Notation Definition and 1000 Threads

I've been looking around a few places to try to understand some notation. I'm not sure exactly what to call it(set notation?) but basically things like g: [a, b] → R and stuff like that. I think it means something like g is defined on [a,b] in the real numbers, but is there a resource I can use...

1. The problem statement, all variables and given/known dat A car travels 20 mi at 60 degrees north of west, then 35 mi at 45 degrees north of east. Express each displacement vector in unit vector notation. Take the +x-axis due east and the +y-axis due north. Use the component method to obtain...

I'm new to bra-ket notation and am slightly confused; given an infinite square well with eigenvectors: \phi = \sqrt{2/a}\sin( (n\pi x)/a) And we assume the form: H |φ> = E_n |φ> How would you then represent φ in terms of a column matrix, because that what I thought |φ> represents. Given...

Hello all, I have a very quick quesion: (This is not a HW question, its simply a notation question) I need to show for f,g \in K[x] (where K is a field and K[x] is the set of polynomials) that deg(fg)=deg(f)+deg(g) and deg(f+g) \leq max\left \{ deg(f),deg(g) \right \} My question is...

Which course/book introduce asymptotic notation a deep and rigorious level, yet assume students did not know asymptotic notation before. It should nvolve proof of big O notation like superpolynomial and subexponenial.

This may seem a bit pedantic but I'm writing a report and have radicals in it and notice that some papers put the dot in different places, so my question is does it matter where you put the dot? thanks for any advice

Hi, doing Fourier series and noticed that with period $2\pi$ the coefficient formula integrates w.r.t. x (for f(x)) However adjusting for f(x) with period 2L, they write, for example: $ a_n=\frac{1}{L} \int_{-L}^{L}f(t) Cos \frac{n\pi t}{L} \,dt $. Why use that intermediate variable? I have...

Hi, I have a paper that for a gas mixture writes Ar/25%O2 implying that 25% of the atmosphere of the gas is oxygen. I have another paper that writes 0.02 mol frac O2 for a Ar/CO2 atmosphere. Please could someone tell me how I would write the 0.02 mol frac O2 in the form Ar/X%CO2 and what X...

Hi. I'm just starting QFT for the first time. I've just finished a course in relativity but I'm confused about the index notation I've found in QFT. Here are 2 examples yi = Σ Mij xj and yj = δij yi . These examples don't seem right after what I have learned in relativity unless the index...

Quick question, not even sure if I should post it here, but I can't think where else. If I wanted to write the short hand of A is an invertible matrix, would it be ok to just write A \ \exists A^{-1} ?

I'm not sure if this warrants a full post, but I am doing my homework and I came across notation I'm not familiar with. Skimming the chapter it's not in there either. It says "Draw W6" but W6 has a bar over it, like complex conjugate. What does this mean? I know what W6 looks like.

I am having trouble showing that ##(A_{ik}B_{kj})_{mm} = (A_{ki}B_{jk})_{mm}## Wouldn't the right side end up having a different outcome? Or can we assume its symmetric?

I am confused at why ##V_{i,j}V_{j,k}A_{km,i}## the result will end up being a vector (V is a vector and A is a tensor) What are some general rules when you are multiplying a scalar, vector and tensor?

If my understanding is correct the definition of a derivative is lim h->0 (f(x+h)-f(x))/h However, I've also seen this used: lim x->c (f(x)-f(x))/(x-c) are these both considered valid definition for the derivative or does the derivative have to tend towards zero? I am a bit confused because I...

Can anyone explain how to take the derivative of (Aδij),j? I know that since there is a repeating subscript I have to do the summation then take the derivative, but I am not sure how to go about that process because there are two subscripts (i and j) and that it is the Kronecker's Delta (not...

Homework Statement http://postimage.org/][/PLAIN] image url Homework Equations N/A The Attempt at a Solution I have to solve a different question using a similar method to this one but I cannot figure out how they got the sigma notation into the last equation format. I tried writing out the...

Homework Statement The Tensions in four cables are equal: |T1| = |T2| = |T3| = |T4| = T Determine the value of T so that the four cables exert a totl force of 12,500-lb magnitude on the support. (Inser a picture of 4 connected cables angled 9, 29, 40, 51 degrees respectively) My question...

