content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Convergence of elliptic operators
up vote 2 down vote favorite
1
Let $A_t$ be family of second order, positive, elliptic differential operator mapping Sobolev $H^2$ of a compact smooth manifold (or bounded domain) to L^2. Suppose that the coefficients of $A_t$
converge uniformly in $C^k$ for every $k$ to the coefficie... | 5 | [
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0.052490234375,
0.051513671875,
0.006011962890625,
... | 8,600 | 8600 | |
Bilinear mapping
From Encyclopedia of Mathematics
2010 Mathematics Subject Classification: Primary: 15-XX [MSN][ZBL]
bilinear function
A mapping $f$ from the product $V\times A$ of a left unitary $A$-module $V$ and of right unitary $B$-module $W$ into an $(A,B)$-bimodule $H$, satisfying the conditions
$$f(v+v',w)=... | 4 | [
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Convert Weiestrass Form to Legendre Form
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
If an Elliptic Curve is of the form E:y^2=x^3+ax+b then how do we convert this Legendre Form y^2=x(x-1)(x-L)?
elliptic-curves
F... | 4 | [
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... | 8,602 | 8602 | |
Integrating a function of compressibility
February 5th 2009, 05:29 AM #1
Newbie
Joined
Feb 2009
Posts
2
Integrating a function of compressibility
Hi, i have a differential equation I am trying to integrate, but I do not know how to do it. The equation is:
dp = rho*g*dx
rho = rho_0 + (p(h)-p_0)/... | 5 | [
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Application of differentiation
March 18th 2007, 03:31 PM #1
Junior Member
Joined
Nov 2006
Posts
59
Application of differentiation
A baseball diamond is a square with side 90 ft. A batter his the balls and runs toward first base with a speed of 24ft/s.
a. At what rate is his distance from the second b... | 5 | [
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A trick or a general technique? (Probabilistic Method)
up vote 8 down vote favorite
1
Suppose we have some positive quantites $P$ and $Q$ which depend on some choices that we make, and we want to show that some choice makes the quotient $P/Q$ fall below some cool bound.
One idea is to make our choices randomly in som... | 4 | [
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0.0373535... | 8,605 | 8605 | |
Solving inequality by multiplying across
September 25th 2013, 01:41 AM
corbomite1
Solving inequality by multiplying across
Just looking for some guidance on the following problem:
Find the least value of n (Natural number) for which (5n + 3 / 7 - n) < 1, n <> 7
One approach:
5n + 3 < 7 - n
6n ... | 4 | [
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[SOLVED] Calculating an improper integral via complex analysis
October 25th 2009, 10:05 AM
arbolis
[SOLVED] Calculating an improper integral via complex analysis
I must calculate $\int _0 ^{\infty} \frac{dx}{x^4+1}$.
My attempt :
Let $f(z)=\frac{1}{z^4+1}$. I've calculated the poles of $f$ to be $z_i=\fr... | 5 | [
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max min problem
August 30th 2011, 10:51 AM #1
Newbie
Joined
Aug 2011
Posts
3
max min problem
rectangular plot of farm land will be bounded on one side by a river and the other 3 sides by a single strand of electric wire. With 800 metres of wire at your disposal what is the largest area
you can enclos... | 4 | [
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Computing the Mode in a Multimodal dataset
January 22, 2013 at 9:05 am 3 comments
In a recent project in which I participated, one of the main metrics the user wanted to visualize involved mode values. I will write about some of the complexities we encountered while implementing
it, but before diving into it let’s re... | 5 | [
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Computing colimits in a Lawvere theory
up vote 6 down vote favorite
3
Let Prod(C, D) be the set of finite-product preserving functors from C to D. Is it true that for any Lawvere theory L, Prod(L, Set) has small colimits? This seems to be the case, as it is invoked
here:
http://ncatlab.org/nlab/show/database+of+categ... | 4 | [
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tangent hyperplanes and tanget planes, a bit confused about dimensions
March 16th 2011, 08:35 PM
Volga
tangent hyperplanes and tanget planes, a bit confused about dimensions
I thought I understood tangent planes until I saw tangent hyperplane and 3-d contour here. So a little bit of help will be most welcome. (i... | 5 | [
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Permutation of theory
May 18th 2008, 05:15 PM
Jigglypuff
Permutation of theory
Each permutation of the letters in THEORY is written on a slip of paper and tossed into a bowl. One slip is drawn at random, what is the probability that the letter T willappear in the last
position?
