Notation Definition and 1000 Threads

Homework Statement [/B] Prove the following identity: \vec{\nabla}(\vec{A} \cdot \vec{B}) = (\vec{A} \cdot \vec{\nabla})\vec{B} + (\vec{B} \cdot \vec{\nabla})\vec{A} + \vec{A} \times (\vec{\nabla} \times \vec{B}) + \vec{B} \times (\vec{\nabla} \times \vec{A}) Homework Equations Kronecker's...

In a book on atmospheric physics I'm reading, the author begins a derivation by examining a fluid element of volume V = δxδyδz. In this context, what purpose is delta δ serving? Is it just a placeholder for an unspecified volume in the x, y, and z directions, or is it referring to an...

Homework Statement Find the derivative of ##y=cos^3(πx)## *Must be in Leibniz notation Homework EquationsThe Attempt at a Solution (i) $$Let~ w=y^3 , y=cos(u), u=πx$$ (ii) $$\frac{dw}{dy} = 3y^2,~ \frac{dy}{du} = -sin(u),~ \frac{du}{dx}=π$$ (iii) By the Chain Rule, $$\frac{dw}{dx} =...

I want to prove Cauchy–Schwarz' inequality, in Dirac notation, ##\left<\psi\middle|\psi\right> \left<\phi\middle|\phi\right> \geq \left|\left<\psi\middle|\phi\right>\right|^2##, using the Lagrange multiplier method, minimizing ##\left|\left<\psi\middle|\phi\right>\right|^2## subject to the...

I have a simple question about the notation of the nabla operator in Vector Analysis. The nabla operator is a vector differential operator and it is written as: $$\nabla = \hat{x} \frac {∂} {∂x} + \hat{y} \frac {∂} {∂y} + \hat{z} \frac {∂} {∂z}$$ Is it okay if we accented nabla by a right...

A popular response to a novice asking whether .999... = 1 is for an expert to demand that novice define what the notation ".999..." means. I think this is the best response. However, I note that many experts tend to accept the "..." notation in other contexts without demanding an explanation...

Homework Statement Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>...

Prove by math induction that n sigma 3i + 1 = n/2 (3n + 5) i = n

Hi all, just had a question about tensor/matrix notation with the inverse Lorentz transform. The topic was covered well here, but I’m still having trouble relating this with an equation in Schutz Intro to GR... So I can use the following to get an equation for the inverse...

In Arnold's book, ordinary differential equations 3rd. WHY Arnold say Tg:M→M instead of Tg:G→S(M) for transformations Tfg=Tf Tg, Tg^-1=(Tg)^-1. Let M be a group and M a set. We say that an action of the group G on the set M is defined if to each element g of G there corresponds a...

A very simple question. How do we represent a vector with Newton's notation (writing the arrow symbol with the overdot notation)? Can we write them both above each other. First, the overdot notation and then the arrow symbol? Thank you a lot for your help...

Hello I am doing some exercises in continuum mechanics and it is a little bit confusing. I am given the following equations ## A_{ij}= \delta_{ij} +au_{i}v_{j} ## and ## (A_{ij})^{-1} = \delta_{ij} - \frac{au_{i}v_{j}}{1-au_{k}v_{k}}##. If I want to take the product to verify that they give...

In a PDF i was looking through i came about a question for the operator P = |a><b| find Px(adjoint) the adjoint was defined as <v|Px|u> = (<u|P|v>)* where u and v can be any bra and ket now for the question: (<u|a><b|v>)* = <v|Px|u> this is the confusing step , i thought conjugated simply...

Stumbled on a potential pitfall that can arise if you combine Newton's overdot notation (for time-derivatives) with boldface/non-boldface notation for vectors/vector-magnitudes. Say you have ##\textbf{v}## for velocity and ##\dot{\textbf{v}}## for acceleration. Speed is then ##v## (magnitude of...

hey guys just a quick question , within the Dirac notation I we have bras and kets.Is it allowable to simply hermitianly conjugate everything , e.g: <w|c> = <b|c> - <d|c> Can we then: <c|w> = <c|b> -<c|d> Or is there some subtly hidden rule.

