Notation Definition and 1000 Threads

Homework Statement In order to show that if ##(\vec E (\vec x, t), \vec H (\vec x, t))## is a solution to Maxwell's equation then ##(\vec E (\vec x -\vec L, t), \vec H (\vec x-\vec L, t))## is also a solution, my professor used a proof and a step I do not understand. Let ##\vec x' =\vec...

Notation for Heisenberg Hamiltonian ## H_{exch}=-\sum_{i<j}2J_{i,j}\vec{S}_i \cdot \vec{S}_j ## where the sumation extends over all spins pair of the crystal lattice. Suppose we have chain with four sites and periodic boundary condition ## H_{exch}=-J_{1,2}\vec{S}_1 \cdot...

I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation of Section 1-2 Direct Products and Sums (pages 5-6) - see attachment). In section 1-2.1 Dauns writes: ================================================== ====== "1-2.1 For any arbitrary...

I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation in section 1-2 (see attachment) My issue is understanding the notation on Section 1-2, subsection 1-2.1 (see attachment). Dauns is dealing with the product \Pi \{ M_i | i \in I \} \equiv \Pi M_i...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 5) Express .00024 in Sci Notation My answer: 2.4 x 10^-4 6) Factor the following completely: 3x^3 - 18x^2 + 24x My Answer: (3x)(x - 4)(x - 2)

Suppose I have some function f that depends on three variables, namely x, y, and t; i.e., f=f(x,y,t). Now suppose that y depends on x, i.e., y=y(x). Taking this into account, we see that f is really just a function of two independent variables, x and t. So my question is this: if I write down...

I am reading through this text http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf and am having a bit of trouble with one of the arguments that is put in index notation. Specifically, equation (3.3). I was wondering if anyone could have a look at it and clear up a...

[This is mostly about notation] I was working on a problem where I had to prove that div(B) remains invariant under lorentz transformations. That was not too hard, so I came up with div(B) = \partial_{\mu} B^{\mu} must equal div(B) = \partial'_{\mu} B'^{\mu} so I did a...

I have two questions explain why any subset of a finite set is finite. (prove) and why is empty set is considered to be a subset of any set? I'm confused, because let's say set A is a subset of set B it means that every element of A is an element of B. in the case of empty set being a...

i just want to understand what i read in my algebra book. here what it says: a measurement of 83200 ft. converted to (8.32)x10^4 ft. is now accurate to the nearest hundred feet. if we write (8.320)x10^4 the measurement is now accurate to the nearest ten feet. i want to know why it is nearest...

I have seen over and over statements like: \begin{aligned} &f(x)~\text{is a function of}\dots \\ &\text{Let}~f(x)~\text{be a function that}\dots. \end{aligned} This is probably a dumb question, but am I justified in feeling annoyed at these statements? The annoyance stems from my...

If we have the function f : x \mapsto f(x) = 3x^2, I am used to Lagrange's prime notation for the derivative: f' : x \mapsto f'(x) = 6x. I'm fond of this notation. But it has been mostly abandoned in my engineering courses in favor of Leibniz's notation, using differential operators such...

I'm curious but usually negative exponents mean you're going to put those numbers on the bottom (sorry forgot the exact term it is much earlier than I normally get up) (example 6^-1 =1/6 so why is scientific notation different? Or is it? (Ex: 5x10^-3=.005)

My calc professor always used to use the symbol ##:=## when defining a quantity. For example, say we want to evaluate the integral ## \int x \sqrt{1+x^2} dx ##. So we might say, "Let ##u:=1+x^2 ##" and then continue to easily evaluate the integral. I haven't seen this anywhere else and I'm...

Is there a standard notation for partial derivatives that uses indexes instead of letters to denote ideas such as the 3 rd partial derivative with respect to the the 2nd argument of a function? As soon as a symbol gets superscripts and subscripts like \partial_{2,1}^{3,1} \ f the spectre of...

Preface note: the R and Z in the {}s below should be double-struck, but I couldn't figure out how to do that here. I tried the usual shortcuts to no avail. I am writing pseudo-code for a publication, and am asked to use rigorous math notation, which is new to me. I am trying to express the...

Homework Statement The original printed problems can be found as attachments. The questions ask if a set S is a subset Rn. Give Reasons Question 1.) S is the set of all vectors [x1,x2] such that x12 + x22 < 36Question 2.) S is the set of all vectors [x1,x2,x3] such that: x2= 2x1 x3 = 3x1...

