I've been studying a version of the finite element method.
The author of a paper I was reading refers to the partial derivative of total elastic energy wrt position, partial derivative of surfacic energy wrt position, and partial derivative of strain wrt position.
Does anyone know of a good...
Homework Statement
Find the integral and determine whether Cauchy's Theorem applies. Use partial fractions.
\large \oint \frac{tan \frac{z}{2}}{z^{4} -16} dz C the boundary of the square with vertices ±1, ±i cw
Homework EquationsThe Attempt at a Solution
I just wanted to check if approach is...
Is there a standard notation for partial derivatives that uses indexes instead of letters to denote ideas such as the 3 rd partial derivative with respect to the the 2nd argument of a function?
As soon as a symbol gets superscripts and subscripts like \partial_{2,1}^{3,1} \ f the spectre of...
When expanding a function (for example the determinant of the space-time metric g) as a functional of a perturbation from the flat metric ##h_{\mu \nu}##, i.e. ##g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} ## i would think that the thing to do is to recognize that ##g_{\mu \nu}## and thus also...
i understand the linear case...
example..
#/{(x+5)(x-4)} ----> A/(x+5) + B/(x-4)
but i don't understand this..
example..
#/{(x^2+3)(x^2+9)}------>(Ax+B)/{(x-√3)(x+√3)} + (Cx+D)/(x^2+9)
first of all... (x-√3)(x+√3)= x^2-3, which is nowhere in the original equation.. it's...
Homework Statement
I am given the following equation:
2NO (g) + Cl2 (g) \rightleftharpoons 2NOCl (g)
Kp = 6.5×104
PNO = 0.35 atm
PCl2 = 0.10 atm
I need to calculate PNOCl.
Homework Equations
Kp = \frac{(P_{NOCl})^2}{(P_{NO})^2*(P_{Cl_2})}
The Attempt at a Solution
I...
How do I turn 1/(x4+1) into partial fractions?
This is what I did. Let me know if this is correct
1/(x4+1) = 1/[(x^2+i)(x^2-i)] = (Ax+B)/(x2+i) + (Cx + D)/(x2-1)
Then I set x = 0
1 = (D-B)i .. My first equation would be D-B = 0.
Is that correct so far?
if there is something like (x^2+3x+6) in the denominator for one of the terms in a partial fraction problem, why do we put Ax+B instead of just A? and if the denominator is (x^2+3x+6)^2, why do we do {(Ax+B)/(x^2+3x+6)}+{(Cx+D)/(x^2+3x+6)^2}? i was always just told to memorize it, but why do we...
Determine which value best approximates the area of the region between the x-axis and the graph of ##f(x)=\frac{10}{x(x^2+1)}## over the interval [1,3]. Make your selection on the basis of a sketch of the region and not by performing any calculations. Explain your reasoning.
(a) -6 (b) 6...
Is there such a thing as a total "partial" derivative?
Total Derivative as I've Been Taught
From my understanding, if we have a function s = f(x, y) where the two arguments x and y are related by another function y = g(x), then there is a great deal of difference between ds/dx and ∂s/∂x.
∂s/∂x...
1) integral (upper bound:1, lower bound:0) (x^2+1)/(x^3+x^2+4x) dx
2) integral (upper bound:1, lower bound:0) (x^4+x^2+1)/(x^3+x^2+x-3) dx
Now I know how to use Partial Fractions,My question is:
1) For the first part ln(x) is not defined at 0
¼ʃ1/x dx + ¼ʃ(3x-1)/(x²+x+4) dx
= ¼ ln|x| +...
Homework Statement
Homework Equations
The Attempt at a Solution
I have to solve this question and I know that partial fractions is the intended method. I can do the long division easy, which gives:
Setting up for A and B, I get:
which produces:
4x-15= A(x-2)2 + B(x-2)
From here, I...
Hello I am stuck on an ODE involving substitution. I have done the correct substitutions, but have become stuck on decomposing the fraction.
i have the following
∫(1/x)dx + ∫(u+1)/(u^2+1)du = 0
Im stuck on breaking the u down into a partial decomposition. Could anyone offer some advice on...
Hello all,
I'm working through old exams for an electrical subject (no solutions given) and I think I've gone wrong somewhere and been left with something I'd like to learn how to work with anyway:
\frac{50}{(s+\frac{1}{s}+1)^2-s^2}
\frac{50}{2s+3+\frac{2}{s}+\frac{1}{s^2}}\times...
Question:
http://gyazo.com/bcb6c97ba462cdf4964121a6a40b0753
Mark scheme:
http://gyazo.com/b0475e7cb980ce98fb443932c28deed2
What I don't understand is the question specifies that x is not equal to 1/3 or -2, so why are you allowed to sub them into get the correct value for A B and C?