From this paper, on page 2: https://arxiv.org/pdf/1606.03488.pdf. I know the spectroscopic notation part, but what is the meaning of the symbol after the colon?

Homework Statement 2. Let ##T: \mathbb{P}^1 \rightarrow \mathbb{R} \text{ be given by } T(p(x)) = \int_0^1 p(x)~dx## Describe ##Ker(T)## using set notation. Homework Equations ##p(x) \in \mathbb{P}^1~|~ p(x) = a_0 + a_1x## The Attempt at a Solution ##T: \mathbb{P}^1 \rightarrow \mathbb{R}##...

Hello, What are the semicolons in the this Meijer's G Function (picture is attached)? The notation I saw in different books and in the Internet doesn't include semicolons. Do they signify something that is not in the other notations? Thanks

Is |x+y> = |x> + |y> ? Thank you.

I was taking notes recently for delta y/ delta x and noticed there's more than one way to skin a cat... or is there? I saw the leibniz dy/dx, the triangle of change i was taught to use for "difference" Δy/Δx, and the mirror six ∂f/∂x which is some sort of partial differential or something...

Hello everyone, I am interested on simulating the converse Piezoelectric effect of materials and I have given the mechanical (Youngs modulus and Poissoin's ratio) and electric material properties (Electric Permittivity, Piezoelectric coupling matrix etc). However from the literature I got...

Homework Statement I don't want to clog up the forums with a few "small" problems so I am lumping them together here. 2. Let ##T:P^1 → R \text { be given by } T(p(x)) = \int^b_a p(x)dx##. Describe Ker(T) using set notation. 3. Let ##H = \left\{f ∈ C[a, b] | f'(x) ≥ 0 ~\text for...

Homework Statement I am unsure as to how to write the dot product in terms of the summation notation? May you please explain? Homework EquationsThe Attempt at a Solution

Information Given: In the figure, a square of edge length 17.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.90 g, m3 = 0.800 g, and m4 = 4.70 g. Question: In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.90 g? Attempted...

Homework Statement I have a simple problem relating to the superposition of plane EM waves that I'd to try out using complex notation. Could anyone run through the work to see if my understanding is right? Many thanks in advance! The incident E bit of the wave is $$\vec{E}_I = E_0 \sin(ky -...

Homework Statement For the following notation, D \subseteq \{ z | \exists x,y \in S (z = x - y ) \} I'm wondering if S can only have one element, or does the notation imply that | S | > 1 Homework EquationsThe Attempt at a Solution For example, if I have S = \{ 3 \} is z = 3 - 3? Or...

Prove by mathematical induction that n sigma r^3 = n^2(n+1)^2/4 r = 1 so far I have 1 sigma r^3 = 1^2(1+1)^2/2 r=1 1 = 1(4)/2 1 = 4/2 1 = 2 I'm not sure what to do after this for the k+1 case.

Hi So we write ##g_{ab}g^{ac}=\delta^{(4)c}_b ##, but this simply means to replace ##b## with ##c## or vice versa, so, why don't we write ##\delta_{bc}##? Thanks i.e. the affect is not to replace and raise/lower, it is simply to replace, so I'm a bit confused by the notation...

considering the symbol of an element, under the cambridge curriculum , is the nucleon number written on top or at the bottom on the left side of the element?

On pg. 60 of Nolting Theoretical Physics 1 for the definition of a vector multiplied by a scalar the book shows two little up arrows if the scalar is greater than zero and an little up arrow and then a little down arrow if the scalar is less than zero. Then again on pg. 61 for definition 1.139...

Homework Statement So I have the set {...(1/8),(1/4),(1/2),(1),(2),(4),(8)...} I am suppose to put it in set builder notation.. Homework EquationsThe Attempt at a Solution my answer was { x = {\frac {1}{2^n} : n \in ℤ } } but my books was { x = {{2^n} : n \in ℤ } } I understand both...

