Notation Definition and 1000 Threads

I'm having trouble understanding some of the notation used in thermodynamics. The textbook will write things like: \frac{1}{T} = \left(\frac{\partial S}{\partial E}\right)_{N,V} such as you might use in the thermodynamic temperature in the microcanonical ensemble, and it says that the...

[b]1. what is the domain of the function k(y)=1/(2y+1)? Express your answer in interval notation [b]2. [b]3. I find that 0.5 is a possibility in this function, but since i have not done functions at school, i do not really know much more of this question.

Homework Statement \frac{∂x_{i}}{∂x_{j}} = δ_{ij} Homework Equations \vec{r} = x_{i}e_{i} The Attempt at a Solution \frac{∂x_{i}}{∂x_{j}} = 1 iff i=j δ_{ij} = 1 iff i=j therefore \frac{∂x_{i}}{∂x_{j}} = δ_{ij} Homework Statement r^{2} = x_{k}x_{k} Homework...

Hello, I have a polynomial having the form: \beta x^5 + \beta^2 x^7 + \beta^3 x^9 + \ldots = \sum_{n=1}^{+\infty}\beta^n x^{2n+3} How can I express this with Big-O notation? Please, note that I consider β as another variable (independent from x). I already know that if β was a constant I...

[SIZE="4"]Which of the following numbers can be added directly in exponential notation? 1. 3x10^-4 2. 600x10 3. 32.6x10^-3 4. 0.4x10^-4 _______________________________ a. 1 and 2 c. 1 and 4 d. 2 and 4 b. 1and3

Homework Statement The question is to evaluate the expression e^-iA, where A is a Hermitian operator whose eigenvalues are known (but not given) using bra-ket algebra. Homework Equations See above. The Attempt at a Solution I have been looking around, reading the textbook and...

I am always getting mixed up on derivative notation, so I was just wondering if this below makes sense? \(f(x) = 2x^\sqrt{2}\) \(\frac{df(x)}{dx} = 2\frac{d}{dx}x^\sqrt{2}\) The first should probably just be \(\frac{dy}{dx}\), but I was wondering if the other way would work as well.

I have $u_{tt}=u_{xx},$ $x\in\mathbb R,$ $t>0,$ $u(x,0)=0$ and $u_t(x,0)=\chi_{[-1,1]}(x).$ What does mean the last condition? In such case, how to solve the equation then? Thanks!

Homework Statement Here is the context: suppose f=(f_1,...,f_{n+1}) is a smooth retraction of B^{n+1} onto S^nBut what does the following statement mean? \int _{S^n}f_1df_2\wedge df_3 \wedge ... \wedge df_{n+1} Homework Equations The Attempt at a Solution

I am new to astronomy and astrophysics, can anyone point to a great free online place to learn scientific notation? I am quite obsessed with learning the math, but unfortunately have not the funds to attend a proper school. Unfortunately I work for a cheap employer who doesn't even pay for work...

Homework Statement I have a question for which I'm supposed to show that a function maps into "a hyperplane {u in ℝ5:u5=1}". Does this mean that the target space is the set of vectors in ℝ5 such that the dot product of u with itself (5 times) is 1? Doesn't seem right... Any clarification is...

I have to convert.. X=A+((B+C)*D)-E to reverse polish notation I think it's... BC+D*A+E- Is this correct?

Homework Statement I need to plug 0 into an anti-derivative of f, and I'm wondering whether it can be written as: y = \int f(0)dx or do I HAVE to write it as: F(x) =\int f(x)dx y = F(0) Homework Equations See 1. The Attempt at a Solution See 1.

What does this "(12)" represent in the number 0. (12)22293 93645 534? what does this bracket say ??

I have the following summation and I'm attempting to remove the summation notation. It appears to be the sum of a geometric series but I'm having a great deal of trouble with it. X is an unknown constant. $$\sum\limits_{i=2}^n (n - (n-i))x^{n-i}$$ Thanks.

Homework Statement I have trouble with the summation notation. \sum_{i=0}^{k}\binom{k}{i}f_{n+i} How do I write this as a sequence based on the definition of Fibonacci sequence? Homework Equations Definition: f(0)=0 f(1)=1 f(n)=f(n-1) + f(n-2) for n>=2 Example: f(2) = f(1) +...

Homework Statement Consider the following intervals: A = [-3,5), B = (3,8), C = (0,4] Find: A\capB and A\capC The Attempt at a Solution I thought that: A\capB=(3,5) and that A\capC=[0,4] as that is the intersection point, but this book (Schaum's Probability Outlines) says that A\capB=[-3,8)...

