Statement I attached a picture of a sample problem that I was confused about. What I don't understand is why the V2 voltmeter would read 0 volts (according to the answer key). This is because I thought that an inductor produces an induced emf and current. So wouldn't the voltmeter...

This is probably a trivial problem, but I can't get it straight. It's well known and easy enough to show mathematically that the change in enthalpy for the reversible isothermal expansion of an ideal gas is always zero, ΔH=0. But it's also true that the enthalpy change for a process at constant...

Hi All, I am an idiot but I don't understand the parallel transport: Parallel transport should be in surface right? How to keep parallel and still be in surface?

Hi all, I've been digging around in Google as well as searching under physics forum for a while now but I still can't find the answer to my question. If there is already an answer then I'm sorry for wasting the server bandwith and database harddrive usage I learned the formulation for...

A scalar field is conservative, i.e. the line integral does not depend on the path taken, if it has a gradient. Now, can someone give me intuition behind why the gradient would have something to do with this? :) For me the gradient is merely a way of writing up the partial derivates as...

Question : How do i convert an infinite series into an integral? I searched a few sites and the method given is as follows replace r/n by x repalce1/n by dx replace Ʃ by ∫ which works perfectly fine when i tried a few examples but i don't understand the intuition behind it. Why this...

So I took an analysis class which covered chapters 9 and 10 of Rudin's PMA, for those of you who don't know that's multivariable analysis and differential forms, and I have taken a course in vector calculus but never a proper course on differential geometry. Thus my introduction to the subject...

Can someone give me the intuition behind not using time as a parameter for a Cycloid.

I came up with last night and I couldn't figure it out. Can you actually predict what happens in a collision? For instance, suppose a truck and a toy duck is coming from opposite ends, they both have a velocity, now suppose they crash, it should be obvious that the collison isn't going to...

Can anybody tell me tips on how I can develop intution in mathematics. I am Senior. I get great score, but I want to push up limits, i.e. I want to be fast and accurate and also do math questions without any paper. ...

So, when we are talking about geodetic precession, my intuition tells me that the angular momentum vector of the spinning particle should be parallel transported along it's orbit. Because parallel transport of a vector around a closed loop doesn't reproduce the same vector, then the parallel...

This is another simple problem that I have probably over thought on and now have some questions. I am given that the initial velocity of some mass m's vector is v_i = x1 i + y1 j and that its final velocity vector is v_f = x2 i + y2 j. I am then asked to find the net work done on the object...

Hi My calculus textbook is completely crap at explaining recurrence relations. I know the theorems needed to solve difference equations analytically, but I do not understand why they are true. What websites and/or books can I read to get a better intuitive understanding of recurrence...

This has been a curiosity of mine lately. I am wondering about what makes an algebra person an algebra person. I know geometers(at least it seems like it) seem to have a keen ability of spatial visualization. What characterizes the abilities of an algebra person? To clarify, I'm not just talking...

Homework Statement Q1) Suppose the mass of object A is greater than that of object B and that it is moving towards B, which is at rest. Will: A. Object A exerts a larger force on object B B. The objects exert the same size force on each other C. Object B exerts a larger force on object A...

You are no doubt familiar with Heisenberg's uncertainty principle, putting a limit on the accuracy with which we can measure a particle's position and momentum, \Delta x \Delta p \geq \hbar/2 On my course I was shown the derivation, it popped out of a few lines of mathematics involving the...

I'm curious if anyone has and physical intuition that would lead to non commutative geometry? I mean on one hand we have NCG as a branch of math, which explores what mathematics you get if you try to replace som commutativity requirements in normal geometry etc. This may or many not interest...

Hi, I'm currently taking Introductory Mechanics, and the more I progress into this class, the more I realize that I have no intuition when it comes to relating physics to real life. The actual class is pretty easy for me, but the lab is killing me. The hardest questions for me are "What...

From a locked thread: 1)When the car goes forward we tend to go backward and our back is pressed into the sit, so I'd say the balloon does the same, i.e. goes backward. It would be counter intuitive if it went the other way. 2)I have to use common sense here, pure intuition would leave me...

I probably can remember the matrices by just trying to, but I hate having to "remember" things without actually understanding them. Is there no intuition behind these matrices so that I can remember it (the intuition) and then from it produce the wanted matrix? To me the matrices look like...

Hi, although I've studied info theory briefly in the past, now revisiting it, I seem to be scratching my head trying to understand the counter-intuitive logic of it. For instance, I understand that the amount of uncertainty associated with a symbol is correlated with the amount of...

Homework Statement This is not really a homework problem. I'm just trying to learn about tensors by myself. I'm new here (This is only my second post). From what I could gather from the forum rules this seems to be the place for my question. I went through literally hundreds of websites...

