Partial Definition and 1000 Threads

I've been looking at the equation for r tilde prime in the image I attached below, but I cannot understand why it is that they say "Hence, the partial derivatives ru and rv at P are tangential to S at P". How does that equation imply that ru and rv are tangential to P?

I came across a simple equation in classical mechanics, $$\frac{\partial L}{\partial \dot{q}}=p$$ how to derive that? On one hand, $$L=\frac{1}{2}m\dot{q}^2-V$$ so, $$\frac{\partial L}{\partial \dot{q}}=m\dot{q}=p$$ On the other hand...

A sample of argon gas is collected over water at 30.0oC. The level of the water is adjusted until the total pressure in the flask is 771 torr and the volume is 250.0 mL. The vapor pressure of water is 31.8 torr at 30.0oC. A. How many moles of argon are in the flask? B. What is the partial...

Hi, in the above why is the left-hand side simple differentiation, i.e V is only function of t but in the right it is function of t, x, y, and z. It is very strange that one side is different than the other. Would you like to explain it? Thank you.

Homework Statement Use the Chain Rule to find the 1. order partial derivatives of g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t) = st & v(s,t)=s+t The answer should be expressed in terms of s & t only. I find the partial derivatives difficult enough and now there is no numbers in the problem, which...

Hello, I am enrolled in calculus 2. Just having started a section in our textbook about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...

I know its a ridiculous question, but I'm signing up for classes and I wanted to take differential equations and its currently filled up(for now, people drop all the time at my uni) but saw partial differential equations. I assume you need differential equations before partial differential...

Homework Statement I am trying to factor a denominator so I can do a partial fraction decomposition to solve using a Laplace transform. denominator= 2s^3+3s^2-3s-2 Homework EquationsThe Attempt at a Solution

Sorry for the terribly vague title; I just can't think of a better name for the thread. I'm interested in functions ##f:[0,1]^2\to\mathbb{R}## which solve the DE, ##\tfrac{\partial}{\partial y} f(y, x) = -\tfrac{\partial}{\partial x} f(x,y) ##. I know this is a huge collection of functions...

We write the system as an augmented matrix $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}1 & 4 & \phantom{-}1 & 0 & \phantom{-}5 \\ \phantom{-}1 & 6 & -1 & 4 & \phantom{-}7 \\ -1 & 2 & -9 & 2 & -9 \\ \phantom{-}0 & 1 & \phantom{-}2 & 0 & \phantom{-}4 \end{matrix} \right]...

What are some good general textbooks on the properties and solution of systems of partial differential equations? I'm most interested in the general theory of vector and tensor valued PDEs like Maxwell's, Navier-Stokes, and the bulk equations governing elasticity and deformation of solids, etc...

For a conservative force \vec{F}=-\vec{\nabla} U \implies dW=-\vec{\nabla}U \cdot d\vec{s} Where d\vec{s} is the infinitesimal vector displacement. Does the following hold? -\frac{\partial U}{\partial \vec{s}}=-\vec{\nabla} U \cdot d\vec{s}=d W, i.e. the infinitesimal work is minus the...

Homework Statement Suppose ω = g(u,v) is a differentiable function of u = x/y and v = z/y. Using the chain rule evaluate $$x \frac{\partial ω}{\partial x} + y \frac {\partial ω}{\partial y} + z \frac {\partial ω}{\partial z}$$ Homework EquationsThe Attempt at a Solution u = f(x,y) v = h(y,z)...

Homework Statement \frac{d}{dt}\left(\frac{\dot{q}}{\sqrt{1+\left(\dot{q}\right)^{2}}}\right)=0\Rightarrow\frac{\dot{q}}{\sqrt{1+\left(\dot{q}\right)^{2}}}=const\Rightarrow\dot{q}=A\Rightarrow q=At+B Homework Equations Why it ok to say that...

Homework Statement v_{i}=\dot{x}_{i}=\dot{x}_{i}\left(q_{1},q_{2},..,q_{n},t\right) T \equiv \frac{1}{2}\cdot{\sum}m_{i}v_{i}^{2} \frac{\partial T}{\partial\dot{q}_{k}}={\sum}m_{i}v_{i}\frac{\partial v_{i}}{\partial\dot{q}_{k}}={\sum}m_{i}v_{i}\frac{\partial x_{i}}{\partial q_{k}}[/B]...

Homework Statement ∂z/∂x of ycos(xz)+(4xy)-2z^2x^3=5x[/B] Homework Equations n/a The Attempt at a Solution ∂z/∂x=(5+yz-4y+6z^2x^2)/(-yxsin(xz)-4zx^3)[/B] Is this correct? Just trying to make sure that's the correct answer. I appreciate the help. I can post my work if need be. Thanks

Homework Statement The question is stated at the top of the attached picture with a solution 20160303_095831.jpg The correct results of the coefficients are A=2, B=-5, C=1 I have tried this problem multiple times and am still getting ugly coefficients. I have no idea why. A fresh pair of eyes...

