Curves Definition and 778 Threads

Let m : [0,L] → ℝ2 be a positively oriented C1 regular Jordan curve parametrized with arc length. Consider the function F : [a,b] x [a,b] → ℝ defined by F(u,v) = (1/2) ||m(u) - m(v)||2 Define a local diameter of m as the line segment between two points p = m(u) and q = m(v) such that: The...

Homework Statement Let m : [0,L] --> ℝ2 be a C2 regular closed curve parametrized with arc length, and define, for an integer n > 0 and scalar ε > 2 μ(u) = m(u) + εsin(2nπu/L)Nm(u) where Nm is the unit normal to m (1) Determine a maximum ε0 such that μ is a closed regular curve for...

Homework Statement Consider a function f that can be put in the form f(p) = g(|p|) where g : [0,+∞) -> ℝ is C1 with g(0) < 0 and g'(t) > 0 for all t ≥ 0 Assume that |∇f(p)| = 1 for all p ≠ 0 and prove that the set f(p) = 0 is a circle. Homework Equations Given above The Attempt at a...

Hi, All: There is a standard method to construct a nowhere-zero form to show embedded (in R^n ) manifolds are orientable ( well, actually, we know they're orientable and we then construct the form). Say M is embedded in R^n, with codimension -1. Then we can construct a nowhere-...

r = sin 2θ, r = cos 2θ. I'm having some trouble setting this up. $$1/2 \int_{\ -pi/8}^{\pi/8} cos^2 2θ~d\theta - 1/2 \int_{\ -pi/8}^{\pi/8} sin^2 2θ~d\theta $$ Which can be: $$\int_0^{\pi/8} cos^2 2θ~d\theta - \int_0^{\pi/8} sin^2 2θ~d\theta $$ Since there are 8 petals. $$8 \int_0^{\pi/8}...

http://www.mathhelpboards.com/f12/im-clueless-how-start-2322/My math class uses an online homework system. I got the answer wrong to the question, but I can get a similar question. Here is one that is similar to the earlier one. You have two functions that are graphed. y=\frac{\csc^2{x}}{4}...

I was very shocked by the class averages and curve for my quantum mechanics course. The exam was curved to (brace yourselves) 55/100 as an A. Yeah. Kind of shocking, frankly. Of course, the class average was 47.5 or something on that order. My own score was an 80, which I'm not terribly happy...

PROBLEM STATEMENT: I'm looking for a somewhat general method to find the expression for the distance (in \R^2 mortal, euclidean space) between a point in a certain curve and some point outside the line. ATTEMPTS TO SOLVE THE PROBLEM: In the case of the distance between the origin and some...

Homework Statement Consider the area bounded between the curves y=3-x^2 and y=-2x. Suppose two vertical lines, one unit apart, intersect the given area. Where should these lines be placed so that they contain a maximum amount of the given area between them? What is this maximum area...

Hi everyone, I am having hardtime understanding this problem. I have two functions: QD = 5600 – 8P QS = 500 + 4P Why is the graph like the one attached and not the normal mathematical graph where supply curve starts from y=(0,-125)? Do ignore the consumer surplus and producer surplus part. That...

I am learning this right now, and I am having troubles with something. For regular partition, the formula in my textbook is this. x_k=a+k\Delta x, \text for k=0,1,2,...,n. My question is this, how does one find "k"? It is very important clearly!;)

Hi Folks; I am developing a series of pump performance curves for pulp slurries. I am running a closed-loop Lab-Scale pipeline facility. My question is about measuring head vs. flow rate at constant RPMs. I did it for pure water by continuously feeding the system with water, and gradually...

A circle with radius 1 touches the curve y = |2x| in two places(see attachment for picture). Find the area of the region that lies between the curves. I am having a tough time with this one. I figured I could put the radius in a spot where it would form a right angle on the line, then try...

Homework Statement Find parametric equations for the three level curves of the function W(x,y) = sin(x) e^y which pass through the points P = (0,1), Q = (pi/2, 0) and R = (pi/6, 3) Also compute the vectors of the gradient vector field (gradient of W) at the points P, Q an R Homework...

Homework Statement Consider the points P = (1/2, √3/2) and Q = (1,1). They lie on the half circle of radius one centered at (1,0). a) Use the deifnition and properites of the hyperbolic distance (and length) to compute dH(P,Q). b) Compute the coordinates of the images of Pa nd Q...

