Coordinates Definition and 1000 Threads

Griffiths notation kind of bothers me. Can anyone explain why he uses primed coordinates in the attached picture. Wouldn't dl, da, dτ do just as well? Cheers :)

Homework Statement Find the volume of the solid that lies above the cone z = root(x2 + y2) and below the sphere x2 + y2 + x2 = z. Homework Equations x2 + y2 + x2 = ρ2 The Attempt at a Solution The main issue I have with this question is finding what the boundary of integration is for ρ. I...

There are some "standard" coordinate systems in flat spacetime, such as Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation). Is there a "standard" coordinate system in flat spacetime which has at least one null coordinate?

Homework Statement Plot the Following points(given in polar coordinates). Find all the polar coordinates of each point. a. (2, pi/2) b. (2,0) c. (-2, pi/2) d. (-2,0) Homework Equations none The Attempt at a Solution I have plotted it on a graph but could someone explain to me...

Hi, I need some help understanding the solution to a problem. Equations: x = r.cos(θ) y = r.sin(θ) r = x2 + y2 theta = arctan(y/x)Question: Determine the Jacobian Matrix for (x,y)T and for (r, θ)T SOLUTION: I understand and can compute by myself the Jacobian for (x,y)T, but the solution to...

Hello, If you can get me a hint for solving this matter it would be much appreciated. I have the 3D coordinates of three points on a plane A, B, C. There's another point G and we know AG, BG, CG. My problem is to find the coordinates of point G:cry: Thanks in advance!

I recently did an integral of the form: ∫∫1/ρ dρρdθ the extra ρ between dρ and dθ is the cost of switching to cylindrical coordinates. Now I want to know, do you carry out the integration in ρ, keeping the ρ outside the integration (since it's technically a scaling factor that belongs to...

Converting to Spherical Coordinates...then integrating? Am I doing this right? Homework Statement Consider the integral ∫∫∫(x2z + y2z + z3) dz dy dx, where the left-most integral is from -2 to 2, the second -√(4-x2) to √(4-x2) and the right-most integral is from 2-√(4-x2-y2) to...

I'm trying my very best to understand it, but really, I just couldn't get it. I read four books now, and some 6 pdf files and they don't give me a clear cut answer :( Alright, so this integral; ∫e-x2dx from -∞ to ∞, when converted to polar integral, limits become from 0 to 2∏ for the outer...

Homework Statement Do you see how y gets converted to csc? I don't get that. I would y would be converted to sin in polar coordinates.

Homework Statement An airplane flies at an air speed of 300 miles per hour, in the direction toward southwest. There is a head wind of 75 mi/hr in the direction toward due east. (A) Determine the ground speed. (B) Determine the direction of motion of the plane, expressed as an angle...

Homework Statement a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h. Its apex occurs at the point (0,0,h). Suppose a>=b. Calculate the volume of that part of the paraboloid that lies above the disc x^2+y^2<=b^2.:confused: 2. The attempt at a solution We normally do the...

Homework Statement where λ= thermal conductivity \dot{q}= dissipation rate per volume Homework Equations qx=-kA\frac{dT}{dx} The Attempt at a Solution I don't know where to start from to be honest, so any help would be greatly appreciated

Dear all, We can rotate the local coordinates of the element so that the stress tensor becomes diagonal. The new coordinate system would be the principal stress axes of which are in fact the eignevectors of the stress tensor. Once we have the eigenvectors ( which are generally orthogonal)...

Homework Statement Show that ##\iint_{S}(x^2 + y^2)d\sigma = \frac{9\pi}{4}## where ##S = \{(x,y,z): x > 0, y > 0, 3 > z > 0, z^2 = 3(x^2 + y^2)\}## Homework Equations ##\iint_{S}f(x,y,z)d\sigma = \iint_{R}f(r(x,y))\sqrt{[r_x(x,y)]^2 + [r_y(x,y)]^2 + 1}## where ##r : R → ℝ^3, R \in ℝ^2##...

Homework Statement It is given a set defined as: 0≤x≤1, 0≤y≤1-x. With x,y in ℝ. f(x,y)=1 (plane parallel to Oxy plane) They ask you to express the integral ∫∫Setf(x,y)dxdy in polar coordinates and calculate it. Homework Equations x=rcosθ y=rsenθ r=√x2+y2 The Attempt at a...