Hi, I have been using, for the most part, the prime notation when I want to indicate differentiation. As off recently, I have gained more insight into Leibniz's notation. This triggered the following question: how does the prime notation indicate what we are differentiating with respect to? I...

I am reading http://walrandpc.eecs.berkeley.edu/126notes.pdf on the theory of random processes. The authors are making use of some unfamiliar notation early on, and I don't want to move on without understanding their formalisms. First one is the := operator and a union operator that looks like...

How would you go about calculating a number's square entirely in sexagesimal notation (i.e. base 60). For example, how would you calculate the square of 37 + 4/60 + 55/60^2? If you can please show me how to calculate a number's square entirely in sexagesimal notation without using decimals it...

I was just curious as a possible confusion that might occur when graphing a v vs t Graph. Because velocity is a function of time, but time is also dependant on velocity, so how would we denote this on a graph? Hope i got my point across, thanks!

Dear all, I encounter the following formula (for stain energy function) a lot in physics literature: W(\epsilon_{kl}) = \int_0^{\epsilon_{kl}} \sigma_{ij} \textrm{d}\epsilon_{ij} where all indices ranges from 1 to 3, both \epsilon and \sigma are 3x3 matrices. My question is what...

I know that v(t)=dx/dt Then what is v(x) and how? Is it also dx/dt or something else?

I was doing a proof on why the derivative of an even function is odd and vice versa. Now, the way I did the problem was by using the chain rule to rewrite the derivative of f(-x), and the proof worked out perfectly fine. But I had a thought that I can't quite wrap my around, and I think it's...

Homework Statement Notice that ln [∏(k=1)^n a^k] = Ʃ_(k=1)^n * ln (a_k) I couldn't get the LaTeX right on this ^ But k=1 is below the product sign, and n is above. And (a^k) is the formula. From this, as well as some calculus, calculate that: lim as n->∞ ∏_(k=1)^n e^\frac{k^2}{n^3} For...

I am finding it unintuitive to follow a calculation in a certain notation I am not too familair with. To write down the equation $$ z(t) = - y(t) + \tau \frac{\partial y}{\partial t} $$ the following notation is employed $$ z(t) = -(1-\tau \frac{\partial }{\partial t}) y $$ So far so gud...

I am just wondering, is there a difference in meaning/definition between the indices of a tensor being right on top of each other A_{\mu }^{\nu } and being "spaced" as in A{^{\nu }}_{\mu } I seem to remember that I once read that there is indeed a difference, but I can't remember what it...

Homework Statement a_{1}r^{1} + a_{1}r^{2} + a_{1}r^{3} +... + a_{1}r^{n-3} + a_{1}r^{n-2} + a_{1}r^{n-1} = \sum_{n=1}^{?} a_{1}r^{n-1} What value would replace the "?" 2. The attempt at a solution EDIT: I edited this post after receiving your reply Cepheid. My gut would say...

Greetings, Is there a commonly accepted notation for a list in mathematics, of an identical form to Ʃ for a summation? If so, what is the name of the symbol (that would be used in place of L, below), and how would it be typed in LaTeX? For instance, it might look something like...

Homework Statement I'm confused about writing down the equation: \Lambda \eta \Lambda^{-1} = \eta in the Einstein convention. Homework Equations The answer is: \eta_{\mu\nu}\Lambda^{\mu}{}_{\rho}\Lambda^{\nu}{}_{\sigma} = \eta_{\rho\sigma} However it's strange because there seems...

Homework Statement The question is: The Earth formed 4.57 x 10^9 years ago. What is this time in seconds? The answer the textbook is giving is 1.44x10^17 seconds. The answer I keep getting is 1.44x10^15 seconds. Is the textbook wrong or am i wrong?

{Edit: as of 3:55 eastern time, made corrections to tex and itex mistakes}Is this all kosher in terms of demonstrating accuracy and comprehension of the notation {a_{1} + a_{2}...} = \lim_{n\rightarrow ∞ } \sum_{n=1}^{n} a_{n} So the lower case represents sequences and upper case represents...

Hi, Reading http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1 I've run into a notational question of atomic p orbitals. The authors use symbols like p_\sigma and p_\pi. From their fig. 3 (attached), they do look like p_x and p_z orbitals, respectively, rather than anything close to σ or π bonds...

Homework Statement Confirm explicitly that ##\frac{1}{2m}\langle \hat{p}_x \Psi | \hat{p}_x \Psi \rangle## cannot be negative. Homework Equations ##-i\hbar \frac{\partial}{\partial x} = \hat{p}_x## The Attempt at a Solution i seem to get: ##\frac{1}{2m}\langle \hat{p}_x \Psi | \hat{p}_x...

