Notation Definition and 1000 Threads

I'm not sure if this is the correct place to ask this question, so please let me know if there is a better place for me to post it. I'm having trouble understanding index notation. I understand the basics, such as in the following examples: (a x b) = εijkajbk εijkεiab = δjaδkbδjbδka...

Homework Statement This is from lecture, not a homework problem per se. But I need assistance. The problem was to write this form of a flow equation in Einstein's notation: Homework Equations \frac{\partial }{ \partial x_1}(K_1 \frac{\partial h}{\partial x_1}) + \frac{\partial }{...

I'm solving some trig functions and ran into a notation that says Sin(90°-θ) What does it mean? I know what Sin θ is and I know that Sin 90° = 1.

I just started an E&M class and right from the beginning the notation seems so confusing it has to have been done as a joke. Trying to do a problem I run into about 10 different r's I have to keep track of. Capital R Lower case r Lower case r prime The r in spherical coordinates The "squiggle" r...

Folks, I am struggling to see what is happening here particularly when ## \displaystyle \sum_{i=1}^{n-1}## transforms into ##\displaystyle \int_{x_1^e}^{x_{n}^e}## ##\displaystyle 0=\sum_{i=1}^{n-1} \left [ \int_{x_i^e}^{x_{i+1}^e} (a \frac{dw}{dx} \frac{du}{dx}+cwu-wf )dx- \left [ w(x)...

"The average wavelength of white light is 5.0 x 10-7m. What would this be in nanometers? The textbook answer key stated the answer as 500n but I have no idea how that is the answer. I know that the value of nanometers is 10-9 so I figured you add -7 and -9 to get -16... Thanks,

Im not sure how to interpret the notation, specifically the one on the left, the one on the right seems like you just include everything in the universal set? what does it mean when the line goes over everything? what does it even mean when the line is over the and/or symbol

Hello everyone, I'm a newcomer to this forum! I've been having particular difficulty lately with understanding function notation in higher level mathematics. I felt like it was a general post so I posted in the general math section. I've finished calculus 3 and am going to take engineering...

I just started partial differentiation, and (amoung a few others) it brings up some questions of notation. my first few questions are for the integral. first: doesn't the "dx" at the end of an integral mean "in respect to x"? or any toher variable like "dl", in respect to l? ie: \int...

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Folks, I am stuck on an example which is partial differenting a functional with indicial notation The functional ##\displaystyle I(c_1,c_2,...c_N)=\frac{1}{2} \int_0^1 \left [ \left (\sum\limits_{j=1}^N c_j \frac{d \phi_j}{dx}\right )^2-\left(\sum\limits_{j=1}^N c_j \phi_j\right)^2+2x^2...

Hello, sorry for my english.. I have a problem with weyl's spinors notation. I'm confused, becouse i read more books (like Landau, Srednicki and Peskin) and it's seems to me that all of them use different and incompatible notations.. If i define...

I have attached a pdf setting forth my question. This is a write up of a lesson i just had on yourtutor, in which i think the tutor might have made an error: this is a direct quote from the whiteboard: $Let g(x)=2x, f(y)=e^y\Rightarrow(fog)(x)=f(g(x))=f(2x)=e^{2x}$$\\Now...

Can anyone point me to how to interpret Dirac notation expressions as wave functions and integrals beyond the basics of     <α| = a*(q)     |β> = b(q)     <α|β> = ∫ a* b dq For example in the abstract Dirac notation the expression     |ɣ> (<α|β>) can be evaluated as     (|ɣ><α|) |β>  ...

Hi, in the book "Applied analysis by Hilbert space method", I have no idea what is happening in the last step here: <L(f), g>=\int^{1}_{0} L(f)\overline{g}dx=-\int^{1}_{0} f''\overline{g}dx=-\int^{1}_{0}\overline{g} d(f') where L(f) = -f'' and both f and g are functions of x. It...

In my Classical Mechanics book, one of the example problems makes a step that I do not understand. The steps are in the picture in the attachment. I do not understand how the left hand side goes from what it is in the first step to what it is in the second step. I have a poor understanding of...

I'm reading Hobson, Efstathiou and Lasenby, where on page 490, some notation is used that I am not familiar with. In the rather long equation (17.62), some terms contain things like \partial_{(\mu} h^{\rho}_{\nu)} . The author(s) then says "where we have made use of the symmetrisation...