I'm sure you are all familiar with calculating the inductance of a long transmission line. We first calculate the partial self inductance and we add to the partial mutual inductance due to the current in the other conductors. Looking at the image of a single-phase system, where I1 + I2 = 0...

I'm trying to find the partial derivatives of: f(x,y) = ∫ (from -4 to x^3y^2) of cos(cos(t))dt and I am completely lost, any help would be appreciated, thanks.

Sorry about the title, had a hard time trying to fit the question on the given space. The question is quite simple : If F = F(x_1,...,x_n,t) , Under what conditions is \frac{d }{dt} \frac{\partial F }{\partial xi} = \frac{\partial }{\partial xi} \frac{dF }{dt} true?

(Hope it's okay that I'm posting so much at the moment, I'm having quite a bit of trouble with something I'm doing) Homework Statement I'm having trouble with the simplification of the following equation. The answer is shown, but I can't figure out the process to get to it. \frac{d}{dt}...

Homework Statement [/B] The area of a triangle is (1/2)absin(c) where a and b are the lengths of the two sides of the triangle and c is the angle between. In surveying some land, a, b, and c are measured to be 150ft, 200ft, and 60 degrees. By how much could your area calculation be in error if...

What does it mean when it says to classify the second-order partial differential? (See attached) How would I get started?

Homework Statement the equation is E= k((xy)x[hat] +(2yz)y[hat] +(3xz)z[hat]) Homework Equations partial of x with respect to y on the x component partial of y with respect to x on the y component The Attempt at a Solution my professor said during class that the partial of x with respect to y...

Hey guys, so my professor told me to take a look at an equation, because he thinks that there is a mistake. We are basically talking about exercise 6.3 (on last image). The pictures will show you the text, so that you have all the information, that I have http://puu.sh/mrNDl/ec19cdff63.png...

In my book, applied analysis by john hunter it gives me a strange way of stating an infinite sum that I'm still trying to understand because in my calculus books it was never described this way. It says: We can use the definition of the convergence of a sequence to define the sum of an...

Hello everybody! I have to decompose to simple fractions the following function: V(z)=\frac{z^2-4z+4}{(z-3)(z-1)^2}. I know I can see the function as: V(z)=\frac{A}{z-3}+\frac{B}{(z-1)^2}+\frac{C}{z-1}, and that the terms A, B, C can be calculated respectively as the residues in 3 (single pole)...

Homework Statement Consider the following experiment: Alice and Bob each blindly draw a marble from a vase that contains one black and one white marble. Let’s call the state of the write marble |0〉 and the state of the black marble |1〉. Consider what the state of Bob’s marble is when Alice...

Homework Statement Decompose \frac{2(1-2x^2)}{x(1-x^2)} I get A = 2, B =-1, C = 1, but this doesn't recompose into the correct equation, and the calculators for partial fraction decomposition online all agree that it should be A = 2, B = 1, C = 1. Here is one of the online calculator results...

take the function f(x,y,z) s.t dF=(d'f/d'x)dx+(d'f/d'y)dy+(d'f/d'z)dz=0 where "d'" denotes a curly derivative arrow to show partial derivatives Mod note: Rewrote the equation above using LaTeX. $$df = (\frac{\partial f}{\partial x} ) dx + (\frac{\partial f}{\partial y} ) dy + (\frac{\partial...

Mark44 submitted a new PF Insights post Partial Fractions Decomposition Continue reading the Original PF Insights Post.

I've just done a derivation and had to use the following u_{b}u^{c}\partial_{c}\rho = u_{b}\frac{dx^{c}}{d\tau}\frac{\partial\rho}{\partial x^{c}} = u_{b}\frac{d\rho}{d\tau} We've done this cancellation a lot during my GR course, but I'm not clear exactly when/why this is possible. EDIT: is...

Hi all, I know that the dimension of a partial decay width or a cross section should be GeV or pb respectively. But what if i have a decay width probational to ## \Gamma = 10^{-3} GeV^3 G_\mu ## where I calculated all the masses and constants in ## \Gamma ##, ## G_\mu ## is the Fermi...

Homework Statement Given n=(x + iy)/2½L and n*=(x - iy)/2½L Show that ∂/∂n = L(∂/∂x - i ∂/∂y)/2½ and ∂/∂n = L(∂/∂x + i ∂/∂y)/2½ Homework Equations ∂n Ξ ∂/∂n, ∂x Ξ ∂/∂x, as well as y. The Attempt at a Solution ∂n=(∂x + i ∂y)/2½L Apply complex conjugate on right side, ∂n=[(∂x + i ∂y)/2½L] *...

Homework Statement From the transformation from polar to Cartesian coordinates, show that \begin{equation} \frac{\partial}{\partial x} = \cosφ \frac{\partial}{\partial r} - \frac{\sinφ}{r} \frac{\partial}{\partialφ} \end{equation} Homework Equations The transformation from polar to Cartesian...

