Partial Definition and 1000 Threads

Homework Statement \frac{\partial f}{\partial t},\frac{\partial f}{\partial x} where f=f(x,t,\frac{dx}{dt}) Homework Equations The Attempt at a Solution I think it's impossible to consider it as a simple partial derivative.

Homework Statement Find the first partial derivatives ∂z/∂x and ∂z/∂y of sin(0x+5y+z)=0 at (0,0,0). Homework Equations sin(0x+5y+z)=0 The Attempt at a Solution 0x+5y+z=kπ z=kπ-5y So, ∂z/∂x= 0 and ∂z/∂y= -5 What I do not understand is WHY 0x+5y+z=kπ is an acceptable...

The question is: a) Find explicit expressions for an ideal gas for the partial derivatives: (∂P/T)T, (∂V/∂T)P and (∂T/∂P)V b) use the results from a) to evaluate the product (∂P/V)T*(∂V/∂T)P*(∂T/∂P)V c) Express the definitions of V(T,P) KT(T,P)an BT(T,V) in terms of the indicated independent...

My professor asks us to solve the integral of: [x/(x^4 + 1)]dx This expression is not factorable; what should I do? She is asking us to solve specifically using PFD, not u-substitution.

I have a function Z = f(P,T) and would like to calculate the partial differentials \left ( \frac{\partial Z}{\partial P} \right )_T and \left ( \frac{\partial Z}{\partial T} \right )_P at values of P and T. The function Z is compressibility factor (Lee and Kessler equation of state), P...

Homework Statement At 1 atm of pressure a volume of 22 liters of N2 gas is passed in a closed system over a boat containing Hg liquid at 100°C. The flow of N2 is slow to allow the gas to become saturated with mercury. At 20°C and 1 atm, the nitrogen was found to contain 0.0647g of Hg...

Here is the question: Here is a link to the question: Integral of ((19x^2)-x+4)/(x(1+4(x^2)))? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Question 2 from http://math.berkeley.edu/~mcivor/math53su11/solutions/hw6solution.pdf here. I do not understand b) and e). How do I think of the slope with respect to y? Homework Equations The Attempt at a Solution I do know that the partial derivatives are...

Homework Statement suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1 Homework Equations Sn= (-2n+9)/(6n+15 The Attempt at a Solution So I attempted to subtract S(n-1) from S(n) to get each...

Homework Statement Write out the form of the partial fraction decomposition of not determine the numerical values of the coefficients. Homework Equations x^4 -2x^3 + x^2 +2x -1 / x^2 -2x +1 The Attempt at a Solution I did the division and I got x^2 + ((2x-1)) / (x^2 -2x +1)...

Hey guys, i have read many posts on physics forums but this would be my first post. I am quite stuck so any help would be much appreciated. Homework Statement Use Laplace transforms to solve the initial value problem: f''(y) + 4f'(y) +8y = u(t-1) where y(0) = 1 and y'(0) = -1 Solve...

Greetings, In Griffiths E&M, 3rd. Ed., on page 214, the following is part of the derivation of the continuity equation (the same derivation is shown on the Wikipedia article for the current density, under the continuity equation section: http://en.wikipedia.org/wiki/Current_density)...

Homework Statement If ##z=x\ln(x+r)-r## where ##r^2=x^2+y^2##, prove that $$\frac{∂^2z}{∂x^2}+\frac{∂^2z}{∂y^2}=\frac{1}{x+y}$$Homework Equations The Attempt at a Solution Since ##r^2=x^2+y^2##, ##∂r/∂x=x/r## and ##∂r/∂y=y/r##. Differentiating z w.r.t x partially...

Hi everyone, Z=y+x^2*y+x^2+x^3+x^4+5 I would like to find the partial derivative of: diff(z,x) ? diff(z,y)? Kindly give me a step by step solution. Hope to hear from you soon. Thanking you all in advance for your replies.

Homework Statement ∫(2e^x)/(e^(2x)-1)dx Homework Equations The Attempt at a Solution I was told to solve using partial fractions. When I set up the partial fraction I got: A/e^x+1 + B/e^x-1 = 2e^x When I broke it up, I solved for A and B and got that A and B should both...

