Exponential Definition and 1000 Threads

how to compute the nonconstant matrix exponential؟ i.e. if there is a matrix A(t), how i can find exp(A(t)) ?

Homework Statement http://d.imagehost.org/view/0659/Capture Link to wolfram alfa:http://www.wolframalpha.com/input/?i=integrate%28cos%28e^x%29*e^x What i don't understand is why whey do it like this and why i can't integrate by parts in this case? Thanks for any replies!

I really appreciate if anyone could indicate me how to handle this inverse Laplace transformation (ILT): L-1[Exp(-c0*Sqrt(a(s)))/Sqrt(a(s))] where a(s)=(s2+c1s)/(c2s+c3) c0,c1,c2,c3 are all constants. I searched some literatures regarding the ILT of Exp funtions but no such form. I used...

Homework Statement If there is a quantity T comprised of two other quantities such that T=L+B, and quantity T and B are both increasing in every period at a fixed percent such that %growth T > %growth B, it will be true that %growth L > %growth T. It will also be true that as n approaches...

Hello, Something I've wondered about for some time is what happens to units once we pump them into a exponential or log function. For example in neutron attenuation I(x) = I_0 * exp(-Sigma * x) I feel like this something I should know, but I just don't get it. I suspect what's...

I am having difficulty trying to rearrange this equation to solve for one unknown variable. i=(io)exp(z*α*F*∆V)/(R*T) How would I rearrange this equation if i wanted to solve for io, also how would I rearrange this equation to solve for say α.

Homework Statement Show that e^{tA} = I - A + e^{t}A t \in T \ \ \ \ T \subset R R being the set of real numbers and T some interval. The matrix A is a projection matrix. i.e. A^2 = A The Attempt at a Solution First attempt at the problem involved showing that e^{tA}...

start point (1-Exp[-i x])^2, (i^2 = -1) finish point Sin^2(x)

I know how to do Frobenius on variable coefficient ODE's but only when the coefficients are powers of the independent variable. Can I do method of Frobenius on something like: y'' + e-xy = 0 ? What form would I assume a solution of? Just the regular y=sum(Akxk+r ? Thanks for the help!

Homework Statement Find the general solution to x'' + e^(-2t)x = 0, where '' = d2/dt2 Homework Equations - The Attempt at a Solution First I did a change of variables: Let u = e^(-t) Then du/dt = -e^(-t) dx/dt = dx/du*du/dt = -e^(-t)*dx/du d2x/dt2 = d/du(dx/dt)du/dt =...

I don not know whether I was right or not, please give me a hint. (R3,+) can be considered a Lie group. and its TG in 0 is still R3. suppose X as a infinitesimal generater, it can give a left-invariant vector field and also an one-parameter subgroup. but i think, this one-parameter...

Homework Statement I was given three plots of solutions for a forced exponential diffeq: y'[t]+1.85 y[t]=0.7t^2 with starter values on y[0] equal to -6, 0,and +7 The three plots eventually merge, how do I give the formula for this parabola? Homework Equations E^(-r t)...

I was given three plots of solutions for a forced exponential diffeq: y'[t]+1.85 y[t]=0.7t^2 with starter values on y[0] equal to -6, 0,and +7 The three plots eventually merge, how do I give the formula for this parabola?

Homework Statement Here is the question: solve y'[t]+0.2y[t]=Sin[t] with y[0]=15.3 How do I come up with a formula for y[t]? Thanks in advance! Homework Equations y[t]= starter+e^-rt The Attempt at a Solution I attempted to solve the equation as is. After doing some algebra...

Homework Statement Expand (1+e^(2x)), and (1+e^x)^2. Are they any different. I am confused please help Homework Equations The Attempt at a Solution

if i have a set of data, where as time increases, so does y, but is bounded by a number say y=c, how do i formulate my equation? how do i find the constants? i have y=c-a-x*b this is basically a transformation of y=b*ax+c

Homework Statement The problem is 3^2x+3^(x+1)-4=0 I know I had to solve it by substitution Homework Equations The Attempt at a Solution I had u = 3^x I put it in: (u )(u ), but I was not sure how to get the middle term 3^(x+1)

Does e^[(-infinity)+(i*w*infinity)] = 0 or 1? w = omega

Homework Statement Starting from the Gamma function: \Gamma (s) = \int^{\infty}_{0} dx \, x^{s-1} e^{-x} Make a change of variable to express it in the form: \Gamma (s) = f(s) \int^{\infty}_{0} dy \, \exp{\frac{-A(y)}{\zeta(s)}} And identify the functions f(s), A(y)...

e^2x = 5e^3x I understand that I need to take a natural log of both sides here, what I am thrown about is the constant "5". Can I bring that up as an exponent? So, e^2x = e^(3x)^5?