Homework Statement integrate (4x+3)/(x^2+4x+5)^2 Homework EquationsThe Attempt at a Solution I know to solve this problem you have to work with partial fractions, in the solution we were given they solve as followed 4x+3=A(x^2+4x+5)'+B I don't know why they take the derivative of x^2+4x+5...

x2y2 + (y+1)e-x=2 + x Defines y as a differentiable function of x at point (x, y) = (0,1) Find y′: My attempt: ∂y/∂x =2xy3 + (-y-1)e-x=1 ∂y/∂y = 3x2y2 - e-x=0 Plugging in for x and y ⇒ ∂y/∂x = -3 ∂y/∂x = -1 For some reason I think y′ is defined as (∂y/∂x) /(∂y/∂y) = 3 At leas this give...

I have a question where f(x) = 20-2x^2/(x-1)(x+2)^2 and have solved for constants A,B and C. A = 2 B = -4 C = -4 I have worked this out myself. Now I am told to compute the indefinite integral and I am getting this answer but apparently it is wrong and I don't understand how? My answer...

We have a function: ##\phi'(t',x')##. We want to find: ##\frac{\partial\phi'}{\partial x}##. I know that the answer is: ##\frac{\partial\phi'}{\partial x} = (\frac{\partial\phi'}{\partial t'} \cdot \frac{\partial t'}{\partial x}) + (\frac{\partial\phi'}{\partial x'} \cdot \frac{\partial...

Is my background enough to learn partial differential equations? I have completed up to calculus 2 and linear algebra. I am currently taking Cal 3 and Ordinary Differential Equations. I am doing well in both courses. I would like to learn PDE and a bit more Linear Algebra, during the winter...

F(r,s,t,v) = r^2 + sv + t^3, where: r = x^2 +y^2+z^2 /// s = xyz /// v = xe^y /// t = yz^2 find Fxx i have 2 solutions for this and i am not sure what is the right one the first solution finds Fx then uses formula : Fxx = Fxr.Rx + Fxs.Sx + Fxv.Vx+Fxt.Tx the 2nd solution find Fx then uses the...

Hello Is what I have done calculated here correct? Please correct me if I have done something wrong. Thanks in advance.

so last night I get on a sleep number bed and the remote reads 35 (unitless - I am assuming this number is related to pressure.) I click it down once to 30 and it deflates nearly completely. I get off the mattress, the reading drops to 5 or 10 and the mattress begins to inflate to 30. So this...

Homework Statement Homework Equations Chain rule, partial derivation The Attempt at a Solution dv/dt=dv/dx*dx/dt+dv/dy*dy/dt dx/dt=-4t -> evaluate at (1,1) =-4 dv/dt=-4dv/dx+4(-2) dv/dt=-4dv/dx-8 How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!

Hello I'm currently trying to solve these two problems: 1) Find the partial derivatives ∂m/∂q and ∂m/∂h of the function: m=ln(qh-2h^2)+2e^(q-h^2+3)^4-7 Here, I know I should differentiate m with respect to q while treating h as a constant and vice versa. But I'm still stuck, and I'm not sure...

\begin{array}{l} u = u(x,y) \\ v = v(x,y) \\ and\\ {u_x} + 4{v_y} = 0 \\ {v_x} + 9{u_y} = 0 \\ with\ the\ initial\ conditions \\ u(x,0) = 2x _(3)\\ v(x,0) = 3x _(4)\\ \end{array} Easy, u_{xx}-36u_{yy}=0 and v_{xx}-36v_{yy}=0 General solution u\left ( x,y \right )=h\left ( x+6y \right...

I was looking over a derivation to find the laplacian from cartesian to cylindrical and spherical coordinates here: http://skisickness.com/2009/11/20/ Everything seems fine, but there is an instance (I have attached a screenshot) where implicit differentiation is done to find $$ \frac {\partial...

Let ##f(x,y)## be a scalar function. Then $$\frac{∂f}{∂x} = \lim_{h \rightarrow 0} \frac{f(x+h,y)-f(x,y)}{h} = f_x (x,y)$$ and $$\frac{∂}{∂y} \left (\frac{∂f}{∂x} \right ) = \lim_{k \rightarrow 0} \frac{f_x(x,y+k)-f_x(x,y)}{k} = \lim_{k \rightarrow 0} \left ( \frac{ \displaystyle \lim_{h...

I am working on implementing a PDE model that simulates a certain physical phenomenon on the surface of a 3D mesh. The model involves calculating mixed partial derivatives of a scalar function defined on the vertices of the mesh. What I tried so far (which is not giving good results), is this...

Let the PDE $u_{xx}-4u_{xy}+4u_{yy}=0.$ Reduce to the canonical form.Good Morning MHB :). My problem is find the canonical form of the PDE know an variable change. But how I can transform the equation? Thanks.