Homework Statement Firstly sorry for my bad english,i have a one question for you(İ try it but i didn't solve it ) Homework Equations The Attempt at a Solution i know problem will be solved spherical coordinates but i don't know how i get angles (interval) theta and fi ...

Homework Statement find the over lapping area of the following equations r=3sin(x) r=1+sin(x)Homework Equations area =1/2 ∫ f(x)^2 dxThe Attempt at a Solution first off I started by finding the intersecting angle by: 3sin(x)=1+sin(x) 2sin(x)=1 sin(x)=1/2 x=pi/6 and the peak is at pi/2 so I...

hello EveryBody, In the 3D Coordinates I always find 4 parameters instead of 3. A = (X, Y, Z, 1) I wonder why? thank you.

Homework Statement The Attempt at a Solution I don't understand where 2v1 + 3v2 and 4v1 - 3v2 came from.

This might seem easy, but I am sort of rusty on the math since i haven't taken a math course in a while. Homework Statement A 2 meter long bar lies in the xy plane with one end at the origin. find position at the xy plane of the other? end point of the bar if the angle the bar makes with...

Homework Statement Express the given vector in terms of its coordinates: The vector from the origin to the end point of the vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4) The Attempt at a Solution I don't even know the algorithm for solving this...

I am asked to consider the following graph: r2=a+sin(θ), where a=2 I have a picture of this plot, which I have attached, We are asked to find the area of the upper 'cresent' of the curve, contained at the top How would I go about calculating that? I've found that if I plot...

Homework Statement Use polar coordinates to evaluate: ∫sqrt(2)0 ∫sqrt(4-y2)y 1/(1+x2+y2) dxdy Homework Equations The Attempt at a Solution I graphed it and I see r is the part of the elipse sqrt(4-y2) and goes from 0 to ∏/4. I'm not sure how to make the bounds for r or how to...

Homework Statement The lecture notes say that ∇ = urr + (1/r)ur + (1/r2)uθθ. I'm not sure how this comes about. The notes never explain it. Homework Equations (?) The Attempt at a Solution No attempts on the actual homework problem until this ∇ thing is cleared up.

Doesn't a linear change of coordinates preserve complete intersection for a set of homogeneous polynomials, all of the same degree, in a polynomial ring? That is, apply a change of coordinates to a set of homogeneous polynomials {f_1,... f_k} in C[x_1,...,x_M] to obtain {h_1,..., h_k}. Suppose...

Homework Statement Consider a 2D spacetime where space is a circle of radius R and time has the usual description as a line. Thus spacetime can be pictured as a cylinder of radius R with time running vertically. Take the metric of this spacetime to be ds^{2}=-dt^{2}+R^{2}d\phi^{2} in the...

Homework Statement Calculate volume of the solid region bounded by z = √(x^2 + Y^2) and the planes z = 1 and z =2 Homework Equations The Attempt at a Solution

Hi I'm working on area and volume integrals. I was wondering, when you convert to do the integral in polar, cylindrical or spherical co-ordinates, is there a standard set of limits for the theta variable in each case? for example from 0 -pi for polar, 0-2pi for cylindrical? If not how...

Homework Statement Find the area of the shaded region. r=sqrt(θ) Homework Equations A = integral from a to b 1/2r^2dθ The Attempt at a Solution I know how to solve the question, I just don't know what to use for a and b. I tried 0 and 2pi but I am getting the wrong answer...

Hi guys, I have to brush up my knowledge about self-dual Yang Mills and I'm reading an ancient paper by Yang about it...and of course I'm stuck...although Yang writes 'it is easy to see that'... Ok, so the self-duality condition of the YM field strength tensor is defined as...

∅θ,θI've come across two distinct 'versions' of the spherical coordinates. Could someone tell me which is correct or if both are fine. Version 1: A spherical coordinate is (rho,θ,∅) x=rhocos(θ)sin(∅) ; y=rhosin(θ)sin(∅) ; z=rhocos(θ) Version 2: A...