Hello everyone! Is there a conventional notation for some common arithmetic operations, like element-wise product, or element-wise power? Thanks!

I posted this question in homeworks section but no one can help, or seems unable to answer my question. I am hoping if I post it here, someone might be able to clear it up for me: https://www.physicsforums.com/showthread.php?t=621238 Thanks in advance.

Preface: Can't understand notation from 1st year Real Analysis textbook that they pulled out of thin air without defining. 1. The thing statement that they're proving Let A and B be sets. Moreover, let f : A \rightarrow B be some injective map. Calculate f^{-1} \circ f. SOLUTION: To every...

Hello, everyone. I've trouble attempting to read the following. One of the things we assume for the set of real numbers is. A map $\left(\xi, \eta\right) \to \xi+\eta$ from $\mathbb{R} \times \mathbb{R}$ into $\mathbb{R}.$ Could someone read the above in plain English, please. Does it mean all...

Homework Statement \left(ln\stackrel{2}{}(1+x)=4\right) I've never seen a number above the ln like that, usually it's on another term or simply ln(2). What does that numer mean? Is it Log(e)^2 i.e. (Loge)(Loge)? That doesn't make any sense to me. Homework Equations - The Attempt at a...

\vec{v} = v^i\vec{e}_i = g(\vec{v},\vec{e}_i)\vec{e}_i The last bit is a sum over i but will need a Ʃ because the Einstein rule only applies to matched superscripts and subscripts and here bot the i are subscripts. Even if I write out the metric in the basis it doesn't work...

I've found a lot of help on this forum for awhile but just registered. I'd like to retroactively say thanks for a lot of help the past few semesters. Im using the 4th edition of spivak calculus. I tried looking for what the solutions to *'ed problems but could not find anything. I have the...

Hey. I'm self studying my way through an algorithms book, and one of the questions at the end of a section is to prove that log(n!) \in \Theta (n log(n)). I wrote up what I believe is a valid proof. However, I don't have much experience writing formal proofs (and even less experience with...

Square integrable functions -- Hilbert space and light on Dirac Notation I started off with Zettilis Quantum Mechanics ... after being half way through D.Griffiths ... Now Zettilis precisely defines what a Hibert space is and it includes the Cauchy sequence and convergence of the same ... is...

Homework Statement The area element of a sphere in spherical coordinates is given as following dA = r^2 \sin(\phi)\; d \theta \; d \phi using the notation in the following figure: However, while going through some E&M books I ran into the following notation Surface \; Area = r^2 \...

I'm having trouble seeing how an operator can be written in matrix representation. In Sakurai, for an operator X, we have: X = \sum \sum |a''> <a''| X |a'> <a'| since of course \sum |a> <a| is equal to one. Somehow, this all gets multiplied out and you get a square matrix with the...

In Sakurai's Modern Quantum Mechanics, he develops the Dirac notation of bras and kets. In one part, he states (page 17): <B|X|A> = (<A|X^|B>)* = <A|X^|B>* where X^ denotes the Hermitian adjoint (the conjugate transpose) of the operator X. My question is, since a bra is the conjugate...

I have a problem on how to generalize this sequence. Problem: In sequence a,b,x1,x2,...xn,...,each term is equals to the arithmetic mean of its two preceding numbers.Using a and b, find: 1.xn 2.lim(n->∞) xn My working: x1 = (a+b)/2, x2=(b+x1)/2 x3 = (x2+x1)/2... Ok, so I did the same thing...

I have a problem on how to generalize this sequence. Problem: In sequence a,b,x1,x2,...xn,...,each term is equals to the arithmetic mean of its two preceding numbers.Using a and b, find: 1.xn 2.lim(n->∞) xn My working: x1 = (a+b)/2, x2=(b+x1)/2 x3 = (x2+x1)/2... Ok, so I did the same thing...

Hi I have a question regarding notation. I have a function f(x, y), which I would like to integrate as \int_{x>0,y<x\frac{1}{\sqrt{\pi}}+1}{f(x, y) dxdy} My question is very simple, and probably very silly: What there a notation which enables me to write the condition for the integral (x>0, y...

