Variables Definition and 1000 Threads

For the system of equations $$ \mathbf{x}' = \begin{pmatrix} a\cos 2t & a\sin 2t\\ a\sin 2t & -a\cos 2t \end{pmatrix}\mathbf{x}, $$ verify that under the change of variables: $$ \mathbf{x} = \begin{pmatrix} \cos 2t & \sin 2t\\ \sin 2t & -\cos 2t \end{pmatrix}\mathbf{u}, $$ the equations for $u$...

Hello, I often encounter some confusion. For example, we have the equation for a circle of radius one given by: x2+y2=1 Now we can't express this as a function in R2 because it's a relation. however, we can still find derivatives like dy/dx or dx/dy using implicit...

How do you make a number of input file streams, one for each input file so that can copy/append the contents of these files to one output file? The number of input files is only known at run time and varies from run to run of the program. The input file names are first stored in a linked list...

Homework Statement A 4.27-kg object is thrown vertically upward from the surface of Mercury, where the acceleration due to gravity is g1 = 3.70 m/s2. The initial velocity is v1, and the object reaches a maximum height of y1. What is the maximum height, y2, if the object is thrown with a...

please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches... your help is highly appreciated!

Homework Statement A rocket is shot straight up with an initial speed at 500 m/s. Homework Equations The equations the teacher went over beforehand were Yf = 1/2 A(T)^2 + Vi(T) + Yi Vf = A(T) + Vi The Attempt at a Solution So far I have Vf = (-9.8)(T) + 500 m/s Yf = 4.9T2 +...

we have a well known and simple equation for curl in cartesian coo. now we want it in let's say cylindrical coordinates. question is...can we transform every thing to cylinderical and then use the formula for cartesian?I mean writing basis vectors of cartesian in terms of r and theta and z and...

1.A tennis ball is dropped from 1.3 m above the ground. It rebounds to a height of 0.956 m. With what velocity does it hit the ground? The acceleration of gravity is 9.8 m/s^2 (Let down be negative.) Answer in units of m/s 2.With what velocity does it leave the ground? Answer in units of m/s...

Hi Guys, I have a Year 11 Project weighted 15% of my year mark due in 5 weeks. For my project I've decided to build a classic combustion potato gun. This gun will consist of pvc piping, barrel, Lantern lighter, any other components and of course hairspray (combustion) Anyways It is still only...

Homework Statement Take Ω = [0, 1] and P the uniform probability. (a) Give an example of two random variables X and Y defined on Ω that both have the same Bernoulli distribution with parameter θ = 1/3. (b) Give an example of such random variables that are independent, and not independent...

Hi all Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this? Also y'' =0. Is the same as. y''dx =0 dx Why is this legal?Thanks in advance

-2((1/((x^2 + 1)^2 )) - ((4x^2 )/(x^2 +1)^3 )) = 6x^2-2/(x^2+1) This is actually the last step of this problem. I understand everything they did up until here, but I'm a bit confused as to how they got from their last step, to the actual answer. Could someone explain?

Hello everyone! I am fairly new to SDE theory, so I'm sorry if my question may be a bit naive. I have the following coupled set of SDE:s d\phi = \frac{v - v_r}{R}d t + \frac{\pi}{\sqrt{t_c}}d W d v = A\cos(n\phi - \phi_w)d t + a_v d t + \sigma_v d W. W denotes a Wiener process, and the...

I know UC San Diego is good, Rothschild and Ebenfelt are there, but are there any other ones that stand out in these and related fields? Thanks a bunch

Let U and t be independent real variable. In the limit: t/U \rightarrow 0 Can I say that t^2/U \rightarrow 0 too? Or I can compare only same powers of both? Regards.

I'm having difficulty deducing that Re z = 0.

solve the following equation for z in terms of x and y 3y^{2}+2yz-5z-2x=0 i've spent a lot of time on this question, but i keep getting something along the lines of 0=0 i tried solving for x in temrs of y and z to replace the x but i get 0=0 Homework Statement Homework Equations The Attempt at...

Hello. How do I evaluate, in Mathematica, limits like this: "X+Y" when X is much bigger than Y, i.e., when Y/X->0. The unswer should be X+Y->X. Regards.