Homework Statement if z = -2 + 2i find r and θ The Attempt at a Solution our teacher told us that when we have z = a + bi r = sqrt(a^2 + b^2) and θ = tan^-1(b/a) so here it's supposed to be r = sqrt(8) and θ = - pi/4 but using wolfram alpha to see if the results are...

Homework Statement A concession stand serves customers with each customer starting as soon as the prior one finishes. The wait times are from an exponential distribution with mean = 2 minutes. Therefore the Total time is the summation of xi for i 1 to 4. Find the mean , variance and...

z_k=\sqrt[n]{u}=\sqrt[n]{r}e^{i\left(\frac{\phi+2k\pi}{n}\right)}, k=0,1,2,...,n-1 and z_k=\sqrt[n]{u}=\sqrt[n]{re}^\frac{\phi+2k\pi}{n}, k=0,1,2,...,n-1 Which one is incorrect (note that in the first, e is out of the root)?

Homework Statement According to the Inverse Function Theorem, for every z_0 \in C there exists r > 0 such that the exponential function f(z) = e^z maps D(z0; r) invertibly to an open set U = f(D(z_0; r)). (a) Find the largest value of r for which this statement holds, and (b) determine the...

Hello, I am trying to evaluate the series \sum{\frac{x^n}{n!}e^{cn^2}} where c is a constant. I think this problem is equivalent to find f(x) such that \frac{d^{n}f(0)}{dx^{n}} = \frac{e^{cn^{2}}}{n!} I believe this must be a modified exponential since for c=0, it reduces to...

Homework Statement I need to integrate the following function: y = \int e^{-\frac{n}{\omega}cos \omega t} dt Homework Equations How should I solve this? Will this lead me to Bessel function? 2. My attempt a=\frac{n}{\omega} u=-a cos (\omega t) du = a\omega sin...

Homework Statement find three independent solutions using complex exponentials, but express answer in real form. d^3(f(t))/dt^3 - f(t) = 0 Homework Equations The Attempt at a Solution after taking the derivative of z = Ce^(rt) three times I put it in the following form...

Homework Statement write e^z in the form a +bi z = 4e^(i*pi/3) --------------------------------------- My guess: z = 4*(cos(pi/3) + i*sin(pi/3)) e^z = e^(4*(cos(pi/3) + i*sin(pi/3))) = e^(4*cos(pi/3))*(cos(4*sin(pi/3)) + i*sin(4*sin(pi/3))) but the solution says...

Hello, I am having difficulty solving the following integral: \int^{\infty}_{-\infty}e{-(a|x|+ikx)}dx I have tried to use an explicit form of the absolute, eg. -(a|x|+ikx) = \left\{\stackrel{-(ik+a)x\ x>0} {-(ik-a)\ x<0} Does this allow me to separate the integral into a sum of two...

The signal x(t) = e^{jt} is periodic. The signal x(t) = e^{-t}e^{jt} is not periodic. The decaying exponential makes the complex exponential decay and converge toward zero, but why is it not periodic? Also, this signal is not considered time limited since it never actually reaches zero...

Homework Statement \int^{\infty}_{0} e^{-y} dy = 1 Homework Equations The Attempt at a Solution Why is this equality true? I understand that the integral and derivative of e^y is always e^y, but I can't make out why this definite integral is equal to 1. I graphed it using a...

Homework Statement 2n=n2 Homework Equations The Attempt at a Solution I know the solution is 2 and 4. But I have no idea how to solve it without guessing...

Homework Statement Write the function for each graph described. Exponential function with y-intercept of 3 and horizontal asymptote of y=0Homework Equations None The Attempt at a Solution I used the base equation f(x)=a^(x+h) + k to get f(x) = 3^(x+1) Was this right? Also, I used guess and...

