Expression Definition and 999 Threads

Homework Statement Electric field for a single pulse of a laser (operating at central wavelength of 800nm): E = E0e^(-(t^2/2a^2))e^(iwt) (the a is sigma and w is omega) Derive an expression for the spectral intensity (irradiance) The Attempt at a Solution One way I know to...

not actually homework, but things I need to know: 1: simplify the expression e^{a ln b} (write it in a way that dosen't involve logarithims) i want to prove the identities: lnab = lna + lnb lna^b = blna \frac{d}{dx}lnx = \frac{1}{x} i also want to derive the useful assumption...

I'm finding the percent error in a S.R. problem and getting a really small number. How can I find the exact percentage? This is the result that needs to be simplified: 6.7x10^(-16) / (1 + 6.7x10^(-16)) If I do an order of magnitude approximation, then the bottom becomes 1, but that will...

If I take e^ln|x|, do I get x or |x|?

I have been asked to simplify this one: 12x3 + 8x2 / 6x2 + 4x By factoring it out I have simplified it to 4x2 / 2x Is there anything I can do to simplify it further? I know the rules of dividing powers and hence if it was 4x2 / 4x I know I could simplify it to to 4x (subtract the...

How can I simplify this expression? As it is already factorised (factored) I do not see what else I can do to simplify it. x(9x+2) / x3(x-2) The only thing that I can think of is if I unfactorise everything to give the following:(although it doesn't seem to be very simplified from the...

Are there any theorems concerning this expression \frac{1}{z}f\left(\frac{1}{z}\right). I appreciate posts of any theorems you can think of.

I know this expression should return a Gaussian distribution but I can't get Mathematica to simplify the integral. What am I missing? \text{Simplify}\left[\frac{\text{Product}\left[\text{PDF}\left[\text{NormalDistribution}[y,\sigma...

Hi, Will anybody help me to find the maximum of the following expression: |\cos^m\theta_1 (c\cos^n\theta_2+se^{i(\gamma-n\lambda_2)}\sin^n\theta_2)+e^{-im\lambda_1}\sin^m\theta_1 (\pm ce^{-in\lambda_2}\sin^n\theta_2+se^{i\gamma}\cos^n\theta_2)|^2 where m,n\ge 2 are fixed positive...

freal Loops? Hi everybody.. I have a question. Recently, I'm using g95 to run my Fortran 95 program. But it occur an error, which is: REAL expression in DO loop at <1> - to enable REAL loop parameters use -freal-loops What is freal loop exactly? and How to solve this problem...

Homework Statement By first expressing the general term in partial fractions, find an expression in terms of n for summation of r=2 to n ( 1 / (r^2 - 1) ). Hence show that summation of r=1 to n ( 1 / r^2) i less than 7/4 for all values of n Homework Equations The Attempt at a...

Homework Statement Derive an expression for the total energy required to asemble a sphere of charge corresponding to a nucleus of atomic number Z and radius R. Assume the nucleus is a sphere of uniform volume charge density \rho Homework Equations \rho = mass / volume = 3Am / 4*pi*R3...

it is given that R1=R2 http://i43.tinypic.com/b8359w.jpg i used voltage divider i tried to calculate it by taking v1 as the midle poit of the left brench and v2 as the middle point of the of the other branch so Vout=V_s/2 -Vs[r/(r+1/jwc )=v_s/2(1-rjwc/2(rjwc+1)) i can't get the...

it is given that R1=R2 http://i43.tinypic.com/b8359w.jpg i used voltage divider i tried to calculate it by taking v1 as the midle poit of the left brench and v2 as the middle point of the of the other branch so Vout=V_s/2 -Vs[r/(r+1/jwc )=v_s/2(1-rjwc/2(rjwc+1)) i can't get the...

Homework Statement Aqueous solutions of hypochlorous acid, HOCl, can be unstable due to the reaction: 2HOCl <--> Cl- + ClO2- + 2H+ (c) Write out the balanced reaction appropriate to basic solution corresponding to the reaction given above. Homework Equations K =...

