
Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 09:24 AM
micromass

1 
46,568 
Since things are a bit quiet here, I thought I would throw out a puzzle I came up with several years ago, after...

Feb1706 03:09 PM
NateTG

7 
1,924 
The definition of Y being connected in a topological space (X, tau) is that you can't find two nonempty, open and...

May2809 10:58 AM
HallsofIvy

4 
2,268 
Hi all, i found this problem in a topology book, but it seems to be of an analysis flavour. I'm stumped.
Show that...

Dec1508 01:56 PM
Citan Uzuki

1 
793 
From Conway's Complex Analysis, page 17, 2.2.5:
Suppose F \subseteq X is closed and connected. If a,b are in F and...

Nov2807 09:23 AM
HallsofIvy

10 
1,983 
Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio...

Jan2710 02:24 PM
daudaudaudau

8 
3,272 
I understand that the indefinite integral is like infinite definite integrals, but how come when we calculate the...

Jan1013 01:34 PM
Whovian

12 
2,247 
Hellow!
I want you note this similarity:
\\ \int xdx=\frac{1}{2}x^2+C \\ \int x^2dx=\frac{1}{3}x^3+C
\\ \sum...

Dec3013 09:32 PM
pwsnafu

1 
624 
If exist a connection between the infinitesimal derivative and the discrete derivative $$d = \log(\Delta + 1)$$...

Apr1814 05:17 PM
Jhenrique

6 
426 
Hey guys,
I'm following a course on vector calculus and I'm having some trouble connecting things. Suppose we have a...

Jan1411 10:10 AM
HallsofIvy

1 
1,781 
conponent(maximal connected set) must be closed, connected, open, disjoint. This is a fact.
But why people still say...

Nov410 08:41 AM
micromass

3 
734 
Hi!
Most of you know that the Frenet formulas written for the trihedron
(\vec{T},\;\vec{N},\;\vec{B})
is
...

Dec107 04:20 PM
Abel Cavaşi

0 
1,924 
Hi
I was wondering, one way that a conservative field can be found is if the line integral of any closed path is 0....

Jun811 09:45 PM
micromass

1 
853 
It seems there are some problems on the test.
I find that Curl F is not zero, that means the field is not exact.
Am...

Dec611 11:00 PM
LCKurtz

1 
871 
This isn't homework. I'm reviewing calculus and basic physics after many years of neglect.
I want to show that a...

Jun1513 12:53 AM
inkliing

2 
729 
My calculus book states that a vector field is conservative if and only if the curl of the vector field is the zero...

Dec609 06:24 AM
HallsofIvy

2 
2,061 
Let f(x,y) = ( \frac{y}{x^2 + y^2}, \frac{x}{x^2 + y^2}) with f : D \subset \mathbb{R}^2 \to \mathbb{R}^2
I...

Dec2411 07:13 AM
Damidami

3 
1,254 
What does this mean ! ?

Jul1708 10:41 PM
mathwonk

2 
1,570 
jjjj

Jan3108 09:44 AM
HallsofIvy

1 
3,878 
Consider the heat equation in a radially symmetric sphere of radius unity:
u_t = u_{rr}+{2 \over r}u_r \ for \ (r,t)...

Aug2709 02:44 PM
tinytim

1 
662 
Use the chain rule to show that
dz/dx = (cos(theta) * dz/dr)  (1/r * sin(theta) dz/dtheta) and
dz/dy =...

Sep813 03:59 AM
CompuChip

1 
659 
I define a consistent family, F, to be a set of intervals such that if I_1 and I_2 are in F then I_1 and I_2...

Feb2808 08:11 PM
Pere Callahan

6 
1,777 
Is there a formula that will calculate time when I know the following...?
Initial velocity = 0 Final velocity =...

Sep1108 07:59 AM
Photon713

3 
1,708 
If we parameterize the arc length of a vector valued
function, say, r(s) and r(s) has constant curvature
(not equal...

Mar2110 11:29 PM
Tinyboss

1 
1,121 
Find a number "k" such that exist only one intersection between the curve exponential k^x e and the straight x·k. This...

Nov1713 05:54 PM
PSarkar

5 
567 
My book (Saff&Snider) has the following theorem
Suppose u(x,y) is a realvalued function defined in a domain D. If...

Jun1409 09:33 PM
Tibarn

4 
1,053 
This is a question that came up in a conversation with my father who was a fighter pilot in ww2... we got to talking...

Mar610 01:20 PM
CompuChip

2 
3,204 
Hi everyone,
I've been racking my brain about this problem, but can't seem to figure it out. It seems like it...

Jun1113 07:49 PM
WannabeNewton

3 
826 
The first order KKT condition for constrained optimization requires that the gradient for the Lagrangian is equal to...

Apr1212 02:56 PM
brydustin

4 
1,015 
Hi,
I want to know the solution of the following equation.
a = argmin_{a} \\
where x_i, y_i are column vectors...

Apr1511 05:29 AM
jasonRF

2 
2,891 
Hi,
I need help with this problem;
minimize x^3, subject to K= xΩπ
so would the solution be
KΩπ=x

Apr1412 07:58 AM
HallsofIvy

1 
1,008 
I'm trying to find the regular parallelepiped with sides parallel to the coordinate axis inscribed in the ellipsoid...

Jul208 09:38 AM
HallsofIvy

1 
1,259 
I have the analytical first and second derivatives of a (multidimensional) lagrangian ( l = f  λh). X is the vector...

Jan2112 05:04 PM
brydustin

0 
964 
Construct a compact set of real numbers whose limit points form a
countable set.

Oct804 09:35 AM
forget_f1

8 
4,526 
Suppose I'd like to construct a C^\infty generalization of a characteristic function, f(x): \mathbb R \to \mathbb R,...

Oct3111 02:32 PM
Citan Uzuki

1 
1,418 
Today, I had the desire to construct a C^{\infty} approximation to a tent function. Specifically, for any positive...

Mar1306 11:39 PM
Hurkyl

5 
1,685 
How do you construct Peano curves? All pictures I have seen suggest that it is iterative process, however, I don't...

Sep2208 05:50 PM
Borek

0 
812 
Hello
I am reading a paper on numerical methods which requires a 2D function to be converted to a 1D function. ...

Mar210 09:43 AM
nkinar

2 
884 
Can you prove that \mathbf{R} and \mathbf{R}\mathbf{Q} have same cardinality?
One way would be to say that...

Sep1908 06:25 AM
morphism

3 
1,826 
This proof I think is related to our construction of R in class using equivalences classes of Cauchy sequences:
Let...

Nov311 04:01 PM
autre

3 
1,107 
I was looking at the construction of the real number system.
I know dedekind cuts can be used(completely worthless...

Mar2511 01:38 PM
Liangpan

16 
2,882 