Hello, just a quick question about interpreting the partial derivative as a rate of change.
My example is the area of a parallelogram: A = absinθ, with a and b being the adjecent sides with θ being the angle between them.
We found the rate of change of the area A with respect to the side...
Hi All,
Please I need your assistance to solve this PDE below:
\frac{\partial^2 X}{\partial t^2} - \frac{\partial^2 X}{\partial z^2} + a(z,t) \frac{\partial X}{\partial t} + b(z,t) \frac{\partial X}{\partial z} +c(z,t) X =\Phi(z,t)
With initial and boundary condition...
Homework Statement
y(x,t) = f(x-ct)
verify this solution satisfies equation
∂y2/∂x2 = 1/c2*∂y2/∂t2
Homework Equations
The Attempt at a Solution
∂y/∂x = ∂f/∂x = 1
∂y2/∂x2 = 0
∂y/∂t = ∂f/∂t = -c
∂y2/∂t2 = 0
Is this the way to do it?
Partial Derivatives
Hi all I was wondering if anyone could help me with this problem. I have a triangle that has a = 13.5m, b = 24.6m c, and theta = 105.6 degrees.
Can someone remind me of what the cosine rule is?
Also (my question is here)
From the cosine rule i need to find:
the...
{Edit: as of 3:55 eastern time, made corrections to tex and itex mistakes}Is this all kosher in terms of demonstrating accuracy and comprehension of the notation {a_{1} + a_{2}...} = \lim_{n\rightarrow ∞ } \sum_{n=1}^{n} a_{n}
So the lower case represents sequences and upper case represents...
Hi Everyone,
I was studying coordinate transformation and I came across this equation, that I couldn't understand how it came up. Let me put it this way:
x = rcosθ
Then if I want to express the partial derivative (of any thing) with respect to x, what would be the expression? i.e. ∂/∂x=...
I'm reading through the book Quantum Mechanics (Second Edition) by David J. Griffiths and it got to the part about proving that if you normalise a wave function, it stays normalised (Page 13).
That part that I don't get is how they say:
## \dfrac{i \hbar}{2m} \left( \Psi^* \dfrac{\partial^2...
Hello MHB,
I got stuck on this integrate
\int_0^{\infty}\frac{2x-4}{(x^2+1)(2x+1)}
and my progress
\int_0^{\infty} \frac{2x-4}{(x^2+1)(2x+1)} = \frac{ax+b}{x^2+1}+ \frac{c}{2x+1}
then I get these equation that I can't solve
and I get these equation..
2a+c=0 that is for x^2
2b+a=2 that is for x...
Let's start with:
$$ \int \frac{dx}{1+x^2} = \arctan x + C $$
This is achieved with a basic trig substitution. However, what if one were to perform the following partial fraction decomposition:
$$ \int \frac{dx}{1+x^2} = \int \frac{dx}{(x+i)(x-i)} = \int \left[ \frac{i/2}{x+i} -...
I'm thinking in particular about Lenny Susskind's lectures, but I've seen other lecturers do it too. They'll be writing equation after equation using the partial derivative symbol:
\frac{\partial f}{\partial a}
And then at some point they'll realize that some problem they're currently...
I have a feeling the question I am about to ask, I won't be able to ask it the way I am trying to...but I will try. I will break it up into two questions.
1) What are its real life applications? Much easier for me to get it when I can see a real life application
2) Why is it the way it is...
Any Conceptual Underpinning for Partial Reflection of Light (QED)?
I recently partially read Feynman's QED. At one point, he says "The situation today is, we haven't got a good model to explain partial reflection by two surfaces;..."
(page 24--can visit Amazon "Look Inside" to read)
My...
I have several questions that are related to something I am designing. I am having a hard time finding the correct formulas I need, so I am here :D
Anything will be helpful, from general topics/ideas to get me in the right direction, to specific formulas. I do not mind abstract ideas, this is a...
What does it mean by 21% oxygen and 79% nitrogen by volume?
Because won't the oxygen and nitrogen have the same volume which is the volume of the whole container?
nTRT/VT=nO2RT/VT+nN2RT/VT so why would we say oxygen is 21% by volume since the volume of the oxygen and nitrogen is the same...
From the two equations given below, find ∂s/∂V (holding h constant) and ∂h/∂V (holding r constant
V = π*r^2*h, S = 2π*r*h + 2*π*r^2
Not entirely sure where to start...
I don't understand the calculus behind this thermodynamics concept:
S = f(T,P)
dS = (∂S/∂T)_P*dT + (∂S/∂P)_T*dP
(∂S/∂T)_V = (∂S/∂T)_P + (∂S/∂P)_T*(∂P/∂T)_V
Basically, I don't get why and how you get (∂S/∂T) when you divide dS by dT. Also, I don't understand why the constant volume...
