Term Definition and 742 Threads

Homework Statement Hey all, I am working through a derivation that my professor gave me to do and I am having trouble understanding one of the formulas that he gave me, namely: "EM waves can be described as: E(x, t) = Eosin(2πx/λ)*sin(2πc/λ)" The the Eo*sin(2πx/λ) term makes sense to...

I'm having a little difficulty in the topic 'Boundary layer Equations' in Fluid Mechanics due to my weak math skills. With reference to the figure in attachment, if we say that "we neglect \frac{∂^{2}u}{∂x^{2}}", does it mean that we will only consider the portion where \delta(x) is almost...

I always remember my dear departed grandmother referring to something called "New Math" when I was a youngster, but at the time I wasn't interested enough in whatever it was to look into it. However, I just read the Wiki page on it: http://en.wikipedia.org/wiki/New_Math And it looks like...

Could you help me to find the general term of the sequence: ## 1 , \frac{5}{3} , 1 , \frac{15}{17} , 1 , \frac{37}{35} , 1 , \frac{63}{65} ,... ## Thank you!

Calc 2 will require some basic knowledge of sequences and series. Since this topic has never been covered in any of my past math classes, I am currently learning about sequences and series from scratch. On youtube, I found a video that contains an explanation of the General Term of the...

I'm new to this forum, so I apologize if this has been raised/discussed before, or if this does not make much sense... I've been watching numerous debates about the Big Bang and the origins of the universe, and I can't help but think that Big Bang is not a good term for describing the early...

Homework Statement Consider the sequence n1, n2, n3, ... that satisfies the recurrence relation nk = nk-1 / k + 1 for all integers k ≥ 2 with the initial condition that n1 = 1. Find the explicit formula nk for the nth term of the sequence? 2. The attempt at a solution I calculated...

Homework Statement Evaluate ∫(0-1)∫(sqrt(y)-1) (ye^(x^2))/x^3 dx dy Homework Equations The Attempt at a Solution First, factor out the y for the inner integral, making ∫(0-1) y∫(sqrt(y)-1) (e^(x^2))/x^3 dx dy And evaluating the inner integral first: y∫(sqrt(y)-1)...

Homework Statement I am trying to solve this problem and need help with one aspect.Homework Equations sequence: 0,-1,0,1 -- repeated.The Attempt at a Solution How do I make every 4th term of the sequence a negative number? for instance i have: (1 + (-1)^n)/2 but i don't know how to...

Homework Statement Prove that any number with zeroes standing in all decimal places numbered 10^n and only in these places is irrational?(yeah,its the easiet question in my list,but I am still not sure about it) Homework Equations The Attempt at a Solution when i think about...

The increasing sequence 1, 3, 4, 9, 10, 12, 13 ... consists of all those positive integers which are powers of 3 or sum of distinct powers of 3. Find the 100th term of this sequence.

Homework Statement evaluate.Homework Equations lim\displaystyle _{x->∞} \frac{2^x - 3^x}{3^x + 4^x}The Attempt at a Solution i tried diving by highest term in denominator (4^x), but got me no where. the solution manual has: (divided by highest term in numerator.)with the answer is zero which i...

(I hope this is the right subforum) I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...

Hello. I am a thermodynamics novice trying to gain a better understanding of state functions, particularly enthalpy. I understand that enthalpy is defined as "A measure of the total energy of a thermodynamic system, including internal energy, which is the energy required to create a...

Decide constant term in $$\left(3\cdot x^3+\left(\frac{-4}{x} \right) \right)^{20}$$. I have problem with this one, I can't find any example about this one in my book, any advice would be great:)

The Majorana mass term is expressed from a single Weyl spinor. But I am a little confused by the expression. For example, see Eq. (2) in http://arxiv.org/pdf/hep-ph/0410370v2.pdf \mathcal{L}=\frac{1}{2}m(\chi^T\epsilon \chi+h.c.) Here \chi is the Weyl spinor and \epsilon = i\sigma^2 is...

I have been doing a bit of studying for my optics course and I have often come across refractive indices or materials being presented as n-1 (which often makes a lot of sense). I was just wondering if there was a special term like for this format or if we still call it just the "refractive...