Homework Statement Find the equation of all straight lines, if any, that are tangent to both the curves y = {x^2} + 4x + 1 and y = - {x^2} + 4x - 1.Homework Equations The Attempt at a Solution Suppose such a line exists and its slope is m. Let ({x_1},{y_1}) and ({x_2},{y_2}) be the tangent...

Homework Statement Sketch the solution to the IVP u_{t}+uu_{x}=0 \\ u(x,0) = e^{-x^{2}} Homework Equations Monge's equations \frac{dt}{d\tau} = 1 \\ \frac{dx}{d\tau}=u \\ \frac{du}{d\tau}=0 The Attempt at a Solution I think I do not really need the Monge's equation, but I have no...

Homework Statement Is there anything special about the tangents to the curves xy=1 and (x^2) - (y^2) =1 at their point of intersection in the first quadrant. The Attempt at a Solution I know what the derivatives of both functions are and what they look like when graphed. But, I'm not...

Homework Statement Consider the family F of circles in the xy-plane (x-c)2+y2=c2 that are tangent to the y-axis at the origin. What is a differential equation that is satisfied by the family of curves orthogonal to F? Homework Equations ∇f(x,y)=<fx,fy> The Attempt at a SolutionMy general...

Homework Statement Sketch the region enclosed by the curves and compute its area as an integral along the x or y axis. y+x=4 y-x=0 y+3x=2 Homework Equations ∫ top function - bottom function dx OR ∫ right function-left function dy The Attempt at a Solution I originally had...

I am trying to find the level curves for the function g(x,y)= k = xy/(x^2+y^2). I get, x^2+y^2-xy/k=0. I know this is an ellipse, but I do not know how to factor, and find values of k for which the level curves exist.

Given value of a line integral, find line integral along "different" curves Homework Statement I think I've got this figured out, so I'm just checking my answers: Suppose that \int_\gamma \vec{F}(\vec{r}) \cdot d\vec{r} = 17 , where \gamma is the oriented curve \vec{r}(t) = \cos{t} \vec{i}...

Hello, I have a question regarding finding the area between two curves. I will link to a well known example that seems to show up in every calculus textbook! http://tutorial.math.lamar.edu/Classes/CalcI/AreaBetweenCurves.aspx In particular on that page, I am referencing Example 6. And in...

Homework Statement Find the area of the region that lies inside both of the circles r = 2sin(x) r = sin(x) + cos(x) Homework Equations A = (1/2)(int from a to b): r^2 dx (I apologize because I do not know how to make calculus look proper in text form) The Attempt at a Solution...

Hello, it is known that if we have a curvilinear coordinate system in ℝ2 like x=x(u,v), y=y(u,v), and we keep one coordinate fixed, say v=\lambda , we obtain a family of one-dimensional curves C_{\lambda}(u)=\left( x(u,\lambda),y(u,\lambda) \right). The analogous argument holds for the other...

General Relatitivity predicts Timelike curves and there are nonlinear extensions of mechanics which resolve the paradoxical aspects of CTC's *i.e. Time Travel, on the other hand Hawking proposed a conjeture to rule out CTCs, the Chronology Protection Conjecture* there are a class of Timelike...

Homework Statement I have this function of two variables: f(x,y)=x^2-4x+y^2 Where I have to compute the level curves for: f(x,y)=-3, -2, -1, 0, 1 Homework Equations - The Attempt at a Solution So yeah well I know that I have to draw the following curves...

Hi Folks, Sorry if this has been asked before but I have searched the forums and can't anything to do with this. Also please correct me if I am posting in the wrong forum. I am making an application with functionality similar to a revolution of a sketch within any CAD program. I...

hi Guys, can anyone suggest me some software by which i can plot IV curve for solar panels by just feeding in open circuit voltage, short circuit current, max power, max current and voltage, efficiency.

for each of the following maps f: ℝ2-->ℝ3, describe the surface S = f(ℝ2) and find a description of S as the locus of an equation F(x,y,z) = 0. Find the points where \partialuf and \partialvf are linearly dependent and describe the singularities of S(if any) at these points f(u,v) = (2u + v...

1. Given the curves r = 2sin(θ) and r = 2sin(2θ), 0≤θ≤π/2, find the area of the region outside the first curve and inside the second curve 2.not sure which equations to use 3. I got 1 and 1/2 as the area and they were wrong. I do not really know how to work this problem. A...

I'm looking for some study materials regarding Closed time-like curves (CTCs). Be it a book, paper or anything other. It is highly accepted, but I'm particularly looking for a book that includes it and similar topics.