Homework Statement Consider the function F(xyz)=x^4+5y^4+2yz+3. Let the uncertainty in x be represented by the variable dx, the uncertainty in y be represented by the variable dy, and the uncertainty in z be represented by the variable dz. Find an algebraic expression for the uncertainty in...

Homework Statement Determine the set on which f(z) = 1/(z^3 +1) is analytic and compute its derivative. Homework Equations Hint: you do not need to appeal to the Cauchy-Riemann equations The Attempt at a Solution Total stuck with this one. everything we have done this far has...

Hey guys, how come when you have a parametric equation with two free variables it creates a surface, but when you have a parametric equation with one free variable it draws out a line? I sort of get it intuitively, one dimension is just a line, two dimensions is a plane, so I guess this sort of...

Hello, I am going through Whittaker's treatise on Classical Mechanics. In chapter 3 he derives the equation of motion for a simple pendulum, and I have a question about his method. Starting from the general form for the equation of energy (s is the path): [SIZE="5"]\frac{m}{2}\dot{s}^2...

Hey guys and gals, this isn't actually an assignment of any sort, so I didn't want to put it in the homework section. This is also my first post, though I have been lurking for quite a while, reading the copious amounts of information available here. :p Anyhow, could somebody please elaborate...

Homework Statement In double integrals, the change of variables is fairly easy to understand. With u = constant and v = constant, along line KL v = constant so dv = 0. Therefore the only contributing variable to ∂x and ∂y is ∂v. The Attempt at a Solution However, in tripple...

what is the ε & δ definition of continuity of f(x) at x=0

I have a differential expression that I want to expand to some order around infinity (it's for calculating weak-field limits in GR). I have two functions, B(r) and n(r), and some expression involving them along the lines of n[r] (3 r B'[r]^2 - 4 B[r] (2 B'[r] + r B''[r])) Basically I want...

$x^2+m^2=2mx + (nx)^2$, $n\neq1$, $n\neq-1$ isolate $x$ rewriting $m^2-2 m x-n^2 x^2+x^2 = 0$ $m(m-2x)-x^2(n-1)(n+1)=0$ I set this to 0 thinking I could factor by grouping but not.. So seem to be stuck on how to to isolate x the books answere to this is $\frac{m}{1-n},\frac{m}{1+n}$ thnx...

Homework Statement The probability of being dealt a full house is approximately 0.0014. Find the probability that in 1000 hands of poker you will be dealt at least 2 full houses Homework Equations I can use binomial distribution. The Attempt at a Solution The probability of getting...

Hi everyone, I'm a Physics student going into my Junior year and I'm currently registering for my courses for the following semester and I have two options for my "complex" course, namely: --------------------------------------------------- Complex Variables Theory of functions of one complex...

Homework Statement ac + bc = (a - c)(a + b) - xabcd^2 Homework Equations Various factoring rules (difference of two squares, etc.)The Attempt at a Solution I got it expanded to: ac + bc = a^2 + ab - ac - bc - xabcd^2\\0 = a^2 + ab - 2ac - bc - bd - xabcd^2 I tried factoring different ways...

I am struggling with this question which appears in every adv. calculus exam paper I practise and would love some help or advice on how to even approach it! I have no trouble getting the extreme points and determining whether they are local minimum, local maximum or saddle points, but proving...

Homework Statement I am performing a change of variables, s --> t and am wondering can I just write g(s) --> g(t) or do I have to alter the function e.g. g(s) --> a*g(t). Homework Equations s = (a/b)* t g(s) is to be found numerically and therefore we do not have it's definition. So...

Hi. I borrowed many multivariable Calculus book so that I can choose one for the next semester. The one I liked most is Multivariable Calculus by Ron Larson. It is full of graphics and colours, somthing that is essential to understand functions of two variables. The only thing is that it does...

i have a question. i just try to learn MATLAB however i couldn't define the functions and variables inside the one script. i open new script file and give the function comment in it for example like this... function [ y ] = betaf( x,Ee) lambda=0.1; y=100*gammaf(Ee)*lambda/(2*pi*x)...