Homework Statement Write the partial fraction decomposition of the rational expression. Check your result algebraically. (x2 – 7x + 16)/[(x + 2)(x2 – 4x + 5)] The Attempt at a Solution [A/(x+2)] + [(Bx+C)/(x2-4x+5)] x2-7x+16= A(X2-4x+5)+(Bx+C)(x+2)...

Homework Statement cos(2 * arcsin(2x)) Use a triangle to simplify each expression. Where application, state the range of x's for which the simplification holds. Homework Equations cos(2t) = cos^2(t) - sin^2(t) = 1-2sin^2(t) = 2cos^2(t) - 1 The Attempt at a Solution My attempt was the...

Homework Statement Use double-angle and addition formulæ and other relations for trigonometrical functions to find an expression for sin(3x) in terms of sin x alone. My problem is I don't know what is meant by "find an expression for sin(3x) in terms of sin x alone.". I know the relevant...

How do I calculate the limit: lim x-> infinity ((2x+1)^13(3x-7)^17)/((3x+5)^30) Should I use the binomial theorem to open it up?

Homework Statement Given the luminosity profile L(r)=L0e(-r/D) and the density profile p(r) = v02/(4piGr2) find an expression for the mass-to-light ratio as a function of distance from the center of the galaxy r. Assume the ratio is unity at r = D. The Attempt at a Solution At first I...

When we are resolving a periodic piecewise continuous function in a fouriers series of harmonic terms, as follows: f(x)= a0/2 +Σancos nΠx/L + Σ bnsin nΠx/L, period 2L we are essentially expressing a sectionally discontinuous function (with finite no of such finite discontinuities, if at...

Homework Statement Consider the power series. sigma (n=1 to infinity) x^n / [n(n+1)] if f(x) = sigma x^n / [n(n+1)], then compute a closed-form expression for f(x). It says: "Hint: let g(x) = x * f(x) and compute g''(x). Integrate this twice to get back to g(x) and hence derive...

Hi, I have: \frac{a}{b+a+s} + \frac{c*b}{(b+a+s)(c+s)} I can rearrange that to: \frac{a-c}{b+a-c} * \frac{b+a}{b+a+s} + \frac{b}{b+a-c} * \frac{c}{c+s} Is this correct? If so, can someone tell me why the +s changes into a -c?

Homework Statement Consider the vector \vec A whose origin is \vec r. 1)Express the vector \vec A in a basis of Cartesian coordinates, cylindrical and spherical ones. 2)Repeat part 1) if the origin is \vec r + \vec r_0. Homework Equations None given. The Attempt at a Solution 1)In...

f(z) = SUM [(-1)n Where SUM = sum from n=0 to infinity Looks to me like there isn't but there must be a simpler way to write that. Thanks

Homework Statement I have two sets E and L. I have to show that E is a subset of L, using only complement, union and the empty set. I.e. all members of E also have to be members or L, but L may contain members not included in E.Homework Equations The Attempt at a Solution Am I right in...

the expression for the magnetic flux changing area is : change in m.flux=B.dA and for varying magnetic field change in m.flux=dB.A but for when the both is changing then what will the expression

Homework Statement Sorry if the question sounds a bit off, i wasnt quite sure how to word it. My math question is: given the expression Sn=n^2 + 2n, determine an expression, in simplified form, for Sn-1 in terms of n. Homework Equations NA (i don't think there are any equations for...

p = 4 q = -2 r = 3 s = -5 on that basis, evaluate this expression: 3r - 3p + 5q I make it to be -7 (15 - 12 + (-10) But my math book says the answer is -13. Can anyone explain where I have gone wrong? Thanks

Homework Statement Decompose the rational expression into a sum of partial fractions: (x+1)/(3(x-2)2) I am familiar with the method of decomposing fractions into a sum of partials fractions (solving for A, B, C, etc.). What is confusing me is the coefficient 3 in the denominator. Do I...

In R^3 I have two vectors a and b and the operator D = (d/dx,d/dy,d/dz) What is the interpretation/ picture of (aD)b - (bD)a? This is another vector.

I write MATLAB program on my computer but when I copy the file to another computer and press F5 to run, there is a message 'unexpected MATLAB expression' what should I do?

I write MATLAB program on my computer but when I copy the file to another computer and press F5 to run, there is a message 'unexpected MATLAB expression' what should I do?