Hi, I am trying to work through ordered triples and quadruples, and I want to make sure I am on the right track. Given Kuratowski's set-theoretic definition of ordered pairs: <x,y> = df {{x},{x,y}} it seems that the definition of <a, b, c> = df <<a, b>, c> would be <a, b, c> = df{{a}, {a...

Please see below link for the two different styles of solving a separable equation. http://en.wikipedia.org/wiki/Separation_of_variables#Ordinary_differential_equations_.28ODE.29 Which one is more proper? Why? My DE teacher told me that strictly speaking it's wrong to use the first method...

I am trying to understand summation notation and there are a few inconsistencies in my head that I would like to clear up. Suppose C is an m*n matrix and \vec{x} is a 1*m row vector. Then, \vec{x}C = \sum_{i} x_{i}C_{ij} = \sum_{i} C_{ij}x_{i} = \sum_{i} {C_{ji}}^Tx_{i} = C^T \vec{x}...

(don't have an answer yet) We say that two sequences f,g are f=O(g) if-f there is a c>0 such that |f(n)|<c|g(n)| uniformly as n tends to infinity. If g(n)>2, does f=O(g) imply lnf=O(ln(g))?

Just a quick question, I'm looking to express the normalisation condition formally mathematically, is this acceptable: 1=\int_R|\psi|^2 \ \mathrm{d}\tau For a particle in 3 dimensional region R.

It's been a while since I've done calculus and now a simple derivative is stumping me. This is the issue: d(xf)/dx= ? This is just the product rule, so I think: x(df/dx) + f (dx/dx)= x (df/dx) + f But I'm afraid that I don't even understand my own notation anymore (how...

This problem has 4 parts to it (that are unrelated to each other). I did the first two parts without too much trouble but these next two parts have me stumped! Homework Statement Evaluate the following using Ket-Bra notation a.)exp[if(A)]=? Where A is a Hermitian operator whose...

Is there a common notation for the set of limit points of a set?

Ket Notation -- Effects of the Projection Operator Homework Statement From Sakurai's Modern Quantum Mechanics (Revised Edition), it is just deriving equation 1.3.12. Homework Equations \begin{eqnarray*}\langle \alpha |\cdot (\sum_{a'}^N |a'\rangle \langle a'|) \cdot|\alpha \rangle...

How would I write 1 + n + n(n - 1) + n(n - 1)(n - 2) + ･･･ + n! in sigma notation? If it's possible.

Homework Statement proof if f(n) = O(g(n)) then g(n) = O(f(n)) = stands for element of c is some constant Homework Equations if f(n) <= c*g(n) then f(n) = O(g(n)) if g(n) <= c*f(n) then g(n) = O(f(n)) The Attempt at a Solution I tried to go from the left-hand-side(LHS) to the...

So it says that a particle is going with a velocity of 5i m/s at t = 0 and varying acceleration a = 6√t j. it asked me to find the velocity and position of the particle as a function of time. So i did an integral of the acceleration to get velocity and did the integral of the velocity to get...

So I've seen quite a variety of notations that deviate from what we've learned in our "normal" math courses. In math classes we write a volume integral as: \iiint_W \rho\, d V but somehow once we start doing E&M and QM, professors often just drop the extra integral signs: \int_W \rho\, d V...

This isn't strictly a homework problem but anyway... I'm reading through a QFT textbook that is using index notation, and sometimes a new index symbol will be introduced during some mathematics and it always throws me off. I'll give a simple example, take the Minkowski metric: g^{\mu\nu} =...

It's used in a certain proof that I'm reading. A is a linear map from a vectorspace V onto itself. They say they can rewrite the vector space as \mathcal V = \bigoplus_\mu \mathbb C^{m_\mu} \otimes \mathcal V^\mu and I understand this, but they then claim one can (always, as any linear map)...

My teacher writes 3 dimensions like this: My textbook writes it like this: If my online H/W is not directly written by my teacher and not directly written by my textbook (MasteringPhysics online HW), then when presented with a vector such as: A = (2,1,-4) Should I read...

Homework Statement scientific notation I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power Homework Equations 4 . .... ... ... -9 ... sq rt of 5.2 X 10 4 -9 sq rt of 5.2 X 10 The Attempt at a Solution The answer I...