I know that it corresponds to the 1/r^3 term in the Taylor series expansion of the gravitational force. But Taylor series expansions can't give me any physical intuition. By physical intuition, I mean that I want to know why the coefficients for the 1/r^3 term are the way they are.

Hi there! I have a hard time getting any sense out of what the sandwich: <q'', t'' | Q(t1) | q', t'> where t' < t1 < t'', actually means.. If we skip Q(t1) we get the usual transition amplitude. But how should i interpret this when we use an operator that is timedependet but act on a...

Homework Statement I'm just looking for ideas, like how to proceed with various problems and how to counter them. Almost all problems I have encountered so far haven't been very much like the examples, but instead kind of vague and dependant on trigonometry and vectors. Right now I'm stuck...

Force vectors Nevermind, I figured this one out. Homework Statement There's a pole standing straight in the ground, it is kept stable by two wires so the problem in the textbook looks kind of like a 60 triangle with the pole cutting it in half. One of the wires are longer though, and there...

I want to preface this by saying that these questions are not to find an exact answer, just to build intuition. If you find them ill-posed or incorrect, it would be most helpful if you could show me a "better way" of looking at it. So, I'm trying to gather a geometric viewpoint of...

Homework Statement a rope wraps around an angle theta around a pole. You grab one end and pull with a tension T. The other end is attached to a large object say a boat. If the coefficient of stating friction between rope and pole is mu, what is the largest force the rope can exert on the...

Greetings. For your information, I am an undergraduate college student studying electrical engineering and also intend to get a degree in particle physics. At this point in time I am only beginning to learn calculus. For the past several years I’ve been watching television documentaries...

RE-EDITING POST: I had misread some of my notes. :redface:

Can anyone give me some intuitive arguments about why all the accessible microstates of the system are equally likely in equillibrium state.

Starting on the topic of the Lagrangian, I have been told not to try to make intuitive sense, but just accept the nice differential equations which it goes into. Fine, but it should at least make basic sense. That L= T-V should be stationary means then d(T-V) = dT-dV = 0, i.e., dT=dV, which...

hey, What is physical intuition? How do we use it in physics?

We know the winding number as a curve winds round a point.If a point is inside a closed curve,then the winding number is 1,this is the geometrical intuition. The definition of winding number of closed curve gamma with respect to a is n(\gamma ,a) = \frac{1}{{2\pi i}}\int\limits_\gamma...

When I learn something, especially in calculus, I like to get some intuition on where things come from and why they work, thing is I can't quite fully understand why the jacobian works...I'm not looking for an explanation on how to do it, I already know that, I just want to know why it works, if...

Hi all, Sorry if this is a dumb question, but what exactly do we mean by the term parallel transport? Is it just the physicist's way of saying isometry? Also, in my class we have just defined geodesics, and we're told that having a geodesic curve cis equivalent to demanding that the unit...

when i have a system of only dependant sources and i want to find its norton /thevenin representation i need to add a testing source on the ports from whome we want to see the reaction how to know that i should put a voltage source or current source ?

question: so here is what my problem is. there are two dielectrics between a parallel plate capacitor. distance between the two plates is '2s' and each dielectric is 's' long. each plate has a charge of \itshape \sigma (top being pos. and bottom being neg. and doesn't give an area) how would i...

Ok so I am not a math major and i haven't taken an abstract algebra class but i am curoius about the subject. I have been watching video lectures at UCCS at http://cmes.uccs.edu/Fall2007/Math414/archive.php?type=valid and the proffessor talks about groups and rings. In the introduction the...

One way to add two fractions is to multiply the numerators of both fractions with each other's denominator, then adding the two products, gives us the numerator of the final result. Then we multiply together the denominators of each other--this gives us the denominator of the final result...

Excuse the newby question, but this is bothering me... Could someone explain to me why two identical batteries when connected in series do not form internally a circuit between the touching positive end of one battery and the touching negative end of the other and proceed to short the ends in...

Books to build "physical intuition" All physicists say that it is very important to have this thing called physical intuition. I have a general idea what it means but I don't quite fully get the subtleties between physical intuition about a topic in physics versus understanding the equations...

So how should I approach more difficult math? On a lower math level it is possible to really understand a certain property, relation, formula, ... you can see where it's coming from: intuitive and/or by quickly derivating it in your head. But as the math becomes more difficult, this...

Hi all. I recently picked one of my favorite math books out of my closet and started flipping through it again (Gamelin & Greene's Intro to Topology). I'm continuing through the second half now, which is on algebraic topology. But there was one thing that I never quite "got" in point-set...

I'm new. Now you know. I'm also in the second year of an undergraduate nanotechnology engineering program at a Canadian university, taking a first course in quantum mechanics and simultaneously an advanced (sic) calculus course. The overlap between Hilbert Spaces and Fourier Series /...