# smooth

1. ### smooth progress

Moving as the things progress will help in smooth progress & less frustration. Watch Grammy Awards 2015 Online Grammy Awards 2015 Live Stream Six Nations Rugby 2015 Live Stream Wales vs England Live Stream
2. ### smooth functions and partition unity

Take U \subset \mathbb{R}^{n} where U is bounded. Assume we have an open covering U \subset \cup_{i=0}^{N}V_{i} where V_{i} \subset U for each i. For each V_{i} we have the mappings v_{i} \in C^{\infty}(\bar{V_{i}}). If we let \{ \zeta_{i} \}_{i}^{N} be a smooth partition of unity subordinate...
3. ### Expansion of Green's/Stoke's theorem, find Area of smooth closed plane curve

I was given this question in class and I assume it is a spin off of Green's theorem for finding the area of a closed curve λ in 2D but expanded to 3D I believe. Anyways I am pretty confused about it so if anyone could help I would appreciate it,. Question: Let λ be a simple closed smooth space...
4. ### smooth function

show that f(x,y,z)=\frac{1}{z^2+1}(x^2-y^2,2xy,2z) defines a smooth function f: S^{2}\to S^{2} where S^{2}=\{p\in \mathbb{R}^3, |p|=1\} so I am guessing it is a unit sphere. How do we proceed with such problem? f is a smooth function if all partial derivatives of all possible orders are...
5. ### I need help with piecewise smooth functions

P.S Piecewise smooth functions..
6. ### How do you produce a smooth curve transaction between two velocities

Hi, I have depicted the problem above. I have a machine that is travelling to point A at a speed of 600mm/sec I need to reduce the speed over the fixed distance (200mm) and fixed time (1.5 sec) to the velocity at point B (8mm/Sec) I realise this will be a variable acceleration to solve the...
7. ### Smooth 3d surface plots

Hi, I would really appreciate some help. I have been using excel for many years, however it seems that the 3d surface plots produced are not as smooth as I would like. Does anyone know of any simple to use software or help with producing a more presentable 3d surface plots for presentation...
8. ### Relation between smooth manifolds and discrete math

Hello there, I'm a physicist with less knowledge about math than I'd like, so forgive me if the question sounds a bit vague. I know that in physics we usually deal with smooth manifolds, a trivial euclidean space in classical physics and curved ones in General Relativity (possibly with non...
9. ### Help on smooth manifold!

Why f: R -> R^2 by f(t) = (t^2, t^3) is not a smooth manifold? Just learned the concept of smooth manifold. Really confused about it.
10. ### Help on smooth manifold!

Why f: R -> R^2 by f(t) = (t^2, t^3) is not a smooth manifold? Just learned the concept of smooth manifold. Really confused about it.
11. ### Is this a nonexample of a smooth curve?

I am trying to test my understanding of the definition of smooth curves, as given to me in a text: a smooth curve has a bounded, continuous derivative on the interior of its parametric interval. So, if I let C= \left( t, \frac{-1}{t^2} \right), for t \ge 0 , then C' is unbounded. So C is not...
12. ### not sure why this is smooth

Define g: V \rightarrow \mathbb{R} smooth where V \subseteq \mathbb{R}^n is open. Then define a map, for a fixed x \in V h_i(x) = \int_0^1 \frac{\partial g}{\partial x_i}(tx) dt (we may assume tx is in V) Can anyone explain to me why this function is smooth? Thanks for any help
13. ### Smooth Curve

If x=x(t) has a derivative at every point of [a,b], isn't that derivative automatically continuous? If not, please give an example of a derivative which exists at every point but which is not continuous. All I can think of is a spike in the curve which has different (one sided) derivatives on...
14. ### Smooth Manifolds with Boundary

Let M be a topological manifold, and let \mathcal{A} be a smooth atlas. Then I understand that \mathcal{A} is contained in a unique maximal smooth atlas, \overline{\mathcal{A}}, the collection of charts which are smoothly compatible with the charts in \mathcal{A}. Now let M be a topological...
15. ### smooth function

I have a problem finding a smooth function on R^k that equals 1 on the ball of radius a, zero outside of the ball of radius b, and is strictly between zero and 1 at intermediate points, where 0<a<b. Any suggestion?(Thinking)
16. ### Determining whether a surface is smooth or piecewise smooth

Hello All, I would greatly appreciate any help for this problem for my Calc 3 class: Determine whether the given surface is smooth, piecewise smooth or neither. r(u,v)=<3u,u^2-2v,u^3+v^2> I took the derivative with respect to u, r(u): <3,2u,3u^2> And then with respect to v, r(v)...
17. ### Smooth Function R^3 -> R^4

Is the function F: R^3 -> R^4 defined by F(x,y,z) = (sqrt(x), x,y,z) if x >= 0 and (sqrt(-x), x,y,z) if x < 0 smooth on all of R^3? I'm thinking it is not, because taking the square root messes up smoothness at x=0, is this correct? Thanks.
18. ### Torus and smooth function

Hello, I want to show that this function is smooth: f:T->\mathbb{R} , f(x)=e^1(x)=x^1 T is the Torus defined as: T=\{((R+r*cosv)cosu,(R+r*cosv)sinu,r*sinv) \subset \mathbb{R}^3: u,v \in [0,2\pi)\} and R,r>0 constant. I don't know how f could be differentiated. My Problem is, that f...
19. ### Smooth graph matlab

Hi i have a graph (please see attatched). But i want them to be smooth curves. My teacher has told me to reduce bin sizes. How do i do this? Thanks Adam
20. ### Smooth = continuous?

Is a smooth (infinitely differentiable) map always continuous? I am not sure about this. Here is my problem: I have a smooth map \phi:W \rightarrow \mathbb{R}^3, where W\subseteq\mathbb{R}^3 is open. For p\in W, ive got an open neighbourhood of \phi(p) \in \mathbb{R}^3, say V. It is...