In F term SUSY breaking, is the minimum of V just: V=\sum^{N}_{i}|F_i|^2

Homework Statement Consider the followign function f(x) = x^-5 a=1 n=2 0.8 \leq x \leq 1.2 a) Approximate f with a tayloy polynomial of nth degree at the number a = 1 b) use taylor's inequality to estimate the accuracy of approximation f(x) ≈ T_{n}(x) when x lies in the interval...

I'm trying to do a HW involving the Darwin Term in the fine structure of hydrogen. I'm given that the perturbation from the Darwin term is equal to (times a constant factor which I'll ignore), V_D = [p_i,[p_i, \frac{e^2}{r}]] = e^2\vec{p}^2\frac{1}{r} -2e^2\vec{p}\frac{1}{r}\vec{p} +...

Hi there, I recently discovered a formula for the nth term that works for any finite sequence of numbers. I was just wondering whether a formula has already been discovered, and if not, how and where I should publish it. To give you an example of what i mean: one formula for the nth...

Homework Statement Solve the Boltzmann equation for a homogeneous plasma with not external forces present when the collision term is \frac{\partial f(v,t)}{\partial t} = -\nu (f(v,t) - f_0(v)), where \nu and f_0 are constants. Homework Equations Boltzmann equation \frac{\partial...

Homework Statement find the limit of this sequence 1) An = \frac{\sqrt{n} sin (n! e^{n})}{n+1} 2) An = 4n^{3} sin\frac{1}{n^{3}} Homework Equations The Attempt at a Solution (1) |sin n! e^n)| ≤1 |An| ≤ \frac{ \sqrt{n} }{n+1} |An| ≤ \frac{ \sqrt{n}/n...

http://energy.gov/articles/letter-secretary-steven-chu-energy-department-employees-announcing-his-decision-not-serve Hopefully the next SoE will also have a strong scientific background.

An arbitrary Lorentz transformation ##\Lambda## in 1+1 dimensions can be written as \begin{align} \Lambda=\frac{\sigma}{\sqrt{1-v^2}} \begin{pmatrix}1 & -v\\ -\rho v & \rho\end{pmatrix}. \end{align} Here ##\sigma=\operatorname{sgn}\Lambda_{00}## and ##\rho=\det\Lambda##. I learned today that...

Homework Statement expand sinx about the point x=pi/4 Homework Equations The Attempt at a Solution I know how to find each individual terms but how do I got about finding the general term for this series?

Hi there! I am working on a project that requires some idea of adiabatic processes. I know the basics of the said topic and I'm currently stuck with the reversible adiabatic equation PV^(gamma)=constant.. and want to know what is the constant term i.e. on what parameters it depends and what is...

It is said that the Einstein-Hilbert term in the following couple mass and gravity. Lagrangian = R/(16*pi*GN) [Einstein-Hilbert term] + L (nongravitational) How is the above derived? Is it enough to prove that there should be a theory of quantum gravity since mass and gravity are coupled...

Determine the term containing... (Binomial Theorom) Homework Statement Determine the term containing x^11 in the expansion (X^2 - 1/x)^10 Homework Equations T(k+1) = nC(k)*A^(n-k)*b^KThe Attempt at a Solution x^11 = 10Ck * (x^2)^(10-k)*(-X^-1)^k (taking out the (-) from the x^-1 b/c it...

Hi all. Next year for school, we have a huge, year-long research project. I'm really excited, but I'm not really sure what I should do yet... It can be on pretty much anything (and I'm doing it on something physics-related, hopefully), as long as the teachers approve it. It should be a long-term...

I'm reading something which highlights the Feynman rules for QED, and it talks about what happens if you go along a fermionic line. For example this picture: http://wikipremed.com/image_science_archive_68/010601_68/170750_298px-ComptonScattering-u.svg_68.jpg According to these notes, there...

Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr. nCr formula: n!/r!(n-r)! I've tried everything I can but I don't know how to approach this question.

A few topics ago I asked about possibilities concerning maintaining contemporary tech level with seriously reduced population. Now I will ask a question for the same story. There is a standard, generic incoming doom. The general population is already roughly aware how nasty the situation is...