Homework Statement
Give the partial fraction decomposition of 1/z4+z2
Homework Equations
The Attempt at a Solution
My question is about the final answer. The book gives the answer to be 1/z2+ 1/2i(z+i)- 1/2i(z-i). For my answer I keep getting a negative for both of the 1/2i...
Homework Statement
Consider the spherical well such that V(r<a) = -V0 and V(r≥a) = 0. Calculate the l = 0 partial wave scattering cross section in the low energy limit for this potential.
Homework Equations
σ = \frac{4 \pi}{k^2} * \Sigma (2l+1)*sin^2(\delta_l)
The Attempt at a...
Homework Statement
Hi
In a container of 1.5L there are 2 gases O2 and C3H8.
their partial pressures are O2 = 5atm, C3H8=0.1atm.
the temperature is 20C.
the reaction produces H2O and CO2.
Temperature is constant.
What is the partial pressure of CO2 after the reaction? (need to find...
Homework Statement
Solve the following system of partial differential equations for u(x,y)
Homework Equations
du/dy = 2xyu
du/dx = (y^2 + 5)u
The Attempt at a Solution
I am honestly not sure where to start, my lectures and tutorials this week have not been helpful at all. My guess is to...
Hello,
Could anyone please explain me the steps in these pictures.
I do not understand the second step.
http://imgur.com/AvVbPu5,Ust2Zpx#0
Second one:
Third step ( i don't understand)
http://imgur.com/AvVbPu5,Ust2Zpx#1
If anyone can give me detail explanation, i would really appreciate it.
Homework Statement
The separation of layers is considered to occur at the thermocline, which is defined as the location of the steepest slope in the temperature gradient. Mathematically, this occurs at the inflection point – so the position of the thermocline can be found from the following...
Am I assuming right the pressure in a vessel holding two substances (both being in the both liquid and gas states) will be equal to the saturation prerssure of the one which has the higher SP ? That is, for substance A whose SP at a given temp. is 10 B, for instance, and substance B whose SP is...
In the chapter on partial wave analysis in Griffiths's Introduction to Quantum Mechanics, he considers a spherically symmetric potential and says that for large r, the radial part of Schrodinger's equation becomes,
\frac{d^{2}u}{dr^{2}}≈-k^{2}u
with a general solution of...
Homework Statement
If z=f(x,y) with u= x^2 -y^2 and v=xy , find the expression for (∂x/∂u).
the (∂x/∂u) will be used to calsulate ∂z/∂u.
my question is how to find (∂x/∂u).
I don't know what to keep constant. Maybe the question has some problem.
The answer is (∂x/∂u)=(x/2)/(x^2+y^2)...
Homework Statement
Use partial fractions to find the sum of the series.Homework Equations
\displaystyle \sum^{∞}_{n=1} \frac{8}{n(n+3)} The Attempt at a Solution
I end up with:
\displaystyle \frac{8}{3n} - \frac{8}{3(n+3)}
I am stuck here.
Hello guys!
Lately I've been studying some topics in Physics which require an extensive use vector calculus identities and, therefore, the manipulation of partial redivatives of vectors - in particular of the position and velocity vectors. However, I am not sure if my understanding of partial...
Homework Statement
Where T(x,t)=T_{0}+T_{1}e^{-\lambda x}\sin(\omega t-\lambda x)
\omega = \frac{\Pi}{365} and \lambda is a positive constant.
Show that T satisfies T_{t}=kT_{xx} and determine \lambda in terms of \omega and k.
I'm not to sure what is meant by the latter part of "determine...
Homework Statement
A 32.0 mL sample of hydrogen is collected over water at 20°C and 750.0 torr pressure. What is the volume of the dry gas at STP? (vapor pressure of water at 20°C = 17.5 torr)
Homework Equations
Ptot = Pdry + Pwet
P1V1/T1 = P2V2/T2
The Attempt at a Solution...
I have a partial linearly distributed load on a cantilever and would to determine the bending moment distribution along the beam.
I usually do this by taking cuts along different sections of the beam and finding the expressions for shear force and bending moment. However when I do this...
Homework Statement
If f is homogeneous of degree n, show that f_{x}(tx,ty)=t^{n-1}f_{x}(x,y).
Homework Equations
The Attempt at a Solution
There are many solutions out there, and here's one of them:
The proof is nice, but I just don't get it why from step 1 to step 2, \frac{\partial...
Homework Statement
(x^3+4)/((x^2-1)(x^2+3x+2))Homework Equations
The Attempt at a Solution
Try separating them into Ax+B and Cx+D, then expand until
(A+C)x3+(3A+B+D)x2+(2A+3B-C)x+(2B-D)
then, I was stuck. I can't find any value for A,B,C or D. Is my attempt correct or is there other way to...