Suppose we have a system of particles that interact via conservative forces. I wish to prove that ##K+U## is a constant of the system with tensor analysis. Here is my procedure: The Lagrangian is ##L=\frac{1}{2}m_i\dot{ r_i}^2-\Phi## Lagrange's equations ##\frac{d}{dt}(\frac{\partial...

°Thought just occurred to me.. Is there a standard way of referring to temperature either of a phase change? For example if I write.. "1kg of water is cooled from 20°C to 0°C, how much energy was removed?" ...then potentially two answers might be considered correct depending if you include...

1. The problem is: ( a x b )⋅[( b x c ) x ( c x a )] = [a,b,c]^2 = [ a⋅( b x c )]^2 I am supposed to solve this using index notation... and I am having some problems. 2. Homework Equations : I guess I just don't understand the finer points of index notation. Every time I think I am getting...

X5(p,α)X6 This is an equation/part of a question in my nuclear physics unit, where X5 represents the reactant nucleus and X6 is the product nucleus. The alpha symbol is most likely alpha decay, but I have no idea what it means in conjunction with 'p' like that. The rest of the question is: In...

Homework Statement See uploaded file. Homework Equations I guess one needs to keep in mind this: https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables The Attempt at a Solution Basically, my question is about the notation: 1) What does the subscript "ee" stand for in H_ee? And...

I've been working through some dirac notation and I'm stuck... Here's where I'm at: I understand that an expectation value: <x> = ∫ ψ* x ψ dx = <ψ|xψ> = <ψ|x|ψ> Also, we can say H|ψ> = E|ψ> where E is an eigenvalue of the operator H and |ψ> represents a state your acting on. I get that you can...

Should I sharpen up on using set builder notation? Like, will I ever need it in physics or calculus? I'm currently refreshing my skill at writing in Interval notation for inequalities and the like.

Dear PF Forum. I saw once that sinh-1(x) is arcsinh(x). The reverse of sinh Why not sinh-1(x) is 1/sinh(x)? While x-1 = 1/x Is it just a 'convention' between mathematician? Thanks.

Homework Statement A charged particle of charge q with arbitrary velocity ##\vec v_0## enters a region with a constant ##\vec B_0## field. 1)Write down the covariant equations of motion for the particle, without considering the radiation of the particle. 2)Find ##x^\mu (\tau)## 3)Find the...

I'm reading through one of my profs papers, or starting. Actually it's 2 of my old profs, one I had for linear and one I had for diff eq. My question is in Section 1 of this paper. "We begin with an analysis of a second order quasilinear partial dif-ferential inequality for real valued...

I just started learning index notation and I'm having some trouble understand what I'm allowed to do with it. For example we can write the ##\vec A \times (\vec B \times \vec C)## as ##\varepsilon_{ijk}A_j\varepsilon_{klm}B_lC_m##. I understand that ##(\vec B \times \vec C) =...

Hi there, I was reading up on Holonomic constraints and came across this equation on the Wikipedia page: The page says it is a differential form. Can anyone explain the notation for me or provide a link or two to documents or pages which explain this notation? Thank you very much, Geoff

Index notation in GR is really confusing ! I'm confused about many things but one thing is the order of index placement , ie. is Λa b the same as Λba ? And if not what is the difference ? Thanks If anyone knows of any books or lecture notes that explain index gymnastics step by step...

I am looking at a formula, simplified here, which says that peaks occur at wavelengths: \lambda_{ij}=...(i^{2}+j^{2})... "where i, j correspond to the orders of the 2D wave vector" The peak wavelengths are at \lambda_{10},\lambda_{11},\lambda_{20} (i.e. where (i^{2}+j^{2}) terms are...

Could anyone clarify what is the name of the i,j,k notation for vectors if there even is one?

See these equations: \left | \frac{d \vec{f}}{d \vec{r}} \right | = \left | \frac{d(f_1,f_2)}{d(x,y)} \right | = \frac{\partial f_1 \wedge \partial f_2}{\partial x \wedge \partial y} = \left | \begin{bmatrix} \frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y} \\ \frac{\partial...

Attached is a screenshot of a text I'm trying to follow. However, the author does something that I don't quite understand in line (3.5). They equate the following: A^{\mu}_{\hspace{2 mm}\alpha} x^{\alpha} (A^{-1})^{\beta}_{\hspace{2 mm}\mu} y_{\beta} = (A^{-1})^{\beta}_{\hspace{2 mm}\mu}...