Hey, What does the vertical line with the "I_b" on the bottom right mean? Link here: https://imgur.com/a/nII9g Thanks, -Yael

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of D&K's notation for directional derivatives ... ... D&K's definition of directional and partial...

I am learning about Big-O notation, and am kind of confused. So, Big-O notation is the upper-bound order that measures the amount of required resources as n approaches a sufficient size. It essentially measures the scalability of an algorithm. My question, however, is with the notation.If an...

Having some trouble determining the most mathematically correct way to express something I understand only numerically and physically. Basically I am modeling radiation within a volume. 1. For each point dV within a volume V there is a scalar value e(dV), which is an amount of radiation emitted...

Hi, I came across a derivation notation I didn't recognize: Let ##s## be some four-vector and ##\tau## the proper time. What is the significance of $$\frac{Ds}{\mathrm{d}\tau}?$$ I know ##Ds## can be used to mean the Jacobian, but I've never come across the notation above. Does someone...

Hi, I guess this could be a rather silly question, but I got a bit confused about the "numerator layout notation" and "denominator layout notation" when working with matrix differentiation...

Hello everyone! I have this expression which I have to simplify: ∑i=1log(n) 1(log(n) - i) And my book apparently simplifies it to being log(n). I am struggling to figure out why this is the case. Could anyone help? Thanks!

So , what I was wondering about was a slight difference in notation, for which I am not certain if correct (mine, in particular.). The induction axiom says: If M is a subset of ℕ, and if holds that: a)1∈M b)(∨n∈ℕ)(n∈M→s(n)∈M) then M=ℕ. Now my question is: why do we write (∨n∈ℕ)(n∈M→s(n)∈M)...

Homework Statement Homework Equations Dot is A2. A1-A2 of star is in phase with A1-A2 of delta The Attempt at a Solution I'm getting answer as Y-Delta - 1. Assuming Y is HV. How is C right answer?

I am completely baffled by bit of notation in Quantum Mechanics Concepts and Applications by Zitteli. He is trying to get the differential equation for the ground state of a harmonic oscillator using the algebraic method as opposed to Schrodinger's equation. I suspect he is compressing a lot of...

Harold Simmons defined a simple but powerful notation for transfinite ordinals described in several articles available at http://www.cs.man.ac.uk/~hsimmons/ORDINAL-NOTATIONS/ordinal-notations.html . In summary : - It uses lambda calculus formalism - Fix f \zeta = f^\omega (\zeta+1) = limit...

Hi, I'm studying transformer and am a bit confused. Say for vector group: Dy11, I guess it's the line voltage of LV leads the Line voltage of HV by 30 degrees. Book says phase angle. The phase angle is line voltage right, since the phase voltage of HV and LV will always be in phase with each...

I got my education out of the American continent, yet currently I live in Canada and my son goes to school here (5th grade + some additional math training) What puzzles me is that currently he may write things like $$5\times-1$$ meaning ##5\cdot(-1)##, which I can only read as ##5x-1## (i.e...

Question (a) Write down the quantum numbers for the states described in spectroscopic notation as 2S3/2, 3D2 and 5P3. (b) Determine if any of these states are impossible, and if so, explain why. (Please note that these could describe states with more than one electron.) My Attempt A) I came...

Hello, I'm currently doing vectors in class, but I don't know what these parts mean. Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add? I tried to google, but I couldn't really find...

What notation would I need to use in order to write a mathematical statement to define a System S of simultaneous equations - let's say ax+by=c and ex+fy=g.

In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...

Homework Statement Erica goes swimming three out of the seven days of the week. How many possibilities are there for her swim schedule if she goes swimming on Monday or Tuesday or both? (Define M to be the set of schedules in which Erica goes swimming on Monday. Let T be the set of schedules in...

I am about to do a unit on the wonders of vector decomposition for year 2 in a 3 years science curriculum where the kids follow along with the historical developments of science. It's the science class I wish I'd had before becoming an engineer at MIT. In year 3, we are with Einstein and...