Homework Statement Hey guys. How do I solve this integral? http://img816.imageshack.us/img816/208/68315659.png I've not been doing this for a long time :) Thanks a lot. Homework Equations The Attempt at a Solution

find x for y=5 y = -(((e^x)/(e^-x))/2) + ((e^x)/(e^(-3x)) all i did was a^m / a^n = a^m-n i get here y = -1/2(e^(2x)) + (e^(4x)) after this i get iffy and want to make sure i can do what i did. 5 = -1/2(e^(2x)) + (e^(4x)) ln|5|= -1/2(ln(e^2x)) + ln(e^4x) ln|5|= -1/2(2x) + 4x...

I've been struggling with this problem for more than 4 days now: Let A, B and C be exponential distributed random variables with parameters lambda_A, lambda_B and lambda_C, respectively. Calculate E [ B | A < B < C ] in terms of the lambda's. I always seem get an integral which is...

Homework Statement If X is a random variable with density function: f(x) = \lambdae^{-x \lambda}where X>=0.Homework Equations Why is the expected value of X, or E[X] = \frac{1}{\lambda}?The Attempt at a Solution E[X] = \int x*(\lambdae^{- \lambda}^{x}) dx, where the integral is from 0 to...

Homework Statement I'm working out different pathlengths for different solids but I'm stuck on the following integral: Homework Equations \int x*exp(-C*sqrt[1-x2/A2]) dx exp = exponential func sqrt = square root C and A are constants The Attempt at a Solution I tried to work...

I'd like to do one of two things: 1: Find an example of a non-diagonal matrix whose matrix exponential (defined in terms of series) is diagonal. 2: Prove that no such examples exist. I'm working with matrices over the complex field. My gut tells me that 2 is the way to go. I'd really...

I've tried and searched for a long time, and I haven't been able to prove or find a proof that the following sequence converges (without using another definition of the exponential function): \forall x \in \mathbb{R}. Prove that: \lim_{n \rightarrow \infty} (1+ x/n)^n exists. I can...

Hi i was wondering if anyone could help me with a fairly simple integration. \int exp(iab/c)exp(-iaz) da Where the integral is from 0 to infinity Im not sure how to proceed with this and am basically teaching myself Thanks in advance for any help.

Homework Statement Greetings - can someone please check my work, many thanksHomework Equations If x = 12.4 Find the value of ... correct to two sig fgures 8^(4x/3) / log(base 10) (5x-3/x^0) The Attempt at a Solution = 8^(16 8/15) / log(base 10) (5(12.4)-3 / 1) = 4.8 x 10^14 (via calc...

I just want to make sure that I have this in the correct order. The book I have is very unclear. e^x + e^-x = 6 e^x + 1/e^x = 6 e^2x + 1 = 6e^x e^2x/e^x + 1 = 6 x = ln 6 Thanks.

Hi, I need to solve the equation e^z = -3 The problems arises when i set z to a+bi e^a(cos(b) + isin(b),~b = 0 Then I am left with e^a = -3 However you're not allowed to take the log of a negative number. Also i know that cos(\pi) + isin(\pi) = -1 Obviously 3e^{(\pi*i)} is a solution, but...

Homework Statement Turn y = y(0) * e^(-kt) into a polynomial. Homework Equations The Attempt at a Solution I have no idea of how I would go about doing this. I know you can use taylor series to approximate it, but is there any other way? Thanks, Darthxepher

Dear all, I have exponential integral with polynomial. I tried to solve it but I could not. the integral is :Homework Statement The integral equation is: \int_{-\infty}^{\infty} (ax^2+bx+c) e^{ax^2+bx+c} dx$ Homework Equations The Attempt at a Solution Can anyone help me please. Thanks...

Is it possible to integrate this function \int {e^{x^2}} dx \int \left (y^2) e^{y^2} dy The book says there is no direct method to solve this type of integrals but there is no hint how to solve this.Any one please help. Thanks :) Sorry for the latex code i have put the integration...

Homework Statement Solve for x: 4x+7=18 Homework Equations It becomes 4x=11 The Attempt at a Solution I have no idea where to go from here. We never had a problem with such an immovable number such as 11 to work with. Calculators are not allowed to be used either.

Hello every one, I was doing my research and then I simply struck at a point. The point is that i do not know how to solve the following Integral. I am not at all bad at doing math but some times I got blanked. so, here is the Integral, Integral (infinity,u) exponent^(-u) du...

I have to calculate the exponetial of a large (on the order of 10^5) negative number. I tried using exp(), the exponential function from the cmath library, but I get an answer of 0. So, I tried to use the power series for the exponential function. For numbers from -1 to -14, I get answers which...