For np3, there is a term symbol: 4S I think it is because l are -1,0 and 1 So, L value=-1+0+1=0 However, for np2 , there is not a term symbol: 3S (I assume l are -1 and 1) I know I misunderstand something, but what are they?

I need to know how to identify the expression for the constant term in a power relationship. The power relationship is a relationship I imagined on a graph. On the graph both the values on the x and y axis's would be increasing. The power relationship is between square of rotational frequency...

Homework Statement 1. First, calculate the Taylor polynomial of degree 4 for f(x)=sin(3x) about x=0. 2. Then find the 156th term of the infinite Taylor Series for g(x)=sin(3x) Homework Equations My Taylor polynomial ended up being -4.5x3+3. The Attempt at a Solution I...

Hello all, Recently I've found something very interesting concerning Taylor series. It's a graphical representation of a second order error bound of the series. Here is the link: http://www.karlscalculus.org/l8_4-1.html My question is: is it possible to represent higher order error bounds...

I am looking for a term to describe a sort of "optimization" that I am trying to do. Hi everybody, I am a college student who unfortunately is not smart enough to be a math major. But nonetheless I am obsessed with statistics and numbers. I have a question: I need help figuring out a term...

Sorry I know this may seem banal but it's really bugging me. I'm making space scenes of made up solar systems in a 3d modelling program and I want to name one "a ~ transit". If it was a generic planet, I could call it a planetary transit, or if it was OUR moon, I could call it a Lunar...

I read about long term use of these kinda antidepressants causing hippocampal neurogenesis and stuff like that but I'm focusing more on what long term use does to the various monoamine neurotransmitter pathways. I'll start with SSRIs because they are the simplest. Their main mechanism of action...

the question is ∫dx/ x^2*√(x^2-1) I use x=a sec ∅ x^2*√(x^2-1)= sec^2∅tan∅ x=sec ∅ dx= sec∅tan∅d∅ so it will become something like this ∫sec∅tan∅d∅/sec^2∅tan∅= ∫1/sec∅d∅=∫cos∅d∅ =sin∅+c But how can i change this sin in...

f(x)=(1.2x-11 + 1.5x7)20 (1.25x21 + 1.7x-0.05)50 Given the function above, by binomial expansion, Xn appears to be the term with the largest coefficient. Determine n and hence state the corresponding coefficient. Would like to know the method of doing this question in an easier way.

What is the general term for the sequence 8,12,18,27,... First of all I know that i can make a polynomial or whatever function pass through these points but I make a relation I just want to build the general term of it I took the difference between any two terms I choose 40 8 , 12 , 18 ...

As I understand it, there are the terms: domain - variables that are input to a function range - the variable that is output to a function This works well in a canonical single equation system like z = f( x , y ), but breaks down in an implicit function or set of equations. I was...

Homework Statement 3, -3/2, 3/4, -3/8,... Homework Equations The Attempt at a Solution I began to write, [SIZE="3"](-1)^{n+1} \frac{3}{...}, but I began to despair once I came upon the denominator. I know that every term's, except 3, denominator can be written as a power of two...

Could someone quickly go over my working, as I am not 100% sure I have done it the right way. I will show and explain my working step by step. $$ at^2-4a + 2t^2-8$$ I first grouped the values: (at^2-4a) + (2t^2-8) I then factorised these equations into: a(t^2-4a) + 2(t^2-4) I...

I haven't read the Nature article. However, the newspaper article had a sufficiently complete description to infer what they did to infer. The scientist kept frozen samples of the distant ancestors, i.e., the bacteria that were first placed in a flask. Samples were taken from the flask...

Homework Statement I need help to expand some matrices Homework Equations \pi = \frac{\partial \mathcal{L}}{\partial \dot{q}} = i \hbar \gamma^0 The Attempt at a Solution How do I expand i\hbar \gamma^0 the matrix in this term, I am a bit lost. All the help would be...

Homework Statement L is the langrangian \dot{q} is the velocity with time derivativeHomework Equations \frac{\partial L}{\partial \dot{q}} = -M \frac{1}{2} \frac{1}{\sqrt{1- \dot{q} \cdot \dot{q}}} \frac{\partial}{\partial q_i} (-\dot{q} \cdot \dot{q}) The Attempt at a Solution A few...

What timefram does short term atmospheric retention mean?