Homework Statement http://img857.imageshack.us/img857/2079/dirac.png Homework Equations H|ψ> = E|ψ> L^{2}|ψ> = l(l+1)\hbar^{2}|ψ> L_{z}|ψ> = m_{l}\hbar|ψ> The Attempt at a Solution I know this problem is very simple since I've seen a very similar problem a while ago but I've completed forgot...

The speed of light is 2.99792458 x 10^8 meters/second. What is this speed in miles per hour? (There are 1609 meters in one mile). I used dimensional analysis to get here:(2.99792458 x 10^8 meters/second) * (1 mile /1609 meters) * (3600 seconds / 1 hour) My question is, what do I do with...

This is a pretty trivial question, but how is the Schrodinger equation written out in full, time dependency and all in Dirac notation? I'm interested in this from a purely aesthetic point of view but I'm also a bit confused as to what the bras and the kets really are.

I'm trying to get into quantum field theory, I've seen Einstein notation before and I think I'm grasping it fairly well, but I've ran into two things that I just could not figure out and they both involved derivatives, or gradients. My problem is just mathematical, doesn't have to do with the...

Homework Statement I have elected to put this in the "math" section because it is primarily a math question however, please read to problem knowing that it came from an engineering dynamics textbook. Given: (as written) A particle moving along y= x - (x^2 / 400) where x and y are in...

Homework Statement Find <lz> using \Psi, where \Psi=(Y11+cY1-1)/(1+c^2)). Ylm are spherical harmonics, and <lz> is the angular momentum operator in the z direction. Homework Equations <lz> Ylm = hmYlm The Attempt at a Solution The brackets around <lz> are throwing me off...

Could I write v = 4i + 3j -2k as v = [ 4 | | 3 | * I_3 | -2 ] were I_3 is the 3x3 identity matrix and the other thing it's multiplied by is a 3x1 matrix of values 4,3,-2 I also had a question about the notation f(x) = x^2 + 3 can be written as f: x |-> x^2 + 3 can I write...

Good day all, I received this picture through the facebook network last night. I took it as valid at first sight, but for some reason it bothered me; in other words, my skepticism kicked in. The author mentions and assumes the limit as "n goes to infinity" which is annotated in the...

I have a general question about the notation of min and max functions. I'm wondering if there is an accepted notation, used by mathematicians, for the min and max functions, other than the usual min(x,y) and max(x,y) that I typically see. To give similar examples for what I'm looking for...

Alright, so I was wondering if anyone could help me figure out from one step to the next... So we have defined |qt>=exp(iHt/\hbar)|q> and we divide some interval up into pieces of duration τ Then we consider <q_{j+1}t_{j+1}|q_{j}t_{j}> =<q_{j+1}|e-iHτ/\hbar|q_{j}>...

Homework Statement 2n-1 Sigma (3i+1) = n(6n-1) i=0 prove for all positive n Homework Equations The Attempt at a Solution It holds true for n=1 5=5 then P: m+1 2m+1 Sigma(3i+1) = (m+1)(6(m+1)-1) or 6m^2 + 11m + 5 i=0 then 2m+1 Sigma(3i+1) = m(6m-1) +...

Hello, In the notation adopted by Peskin and Schroeder, the single particle state is \left|\boldsymbol{p}_1, s_1\right\rangle = \sqrt{2 E_{p}} {a_{p_1}^{s_1}}^{\dagger}\left|0\right\rangle How does one write down \left\langle r|\boldsymbol{p}_1, s_1\right\rangle = \sqrt{2 E_{p}} \left\langle...

Homework Statement Homework Equations The question is related to Riemann Sums The Attempt at a Solution I can not understand the notation of the question. Can someone explain the question to me. Or solve the question, i will understand it myself. Thanks

I was looking at an answer regarding resistors, and saw the notation; [SIZE="5"]R = [SIZE="5"]R[SIZE="1"]1 + [SIZE="5"]R[SIZE="1"]// where [SIZE="5"]1/R[SIZE="1"]// [SIZE="5"]= 1/R[SIZE="1"]2 [SIZE="5"]+ 1/R[SIZE="1"]3 I was wondering what the two parallel lines after the R indicate...

Homework Statement http://quantum.leeds.ac.uk/~almut/section2.pdf Please note i am referring to the above notes I basically don't get how the maths works to get (eq(25))(eq(22))(eq(24)) = eq(26) am i missing something interms of the commutator relations ? Homework Equations The Attempt at a...

Homework Statement I'm having a hard time understanding when we approximate higher order powers by order notation, especially when it comes to working out the Truncation Error for Finite Differences. My notes say "We use the order notation O(h^{n}) and write X(h) = O(h^{n}) if there exists a...