Here are the questions: Here is a link to the questions: How do you write the summation notation for: 4 - 24 + 144 - 864 + ... ? - Yahoo! Answers I have posted a link there so the OP can find my response.

Homework Statement Build a notation for the set: ##\{ ... , -8 , -3 , 2 , 7 , 12 , 17 ,...\}## Homework Equations ##2+5(0) = 2## ##2+5(1) = 7## ##2+5(-1) = -3## etc... The Attempt at a Solution ##\{ \ 2+5y \ | \ y \in \mathbb{Z} \ \}## Take note that you could replace ##2## by any...

Is there an equivalent notation to Capital Pi notation (multiplier) and Sigma notation (summer) for raising to the power? e.g. x1^x2^x3^x4...^xn=Notation(i=1 to i=n)(xi) Where "Notation" represents the symbol in question (analogous to Sigma for sums, Capital Pi for multiplication)?

Homework Statement Build a set notation for $$\bigcup_{i \in N}R × [i , i + 1]$$ The Attempt at a Solution ##\{(x,y) \in R : x \in R \ \ \exists z \in N \ \ z ≤ y ≤ (z+1)\}## Last time I tried one of these kind of sets I struggled quite a bit , so I'm interested in knowing how much...

Homework Statement As an exercise , the book I'm reading ask me to build a set notation for the following set: ##\{... \ , \frac{1}{27} \ , \frac{1}{9} \ , \frac{1}{3} \ , 1 \ , 3 \ , 9 \ , 27 , \ ...\}## The Attempt at a Solution After playing with the numbers a couple of minutes , I came...

Homework Statement The book I'm reading ask me to build a set notation for the following set: ##\{-3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 \}##. The Attempt at a Solution I attempted to build a set notation and came with the result: ##\{ x \in R : \exists y\in Z \ \ y(3/4)= x\}## My...

I am having trouble understanding the following: Uf: |x>|y> → |x>|y \oplusf(x)> \oplus being a mod 2 operation (nand)? I suppose I don't understand how to read the "ket" states so well. As far as I understand we have that since x and y can be 0,1 only if |x=1>|y=1> then if f(x) = 1 then...

Hey guys, I was just reading notes on metric spaces and was wondering if the notation of subsequences was such that anm is always further down the original sequence than an? For example suppose you have a strictly decreasing sequnce does the notation imply that anm<an

I need help with some set notation. I am an engineering major and don't know the proper notation. I am trying to write two statements. I have two sets, x_1 = {1,2,3}, and x_2 = {4,5,6}. Verbal Statements: y_1 was measured for all values of x_1 and x_2 y_2 was measured, for all values of...

Homework Statement The circuit below uses ideal components and disguises itself as a second order system when in fact it is really two first order systems. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the peak output voltage V_{0max}, and the time taken for...

I'm just having trouble understanding some of the notations given, when attempting questions such as the following: {f\inF(ℝ,ℝ): f(3)=5}. Is it just saying that, the function 'f' spans all real values?

Hi there, I am trying to get some practice with indicial notation. I am failing as follows, to start with. Given a vectorial function $$v_j = a_j e^{i(k_k x_k - \omega t)}$$ of spatial variables $$x_i$$ and time, given a tensor $$K_{ijkl}$$ I want to compute the quantity $$K_{2jkl}...

I can do this derivation the old fashioned way, but am having trouble doing it with einstein summation notation. Since \vec{B}=\nabla \times \vec{a} \vec{B}=\mu_{0}/4\pi (\nabla \times (m \times r)r^{-3})) 4\pi \vec{B}/\mu_{0}=\epsilon_{ijk} \nabla_{j}(\epsilon_{klm} m_{l} r_{m} r^{-3})...

Homework Statement A baseball strikes a bat. It's moving at 40m/s to the left horizontally. When it hits the bat it leaves at 60m/s with an angle of 30 degrees to the horizontal. The mass of the ball is 0.25kg. Homework Equations P(momentum)=mv Pf-Pi=ΔP ΔP=J(impulse) The Attempt at a Solution...

Homework Statement I'm trying to convert something like 1.25^-03 into it's standard number composed of standard decimals using a calculator (0.0125) - if you know what I mean. Thanks.

Reading this paper http://lanl.arxiv.org/abs/gr-qc/9611042v1 I'm baffled by this bit on page 3, In a footnote on page 4 we are told By this, K·K = 0 and equation 2.1 is nonsense. What have I missed ?