Hi All, I've managed to confuse myself with a simple change of variables. I have an integral of the form: $$ I = \int_f^{\infty} dt \int_0^1 ds\, t\, F(t(1-s),ts), $$ where $F(a,b)$ is some well behaved function and $f$ is a positive number. I want to change variables: $$ x =...

Mathematica:Solving two equations with two variables ?? Hi, I am trying to solve two equations with two unkonwn variables. These equations are equal to zero so my way was first picking one of the variable to one side of the equations and equalize them and find the other unknown parameter...

How to solve this system? \begin{align} & \sqrt{\frac{x_{1}^{2}x_{4}^{2}}{4}-{{({{x}_{1}}-{{x}_{4}})}^{2}}}-\sqrt{\frac{x_{1}^{2}x_{3}^{2}}{4}-{{({{x}_{1}}-{{x}_{3}})}^{2}}}=\sqrt{\frac{x_{3}^{2}x_{4}^{2}}{4}-{{({{x}_{3}}-{{x}_{4}})}^{2}}} \\ &...

∫∫9(x + y) e^(x2 − y2) dA, where R is the rectangle enclosed by the lines x−y=0, x−y=10, x+y=0, and x+y=5 Relevant Equations: The Jacobian: ∂(x,y)/∂(u,v) The attempt at a solution: I began by making u=x+y and v=x^2-y^2 So, u=0 and u=5, but I don't know what to do with the x-y line...

1. A scientist is investigating the effect of different types of radiation on the surface of a piece of Sodium metal. He uses a freshly cut surface on a Sodium plate. 2. a) Which of the variables is the dependent and independent variables? b) Why must the surface of the Sodium...

Can anyone help me on this equation. I want to find a solution for dr/dt. a, b and c are constants.

"separation of variables", but for 2nd order Ok, I know how to separate variables in solving an ODE. I am unable to understand a solution I have for a problem which was the result of reduction of order- we end up with u''*sinx-2u'*cosx=0 so turn this into u''/u'=-2cosx/sinx At this point I...

Hi all. This is my problem. I have two IDL procedures hr2altaz, hour, dec, alt, az -- which takes the HA and DEC and converts it to ALT and AZ altaz2hr, hour, dec, alt, az -- which takes ALT and AZ, and converts it to HA and DEC. What I need to do, is to begin with a certain HA and DEC...

Consider the differential equation where I''+I=e^it where i= sqrt (-1) So I don't know what to do. I do know that The second derivative of c*t*e^(i*t) is -c e^(i t) (-2 i+t) But I don't know what to do for a and b and I need help to get threw this problem before I take my test...

hi, i want to take an x-y data set and find the deviation from another dataset. the master dataset is two identical y=1/x curves of different amplitude; also one only registers at periodic intervals and the second is multiplied by a noise signal. so part of the problem is going to be...

Homework Statement Let's say the independent variable (in statistical terms) A depends on variables B, C and D. We perform tests, and find out that the variable A causes "something" with the values of B, C and D equal to B2, C2 and D2. Let's also say that A with variables B, C and D of B1...

Hi, In Griffiths QM, it is claimed that to solve the Schrodinger Equation, we take the solution wavefunction \Psi(x,t) to be of a seperable form \psi(x)\phi(t). He then says that a superposition of these seperable forms can always give us the general solution. Can someone help me prove that...

Why do we solve for only the pivot variables when we are trying to solve a system of equations using reduced row echelon form? Thank you

I was reading over a textbook that stated the following, where y(s,t) = v(x(s,t),t) \frac{\partial y}{\partial t} = \frac{\partial v}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial v}{\partial t} and \frac{\partial^2y}{\partial t^2} = \frac{\partial^2 v}{\partial x^2}\left (...

Hi all! I'm sorry if this question has been already asked in another post... I'm studying the path integrals formalism in QED. I'm dealing with the functional generator for fermionic fields. My question is: The generating functional is: $$Z_0=e^{-i\int{d^4xd^4y \bar{J}(x)S(x-y)J(y)}}$$...

For single variable functions derivative means slope of tangent what does it mean for functions of more than one variable. book says that a function is said to be differentiable if: f(x + Δx , y + Δy) - f(x , y) = AΔx + BΔy + ε'ψ(Δx , Δy) + εh(Δx , Δy) WHERE ε, ε' → 0 AS Δx , Δy → 0...