Tom Mattson

True' date=' but that problem has been solved by QFT. The Standard Model gives a quantum theoretic account of 3 of the 4 known forces, and work is being done on the 4th. That remains to be seen. Quantum theory has made the only advances in describing a quantum of light. Maybe I missed it, but when you say "complex mathematics" do you mean "complex-valued functions and/or complex variables"? If so, then QM already makes use of that.

OK from your attachment I can tell that I was right. Here we go. This is a rational function, so it should scream "PARTIAL FRACTIONS!" That means you've got to factor the denominator, which factors into 2 irreducible quadratics. Try that, and if you get stuck post what you have and we'll get you un-stuck. You have a quadratic under the radical, which means that you want to do a trig substitution. But you don't have either a sum or difference of squares under there, so you have to complete the square and try to work the radicand into one of the 3 forms that is amenable to trig sub. Try that, and again if you get stuck post what you've got and we'll nudge you.

That doesn't mean anything. Calc 3 is more of a continuation of Calc 1 than Calc 2. The fact that he couldn't do the problems quickly is simply an indicator that he is doing different stuff now' date=' and that the summer was long and fun. I would expect that an average Calc 2 student can solve Calc 2 problems better and more efficiently than an average Calc 3 student. As for your problems, I'm with ecoli. Buddy, you've got to learn LaTeX. Let me see if I can decipher these. OK, now I'm almost certain that you meant this: [math]\int_0^1\frac{2x^3+5x}{x^4+5x^2+4}dx[/math] And here I *think* you mean this: [math]\int\frac{dt}{\sqrt{t^2-6t+13}}[/math] Tell me if I'm right on those, and we'll go from there. If you want to know how I did that, you can click on the equation and the source code will pop up.

The deBroglie relation is: [math]\lambda=\frac{h}{p}[/math], not [math]\lambda=\frac{h}{mc}[/math].

I don't see why there is an equals sign between the last two integrals. Surely if you are cutting the region of integration at zero, you must add the two integrals, right? I would think that it should be either this: [math]\int_{-\infty}^{\infty} |x|^{|x|} \, dx = \int_{-\infty}^{0} (-x)^{x} \, dx + \int_{0}^{\infty} x^{(-x)} \, dx[/math] or this: [math]\int_{-\infty}^{\infty} |x|^{|x|} \, dx = 2\int_{-\infty}^{0} (-x)^{x} \, dx = 2 \int_{0}^{\infty} x^{(-x)} \, dx[/math]

The answer depends entirely on which convention for mass you choose to adopt. Just about every particle physicist and relativist out there rejects the idea of "relativistic mass" and instead adopts the convention that mass is the (Lorentz invariant) norm of the 4-momentum, in natural units. In this convention light has no mass, period. And since that is the convention used by the great majority of physicists, I would advise adopting that one.

What are you interested in studying?

I can only assume that you are talking about those electric circuit elements that are known as resistors. If so, then what do you mean by "accepted resistance"? Are you talking about the nominal value? If so then it's easy to determine that: You read it off the resistor (note that the rating could be reported as a color code). And as for determining the observed value, you connect a Ohmmeter to it and you measure it.

That was a typo. It's fixed now.

What is so difficult about reading the problem statement? Are the terms "dowel" and "lamination" and "eye ring" really so technical as to make it impenetrable? These are things that the clerk at your local hardware store knows about. The first option says that you have to build car whose sole source of energy is a 2kg mass. Obviously that statement is there to prevent you from strapping a 400 hp V8 to the back of the car and blowing away the competition. The second option says that you have to build a tower with a block on top, and that the block has to support a load which hangs down the center of the tower. There are size constraints, which you can make sense of if you try to draw a picture from them, which should have been the first thing that you did. Have you tried that?

When you're asked to prove things, you are supposed to identify what you can assume and then identify a goal. Look at what you are being asked to do. Prove that there exist an invertible matrix P such that B=P-1AP is upper triangular. Assume that P and A are 2x2 complex matrices, and that the product in the problem statement (which is equal to B) is upper triangular. Prove that the matrix P exists and is invertible. So start by writing down general matrices P=[pij], A=[aij], and B=[bij] (just remember that b21=0). Do the multiplication, determine the pij in terms of the aij and bij, and show that the result is invertible.

Start by writing down a general 2x2 upper triangular matrix: [math]A=\left[\begin{array}{cc}a&b\\0&c\end{array}\right][/math] where a,b,c are complex numbers. Now, under what conditions is a matrix not diagonalizable?

A Physics Forums Member (Loren Booda) posted a link to this site on PF, and like a stray puppy I followed it. Will you be my friend?

But it's plainly obvious that you've never studied it!

He's talking about the velocity with which gravitatioal effects propagate. Case in point: The Sun is 8.3 light minutes away from Earth. If the sun were to suddenly vanish, would we fly away from our orbit instantly? 8.3 minutes later? Some other time? The answer would depend on the velocity of gravity.

Light doesn't get excluded at all. Light is described by the same relativity that describes massive bodies.

Causality is violated by faster-than-light travel in a relativisitic universe. And since we live in a relativistic universe, well you can take it from there. Ultimately forces are interactions that are mediated by gauge bosons. We know a enough about the EM, strong, and weak interactions to know that they do not exceed the light speed barrier. That leaves one force: gravity. Efforts are currently underway to measure the speed of gravity and analyze the results. If it is found that gravity travels at the speed of light, then my reply to your question would be this: We say that forces can't travel faster than light because they don't travel faster than light.

Physicists are concerned with that. The predictions of relativity work because we live in a universe in which no inertial observer's claim to reality is preferred over that of any other. Any prejudice against that idea can only come from judgments which are tainted by everyday experience. Admittedly, everyday experience is very persuasive, but it is also misleading.

Why would you require a mechanism? No, relativity was built to predict results.

If a neutron is alone byitself, will it be able to bind electron(s)? Free neutrons only have a mean life of about 15 minutes before they decay into protons. So to your question I say yes, if you wait a little while.

Consistent with what? You talk about this gravitational influence on particle decay as if it is a well-established theory. But it's really just your ad hoc proposal to account qualitatively for that which relativity can already account for qualitatively and quantitatively. You have no idea if the experimental results are consistent with this proposal until you calculate the effect and compare it with measurements.

P-chem covers quantum mechanics. Since your average chemistry student does not take an intermediate course in mechanics, embedding in p-chem a crash course in classical mechanics is pretty standard.