Is \frac{∂y}{∂x}×\frac{∂x}{∂z}=-\frac{∂y}{∂z}?

I am given Z = f (x, y), where x= r cosθ and y=r sinθ I found ∂z/∂r = ∂z/∂x ∂x/∂r + ∂z/∂y ∂y/∂r = (cos θ) ∂z/∂x + (sin θ) ∂z/∂y and ∂z/∂θ = ∂z/∂x ∂x/∂θ + ∂z/∂y ∂y/∂θ= (-r sin θ) ∂z/∂x + (r cos θ) ∂z/∂y I need to show that ∂z/∂x = cos θ ∂z/∂r - 1/r * sin θ ∂z/∂θ and ∂z/∂y = sin...

Hi, I was reading something on conservative fields, in this example \phi is a scalar potential. (Please refer to the attatched thumbnail). It's partial derivatives, but I'm not sure why the d\phi/dx * dx, the dx should cancel out? and that should leave d\phi. So the integral should be -3∫d\phi...

I got 2 questions to ask! I have finished one but not sure if it's correct so I need to double check with someone :) http://imageshack.us/a/img708/1324/83u8.png Here is my worked solution, I took this picture with my S4 and I wrote is very neatly as I could! The reason I didn't type it all...

I'm having problem with task (a) in this problem The question My attempt The solution Why don't I get the same after I take the partial fraction using my calculator? And where does this R(s)=1/s^2 come from

What math subject comes after partial differential equations for physics and electrical engineering majors?

Is partial derivative of ##u(x,y,z)## equals to \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z} Is partial derivative of ##u(r,\theta,\phi)## in Spherical Coordinates equals to \frac{\partial u}{\partial r}+\frac{\partial u}{\partial...

I am venturing in the realm of probability and I came across a concept that I call partial dependence. IE, it is a set of a events which a neither independent nor dependent on each other. They fall somewhere "in between". I have looked on the internet and I really don't understand the...

Hi, I am sort of hung up with a particular step in a derivation, and this has caused me to ponder a few properties of partial derivatives. As a result, I believe I may be correct for the wrong reasons. For this example, the starting term is (\frac{\partial}{\partial x}\frac{\partial...

Hello, the question I have arises from the 4th Edition of the book "Advanced Engineering Mathematics" written by K.A. Stroud. For those who owns the book, it is the example #2 starting at page 379. More precisely, the example is separated into two parts but the first one is very straight...

Homework Statement I found this solved example in an old textbook. I don't think that the solution provided is correct. I'll be very grateful if someone could verify it. Question: xxyyzz = c What is \frac{∂z}{∂x}? Solution Provided: Taking logarithms on both sides: zlog(z) =...

My understanding is that when a fan begins spinning, a partial vacuum is created. Physically, what creates this partial vacuum? Does the motion of the blades create a void in which there are fewer air molecules than in the ambient air and thus the pressure is lower than the ambient pressure?

Hi, As I understand it, if you have a piece of matter (hydrogen) and a piece of antimatter (anti-hydrogen) and they interact with each other they annihilate. What if your matter was Helium and your "antimatter" was anti-hydrogen? or the other way around what if your antimatter was antihelium...

Homework Statement Find Partial Fraction Decomposition of ##(x^4 - 1) / (x^3 + x^2 + x)## Homework Equations The Attempt at a Solution ##(x^4 - 1) / (x^3 + x^2 + x) = (x^4 - 1) / (x)(x^2 + x + 1) = A/x + B/(x^2 + x + 1)## ##(x^4 - 1) = A(x^2 + x + 1) + B(x)## ##(x^4 - 1) = Ax^2 + Ax...

Suppose I have some function f that depends on three variables, namely x, y, and t; i.e., f=f(x,y,t). Now suppose that y depends on x, i.e., y=y(x). Taking this into account, we see that f is really just a function of two independent variables, x and t. So my question is this: if I write down...

Homework Statement Consider the series Ʃ 1/[k(k+2)]; n=1 to infinity Find the formula for the partial sum Sn 2. The attempt at a solution I have calculated the first 5 terms of the sequence as follows, but I can't see any pattern. Am I doing this right? S1=1/3 S2=1/3+1/8=11/24...

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...