Hi all, I've been looking around at formulae for determinants (using them for tensor densities) and I just want to clarify that the expression below is correct (i.e. formulae are correct): |M| = \sum^n_{a_1,a_2, \ldots ,a_n = 1} \epsilon_{a_1a_2 \ldots a_n} M_{1a_1}M_{2a_2} \ldots M_{na_n}...

Hey everybody, I'm a little embarrassed to be asking this question as I feel it is extremely easy, but I will do so anyway. I'm self studying some algorithms, and the book that I'm using claims that a n^2 + b n + c \in \Omega(n^2) Of course, this is equivalent to saying that there...

Homework Statement What does the following notation mean, assuming that I is a set, and i is a member of the set i, and x is an endowment of a member i, and is a vector? Assuming x is (1, 2, 3) for each i, and I = {1, 2, 3, 4} Does mean (1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3) ...

Hello, I have come across the following equation and want to know what the notation means exactly: \frac{-2 \pi \gamma}{\sigma} \frac{[ber_2(\gamma)ber'(\gamma) + bei_2(\gamma)bei'(\gamma)]}{[ber^2(\gamma) + bei_2(\gamma)]} Now, I know ber is related to bessel functions. For example, I...

Hi! I can't understand something in field theory and need your assistance: I wish to understand why a particle of mass m^2<0 can't exist. For a massive particle, in its reference frame, one would write: p_\mu=(m,0,0,0). I understand that. But for m=0, why is: p_\mu=(p,0,0,p) And for m^2<0...

This is not a problem statement this is not homework this is not a textbook exercise. This is my own question about a formula in a textbook. Homework Statement I am trying to understand the way that equation 4.2.2 is rewritten as equation 4.2.3 Homework Equations Source: Stanley...

I see this often and am not sure what it means. Suppose X and M are any two elements: X1-xMx Thanks.

Hi, I encountered some unfamiliar notation in a condensed matter problem: Consider a screened potential of the form: Vsc(r,t)=Veiqre-iwteat+c.c. Could someone please explain to me the meaning of the term "c.c."? From the given context I can gather that it has something to do with...

Homework Statement My teacher likes to teach us the D-notation methods for higher order DE's. I am having a hard time with this one and I can't seem to find the formula for the general solution Find a fundamental set of the equation (D-1)^{2}(D^{2}-6D+13)^{3}y = 0 Homework...

I came across this notation which I've never seen before, it looks a little like feynmann slash notation but I don't think this is the same (see attatchment) It's kind of like 'd slash' dE = 'd slash' Q + 'd slash' W Could anyone give me a helping hand? o:)

I would like to inquire whether there has been any recent work on representing matrices in unit vector notation? Thanks in advance!

Homework Statement What does it mean when lowercase Delta (δ) is used in partial derivative and derivative notation? Does it make any difference? Or is it just a personal preference? Homework Equations - The Attempt at a Solution Google

Homework Statement Could anybody please explain this notation? The only thing I undersand here is the limit. Is r a superscript? If not, what is it? And what does E(variable|condition/equation) mean? I know that in the set theory, | means a separator between the variable and condition (ex...

I was playing a bit with the Riemann Zeta function, and have been struggling with some notation problems. The function is defined as follows \zeta (s) = \sum_{n=1}^{\infty} \frac{1}{n^s} where s \in \mathbb{C} we know that n^s = exp(s\;ln\;n) so I can write \zeta (s) =...

2 4/7 + 1 3/5 = 4 6/35 This is easy on a calculator, but I would like to understand how to do it without using calculators. First I separate the integers from the fractions; 4/7 + 3/5 = Then find the LCM, which I get to be 35 2 4/7 + 1 3/5 = 4/7 + 3/5 = 21/35 2 + 1 20/35 = 3 41/35 Now I...

I'm a little frustrated with the quantum m lectures I've been watching. I've watched Susskind's, one in India and now James Binney's, as well as read about 3 books. They all teach this Bra-ket notation and in none of the three books I have on worked problems do they every give you a chance to...

Just been reading on Christoffel Symbols and I am having a notational mind block. Say we have: \Gamma^{k}_{ij} v^{i} v^{j} The velocity depends on this expression, but I don't read this term v^{i} v^{j} as a velocity squared do I? It's just the one velocity, are the superscripts here...

Homework Statement Taken from Wikipedia's Palindromic number entry, under formal definition header: Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system. Consider a number n >...