I'm interested in coming up with an function that approximates the solution to a non-linear differential equation. (There is no known closed form solution)
The equation is Y''=(1/Y)(Y')^2-Y*A+Y^2*A where "A" is a constant, and Y' and Y'' are the first and second derivatives with respect to...
Homework Statement
This isn't really even a homework question..i've just been reviewing some general math concepts and this one has been driving me nuts..i haven't done math in a while.
At time t = 1, a particle is located at position (1,3). If it moves in a velocity field F(x,y) =...
Hello
Ive come across some approximate cross section formulas during a course of particle physics. And in a reaction like
A + B --> R --> C + D
the cross section should be something like
\sigma = K\frac{\Gamma_R^{AB}\Gamma_R^{CD}}{(s-m_R^2)^2+m_R^2\Gamma_R^2}
Where K is a constant (depending...
I got a relation as follow
\lambda_k = \frac{2 n(\lambda_k) L}{k}
where \lambda_k is a wavelength at mode k, k is integer, n is the index of reflection, L is a constant. I am trying to find the change of wavelength between two adjacent mode approximately, the answer will be...
Hello all. This problem is mostly math based, but is being applied to a programming algorithm.
I'm working on a problem with a massive amount of normalized vectors in a massive amount of dimensions and need to quickly compute the nearest neighbors of anyone vector. More precisely, I need to...
Homework Statement
Found the approximation using Trapezoidal and Midpoint Formulas using 8 rectangles.
How do I estimate the error?
Homework Equations
\int^{1}_{0} cos(x^2)dx
The Attempt at a Solution
Completely confused. I at first tried u-sub but later realized the error was far...
Calculate the approximate frequency of the C-H bond, with the force constant of k = 500 N/m.
Use:
Frequency = (1/2pi) Sqrt(k/((m1m2)/(m1 m2)))
BUTT WHAT DO I USE FOR MY MASS VALUES??
I tried, 12.011g/mol and 1.01g/mol and that is incorrect.
Hello!
I have the following formula -
a*k1 + b*k2 + c*k3 = P
This is a formula I'm trying to build. It will be used to calculate price of a specific good (P) according to criterions k1,k2,k3. Every k have its own value, that's why its being multiplied by coefficients a,b and c.
I have a...
Homework Statement
Use the differential dy or L to approximate cubed root 1.03
Homework Equations
L(x)= f(a) +f'(a)(x-a)
The Attempt at a Solution
I have no clue how to start so that would be the most help, do i just find the derivative of cubed root 1.03 first?
[SOLVED] Approximate eigenvalues
Homework Statement
Use some QR method to approximate the eigenvalues of
[4 3]
[3 5]
and compare with the actual values.
The actual values are (9±√37)/2
Homework Equations
A(0)=Q(0)R(0)
A(1)=R(0)Q(0)
A-α(0)I=Q(0)R(0)
A(1)=R(0)Q(0) + α(0)I...
[SOLVED] Approximate eigenvalues
Use some QR method to approximate the eigenvalues of
[4 3]
[3 5]
and compare with the actual values.
The actual values are (9±√37)/2
[SOLVED] particle in a box
Homework Statement
An electron moves with a speed of v = 10^{-4}c inside a one-dimensional box of length 48.5nm. The potential is infinite elsewhere. What is the approximate quantum number of the electron?
Homework Equations
E_{n} =...
Homework Statement
Homework Equations
So I know that there's an inverse relationship between the value of g and r; the farther I get away from earth, the weaker the gravitational force -> weaker acceleration...
BUT I'm not sure how the (1-x)^-2 thing is related, need help with that...
(** underscores refer to subscripts)
Consider inital value problem y'=2xy, y(0) = 1
Use Eulers Methos to estimate y(1) with 5 and 10 steps.
for 5 steps, increments are by 0.2
for 10 steps, increments are by 0.1
y_n+1 = y_n + h f(t_n , y_n)
where h is step size
the answer to the...
Let be the series
\sum_{p<N}e^{2\pi p ix}=f(x) where the sum is intended to be
over all primes less or equal than a given N.
My question is if there are approximate methods to evaluate this series for N big , since for a big prime the exponential sum is very oscillating would it be...
A new Hilbert-Polya (approximate) Operator??..
IN the Arxiv. they have put a paper on Hlbert-Polya conjecture..so the operator:
H= -\frac{d^{2}}{dx^{2}}+V(x) :confused:
Where the potential V is "constrained" to satisfy the (approximate ) INtegral equation...
the moon subtends an angle of 9.06 x 10^-3 radians amd os 3.84 x 10^8 meters from the earth. What is the approximate diameter of the moon.
so i think it has something to do with formula R=S/theta but I'm not sure how to compare the moon and the Earth information to find the diameter of the...
Math help!
I am home schooled and need some help with a few math problems that I have. These problems are the only thing holding me back from my diploma and i can't figure them out. Can I please get some help?
1. Using the "previous balance method", calculate the finance charge:
Previous...
Use Simpson's Rule and all the data in the following table to estimate the value of the integral
2
S ydx
-4
S=integral sign
x -4 -3 -2 -1 0 1 2
y 0 -4 -8 -9 1 5 -7
Does anyone know a trick for finding "K" in the error bound equations for approximate integration?
The approximate integrations we have learned so far are Midpoint Rule, Trapzoid Rule, and Simpson's Rule.
Thank you.
"Show that for small values of x, the function (1+x)^(-1/2) may be approximated by
1-(1/2)x+(3/8)x^2
Hence obtain the approximate value of 1/root(1.01) to 4 decimals."
im totally clueless. the example we have isn't well explained at all. can someone even just start me off...
Q: Approximate the minimum kinetic energy of an electron confined to a region the size of an atom (0.10 nm)
How would one go about solving this? What equations/principles are involved and how do we use them?
Seems like a simple question but i have no idea where to start? :confused...
I am supposed to find an approximation of this integral evaluated between the limits 0 and 1 using a taylor expansion for cos x:
\int \frac{1 - cos x}{x}dx
and given
cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!}...
i should get a simple series similar to this for...
There exist such a formula for large x:
\arctan(x)\approx \pi/2-1/x+1/3x^3...
I can't understand how it is derived. I tried to get it from Taylor series (for x -> infinity) and understood that here is something different. Can someone help me?
Thank you
Hi Guys,
Is there any whay I can use the following theorem to approximate the value of e^x at x=0?
f(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + ...
If the above function is not used for approximation, then what is it used to do?
Thanks heaps :smile: :smile: :smile:
I am thinking of applying to MIT as a transfer (I know, slim chance). But I am concerned about the amount of coursework; does anyone (perhaps who goes to MIT?) know just how much time it takes? I'm looking for approximate hours per week; I already know it's "a lot."
I have two similar problems. I need to show that
1. \frac{1}{2} \left( T_n + M_n \right) = T_{2n}
2. \frac{1}{3} T_n + \frac{2}{3} M_n = S_{2n}
where:
T is the Trapezoidal rule.
M is the Midpoint rule.
S is Simpson's rule.
This is what I've got:
T_n =...
Coefficient of Friction and Spring constant
What would the approximate value of (kinetic, and if possible, static) friction be for a block of wood of this nature:
\\Attachment 1 and 2
And how about the 'k' value for these springs? How would i go about calculating this sort of problem when...
I think I got pretty close to the answer to this problem. However, I just can't obtain the right approximation at the end. Please, help me find where I made a mistake.
Thanks.
--------------------------------------------------------------
Use a power series to approximate the definite...
Does anyone know what would be the approximate orbital period (time for one complete orbit) for an apple placed in orbit around Earth at the moon’s distance from Earth?