Hello, during a calculation I got the following term: \varepsilon^{i_1 \ldots i_n}\varepsilon_{j_1 \ldots j_n} (a_{i_1}^{j_1}\ldots a_{i_n}^{j_n}) where \varepsilon is the levi-civita symbol and a_i^j are real numbers. Is it possible to simplify that expression?

Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. (ABC)*(DE)=(BCD)*(BF), and: FA+DF- CE=1

in this photo there is the circuit and the KVL of the solution but when i tried to do the KVL i go from the arc(3 lines represents potential zero) in counter clockwise direction so i get V_L + V_C+V_R-V_s=0 when i go against the direction of a current the voltage is on PLUS when in the...

We have been doing research on the differential expression of one gene between two cell lines (A and B cell lines), with high expression in A cell line and no expression in B cell line. We found that ~250 bp in the promoter of the gene has its activity in A cell line, but no activity in B cell...

can anyone tell me how to get the real and imaginary parts of the following function : (x+ i y)* Log( a+i b) where x, y a and b are all real numbers and i =sqrt (-1). Thanks very much

Homework Statement I have a quiz tomorrow and i know a problem like this is going to be on it and i need to figure out the process Homework Equations the expression is: (2x^2-3x+1)(4)(3x+2)^3(3)+(3x+2)^4(4x-3) The Attempt at a Solution i know the final answer(3x+2)^3(36x^2-37x+6)...

Homework Statement Make a BCD 3321 encoder. So if you input 0100, the encoder will output (depending on your design) either a 1001, or a 0101. Similarly, an input of 0101 will output either a 1010 or a 0110 (again, depending on your design).Homework Equations I know you're supposed to use...

The thin, uniformly charged rod shown in the figure below has a linear charge density λ. Find an expression for the electric potential at P. (Use k_e for ke, lambda for λ, a, b, and L as necessary.) Homework Equations dV=k*dq/r lambda*dx=dq The Attempt at a Solution I integrated...

Hey, so I have an assignment and this is one of the questions on it, I did it but I am not sure if what I did is right. What I did was find Ceq=(C1C2)/(C1+C2)) So then Q=CV(t)=(C1C2)/(C1+C2))V(t) Then I found the voltage across C2=Q/C2=(C1C2)/(C1+C2))V(t)/C2=(C1)/(C1+C2))V(t) And...

Homework Statement I have to rewrite the following expression using a radical. I know the correct answer according to my textbook is 4x√x. Homework Equations 4x ^{3/2} The Attempt at a Solution √4x^3 is this the right start?

Homework Statement A small sphere carrying a charge of q with mass m is suspended from point A by a massless thread of length L, as shown in the figure. A second sphere carrying a charge of 2q with mass M is suspended from a fixed rod from point B. The distance between A and B is equal to...

I've recently come across a http://technologyinterface.nmsu.edu/Spring08/" for why power is maximised in a component when its resistance R_L equals the internal resistance R. But in part (5) of method 1, we need to find the minimum non-negative value that the expression k+k^-^1 can take. For...

Homework Statement Rewrite the following expression as a single product. Hint: Perform a change of variable first. Homework Equations The Attempt at a Solution I looked at the example from the book regarding a change of variable. They first started out by calculating the upper and lower...

The problem is to find a closed form for the expectation (mu) and standard deviation (sigma) of the probability density function underneath (Maple notation): f(t) = a*exp(a*t)*BesselK(0, 2*sqrt(exp(a*t)))/BesselK(1, 2) I was able to find an expression for mu:: mu =...

Homework Statement 5^(log510-1) Homework Equations n/a The Attempt at a Solution I have no idea how to approach this.

Hi I have seen the expression for mass flow rate in one of the problems I am working on. I used to simply apply the expression for calculating the mass flow rate with respect to the position as (ρu + (∂u ∕∂x)dx) dy dz). ρ, u are density and velocity component respectively. I would like to...

Hi all. I´m looking for an expression for displacement of the waveform, eta(x,y,t) , of a circular wave that is created when a stone is dropped into a pond. Simplest case, assuming an ideal fluid and neglecting non-linear effects. Thanks, /scepter