Homework Statement Find the area enclosed by the inner loop of the curve r=1-3sinθ Homework Equations A=o.5\int r^2 dθ The Attempt at a Solution I found the integral but i don't know how to find the interval at which i will be integrating from. I tried finding when r=0 and it turns...

Reading through my electrodynamics textbook, I frequently get confused with the use of the del (nabla) operator. There is a whole list of vector identities with the del operator, but in some specific cases I cannot figure out what how the operation is exactly defined. Most of the problems...

I am trying to work the following problem; A rigid body is rotating about a fixed axis with a constant angular velocity ω. Take ω to lie entirely on th z-axis. Express r in cylindrical coordinates, and calculate; a) v=ω × r b)∇ × v The answer to (a) is v=ψωρ and (b) is ∇ × v = 2ω...

what is the best way to graph in polar coordinates say r = 3 - 5 \cos \theta is it to plot several points then make a curve between them or ?

Greetings everyone, I am having difficulties grasping the polar form of the ellipse equation, and there seems to be more than one way to express an ellipse in this form, if I am not mistaken. For example on the following webpage http://farside.ph.utexas.edu/teaching/301/lectures/node155.html...

Homework Statement In cylindrical coordinates, sketch the surface defined by z=6 The hand drawn sketch shown in the answer I have appears to be a rectangular or square plane at z=6 Should the plane be square/rectangular or should it be circular? To illustrate, the blue plane in the diagram...

Homework Statement I need to calculate the integral where the region is given by the inside of x^2 + y^2 + z^2 = 2 and outside of 4x^2 + 4y^2 - z^2 = 3 Homework Equations The Attempt at a Solution So far, I think that in cylindrical coordinates (dzdrdtheta): 0 <= theta <= 2pi sqrt(3)/2 <=...

Homework Statement 1. Use polar coordinates to find the volume of the given solid. 2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4. 2. The attempt at a solution My attempt as following: 2<=r<=4, and 0<=theta<=2pi So I do a double integral of...

I’m a woodworker, a math idiot, my trig hasn’t improved since I flunked it 40 years ago and I need help making a Christmas toy for my grand-kids. The values that follow are arbitrary, were extracted using eng graphics software and should be solid. Problem: I have one 2D surface (that...

Homework Statement Use Polar coordinates to evaluate were C denotes the unit circle about a fixed point Z0 in the complex plane The Attempt at a Solution I've only used polar integrals to convert an integral in sin and cos into one in therms of z, find the residues and then use the...

The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?

Homework Statement The Cartesian coordinates of a point are given. (3,-5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. Homework Equations r^2=x^2+y^2 tanθ=(y/x) →...

Hello. I have a question that has been on my mind for some time. I always see in mathematical physics books that they identify elements of the Lie algebra with group elements "sufficiently close" to the identity. I have never seen a real good proof of this so went on an gave a proof. Let Xi be...

Hi, I am trying to find the last vertex coordinates of a triangle given that Vertex 1 = (2,10) Vertex 2 = (3,6) Angle at Vertex 1 = 75.9638 degrees Angle at Vertex 2 = 70.3462 degrees. I have tried using the equations based on the length of each side, as well as using the cos dot...

Homework Statement Find the coordinates of reflection of the point P (4,8) in the line y=-3/2 x + 14 Homework Equations y= -3/2x + 14 The Attempt at a Solution find a point on the line?

Homework Statement Im righting this down for my roommates since he's having tons of trouble trying to figure this out and I can't answer it. also sorry for having to hotlink it. http://i.imgur.com/afShz.jpg the equation is on the image since its very difficult to type it all out...

I have: $\dot{x}=4x+y-x(x^2+y^2)$ $\dot{y}=4y-x-y(x^2+y^2)$ And I need to find $\dot{r}$ and $\dot{\theta}$ I got as far as: $\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))$ $\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))$ How do I go from here to $\dot{r}$ and...

Homework Statement I have: \dot{x}=4x+y-x(x^2+y^2) \dot{y}=4y-x-y(x^2+y^2) And I need to find \dot{r} and \dot{\theta} 2. The attempt at a solution I got as far as: \dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4)) \dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta)) How do I...