Find the area of the region bounded by the following curves: y=x2-5x and y=3-x2 Answer: So, using simultaneous equations I found the points of intersection (x = -0.5 and x = 3). The book agrees with me on that. I then performed the following: 3-x2-(x2-5x) = -2x2+5x+3 I then...

using namespace std; enum direction {north, east, south, west }; direction right(direction d) { // return the direction to the right (clockwise) switch(d) { case north: return east; case east: return south; case south: return west; case west: return north; }...

The first part of the question asks to find the COG of the curve y=[1-x]*x^2 in the interval x=0 to x=1 I found that correctly as (0.6,0.0571) The next part asks to find the COG of another cubic curve y=x[1-x]^2 But without using integration but by using the result of the first part of...

Homework Statement How to Find the area of ​​the shaded region in the image below: http://i47.tinypic.com/263ed5d.jpg (without space)Hi, please help me with this: How to find the common points in between the curves? and the area?? Homework Equations y= x^2 y= (x-2)^(1/2) x = 0 The...

Homework Statement Set up sums of integrals that can be used to find the area of the region bounded by the graphs of the equations by integrating with respect to y. y= sqrt(x) y=-x x=1 x=4 Homework Equations ∫[f(x) - g(x)] dxThe Attempt at a Solution I did: ∫ (from 1 to 4) [sqrt(x) + x] dx...

I can't figure how to solve this problem. Is says ∫∫(x^2)y dA where R is the region bounded by curves y=(x^2)+x and y=(x^2)-x and y=2. I can't figure how to do the limits with that. Please help!

Homework Statement (a) Sketch the level curves of z = (x^2 - 2y +6)/(3x^2 + y) at heights z = 0 and z =1. (b) Sketch the surface (x−1)^2 + (y+2)^2 + z^2 = 2 in R^3. Write down a point which is on the surface. Homework Equations -- The Attempt at a Solution (a) From the question, I...

sketch the level curve z=(x^2-2y+6)/(3x^2+y) at heights z=0 and z=1 i have already compute the 2 equations for the 2 z values and drawn it in 2d but when it comes to plotting it with the extra z axis i don't know what to do. please help...

Good morning! I'm having a bit of a hard time wrapping my mind around this concept. The part that seems to be troubling me the most is where Riemann Sums and sigma notation come in. I can't seem to find explanations online that help me better understand, so hopefully someone here could help...

Homework Statement find the area enclosed by the two curves y=x+1 y=x^2-3x-4 i've already worked out the points of intersection. these are x=-1 and 5 what do i do now? and how? i'd appreciate if you could tell me because i have loads of these to do, so one good example would...

Hello. I am having trouble conceptualizing and/or decisively arriving to a conclusion to this question. When finding the area enclosed by a closed polar curve, can't you just integrate over the period over the function, for example: 3 cos (3θ), you would integrate from 0 to 2pi/3? It intuitively...

Alright. I completely confused about determining the area between regions of polar curves. However, I do feel that I have a solid grasp in finding areas for single functions. For a given function in polar form, I know that I find the limits of integration by setting the function equal to zero...

i understand that a good black body would produce a plank curve. it is my understanding that plank curves are continuous emmision spectra.. now the sun a good approximation to a black body... but we get and emission/absorbtion spectra.. can you please help me understand where i am going...

In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we find the following text: "It is a fairly straightforward piece of algebraic reasoning to show that there is a right triangle with rational sides having an area d if and only if...

So the problem I am having is I have no idea what I am supposed to do. I read the chapter on spatial pattern in JD Murrays Math Bio Vol 2 and looked through Strogatz Nonlinear Dynamics and Chaos but I am not sure how to solve anything with these modes. I have no idea what to start doing. $$...

Homework Statement A car weighing 3220 lbs rounds a curve a 200 ft radius banked at an angle of 30deg. Find the friction force acting on the tires when the car is traveling at 60mph. Coefficient of friction is 0.9. Homework Equations i rotated the axes such that y-axis is...

Given a function, it is easy enough to plot its curve, just by substituting numerical values. But is the reverse possible? I mean, if you're given a curve's figure, can you figure out the function that represents it (provided that the curve is not a well-known one like a parabola or ellipse) ?

I was talking to my professor and I am tying to generate a phase curve that looks like (see attached).However, I am only been able to generate phase portraits.I need to generate a plot that does that.From these equations,$$\dot{x} = -x + ay +x^2y$$$$\dot{y} = b -ay-x^2y$$Here is what I have been...