I am currently reading "Differential Equatons with Applications" by Ritger and Rose, and I need some clarification about some notation and convention that they are using. I think it all stems from a lack of clarity of the difference between the operator d/dx and the "object" (I don't know what...

Homework Statement What is the difference between this statement being expressed in z-notation and the notation shown? What are the benefits of the two and how do you do the conversion? Nevermind about answering the question itself. if X ~N(mu,sigma) show that P(|X-mu|<= 0.675*sigma) = 0.5...

Homework Statement Hi all, I'm trying to learn how to manipulate tensors and in particular to differentiate expressions. I was looking at a Lagrangian density and trying to apply the Euler-Lagrange equations to it. Homework Equations Lagrangian density: \mathcal{L} = -\frac{1}{2}...

I understand everything (in a really simple way) that lies behind the hydrostatic equation, but I have no idea what this notation (light blue) means. I would really appreciate as much information as possible on this. I want to fully understand it.

If I have a function defined over an integral, e.g. ## F(t') = \int_{-\infty}^{\infty} dt \tilde{F}(t,t') ## is there a standard way to denote this integral as being "Open", that is to say if I write ## H = F(t') G(t) ## I want this to mean ## H = \int_{-\infty}^{\infty} dt \tilde{F}(t,t')...

Homework Statement If a,b,c are three -zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of | a, b, c|2 is |a|2 + |b|2 + |c|2 |a| + |b| + |c| 2(|a|2 + |b|2 + |c|2) ½(|a|2 + |b|2 + |c|2) Homework Equations a.b = ab cosθ |axb|= ab sinθ...

Define the following $$Z= \begin{pmatrix} 0 & A \\ B^T & T \end{pmatrix}$$ where we define $A$ and $B$ as $r \times m $ matrices and $T$ is an $m \times m$ matrix with nonzero distinct indeterminates at the diagonal, that is, $T_{i,i} = t_i$. What is the meaning of $B^T$ ?

Homework Statement A particle is in the state |\psi \rangle = \frac{1}{{\sqrt 3 }}|U\rangle + \frac{{a\sqrt {(2)} }}{{\sqrt {(3)} }}i|D\rangle . The up state |U\rangle = \left( {\begin{array}{*{20}{c}} 1\\ 0 \end{array}} \right) and the down state |D\rangle = \left(...

When writing ##A_{a}\text{ }^{b}## one means ''The element on the a-th row and b-th column of the TRANSPOSE of A" right? Such that ##A_{a}\text{ } ^{b}= A^{b}\text{ } _{a}## ? I would just like a confirmation so I'm not learning the convention in a wrong manner.

Homework Statement I was working on a physics problem that involves integrals and I stumbled upon this: m*g*sin θ − k*x = m*dv/dt =m*v*dv/dx → (m*g*sin θ − k*x)/m =v*dv/dx →∫[(m*g*sin θ − k*x)/m]dx =∫v*dv Notice that we multiplied by dx on both sides and dx has been canceled from the right...

I want to take the arg max over a number of functions as below, however it is possible that there are multiple i's for which the result is maximal. How do i denote that I want to take the last possible i, for example if it results in 3 and 5 I want it to return 5, is there notation available for...

From the wikipedia article Physical Quantity I'm having trouble deciphering the difference here between when roman or italic is appropriate. Any further guidance? Thank you.

Homework Statement Plotting a point in spherical coordinates means using the format ##(\rho, \theta, \phi)## in place of ##(x, y, z)##. Taking a triple integral means replacing ##dV## with ##\rho ^2 sin(\phi) d\rho d\theta d\phi ## As you can see, ##\rho, \theta, \phi ## are all in the same...

Shouldn't it be Pdc = 22kN rather than Pcd? I mean the 22kN force arrow is pointing towards C? Because Pdc means the P from D to C no?

I'm not sure if this step on my calculation is correct or not...

Homework Statement Homework EquationsThe Attempt at a Solution Hello, I just want to make sure I am doing this right $$<a|b> = a_{x}^{*}b_{x} + a_{y}^{*}b_{y} + a_{z}^{*}b_{z}$$ $$= [(1-i)|x>][-i|x>] + (2 |y>)(-3 |y>) + (0|z>)(|z>)$$ $$=(-i + i^{2})|x> - 6 |y> + 0|z>$$ $$=(-1-i)|x> - 6 |y>...