May 18th 2008, 05:31 PM
Unen... | 4 | [
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Number Tricks
A Math Forum Web Unit
Richard Briston's Math Assignments
Back to Table of Contents
People use numbers every day to benefit themselves. Statistics can be misinterpreted simply because of the way the information... | 4 | [
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linear programming
May 25th 2008, 05:08 AM #1
Newbie
Joined
May 2008
Posts
1
hello everyone...
I have a quation here says
Bulldust Inc. blends silicon and nitrogen to produce two types of fertiliser. Fertiliser 1
must be at least 40% nitrogen and sells for $20/kg. Fertiliser 2 must be at lea... | 5 | [
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mathschallenge.net
Perfect Cone
Problem
A cone is designed so that it fits perfectly into a cylindrical container.
Given the volume of the cone is 100 cm^3 and the curved surface area of the cylinder is 150 cm^2, what is the height of the container?
Solution
Volume of cone = ^1/[3] πr^2h = 100 πr^2h = 300.
Curve... | 4 | [
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Linearly independence and dependence of polynomials
July 23rd 2010, 05:27 AM #1
Senior Member
Joined
Oct 2008
Posts
393
Linearly independence and dependence of polynomials
Hi
How do we work out if the vectors in P2 are linearly dependent or independent.
$<br /> p1= 2-x + 4x^2; p2= 3 + 6x +2x^2;... | 5 | [
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Help with induction for Fibonacci Numbers
April 22nd 2007, 08:23 PM
Beginner_gurl
Help with induction for Fibonacci Numbers
Can anyone please help? I don't know if I am doing it right. I am stuck in the inductive step.
Using induction please prove the following formula:
u2 + 2 u4 + 3u6 +...+ n u2n = n ... | 5 | [
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Finding Sample Standard Deviation Help
March 13th 2014, 06:35 AM
Hiccups
Finding Sample Standard Deviation Help
Assume that I created a 95% confidence interval for the mean hours studied for a test based on a sample of 100 students. The lower bound of this interval was 6 and the upper bound was 10. Assume
th... | 4 | [
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Need some Help with MathCad :)
June 22nd 2012, 02:02 AM
Rhys101
Need some Help with MathCad :)
Hey all, Just wondering if anyone uses mathcad prime 1.0?
I'm using it at the moment and trying to find the co-efficients of an 8th order polynomial using boundary conditions.
if anyone can help me set up and... | 5 | [
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-0.05... | 8,619 | 8619 | |
Symmetric Difference
November 27th 2009, 06:43 AM
santiagos11
Symmetric Difference
I have a problem which s related to this symmetric propety.
Show that there exist a unique set $N$ such that $(A \Delta N)=A$ for all $A$. The set $N$ is obviously the empty set. But then how do I prove the uniqueness part of ... | 4 | [
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roots of polynomials outside the unit disc
up vote 9 down vote favorite
4
Is there any "sufficient and necessary" condition for a comlpex polynomial P(z)=a_0+...a_n z^n, in terms of its coefficinets, to have all its roots outside the unit disc(or equivalently inside the
unit disc)?
If not, is there any such condition... | 4 | [
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Surjective implies local affine surjective?
up vote 6 down vote favorite
1
Take scheme morphism $f: X\to Y$ and suppose $f$ surjective. If $y \in Y$ can one find affine open $V \subset Y$ containing $y$ and affine open $U \subset X$ such $f(U) = V$ ? Thank you.
Later: Very good answer of Kevin shows it is not true. I... | 5 | [
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Derivative of velocity then critical points question (Optimization problem)
November 21st 2009, 10:23 AM
s3a
Derivative of velocity then critical points question (Optimization problem)
Question:
(1 pt) A University of Rochester student decided to depart from Earth after his graduation to find work on Mars. B... | 4 | [
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-0.021606... | 8,623 | 8623 | |
Linear Equations - I Need Someone to Check my Work
July 29th 2010, 06:11 PM #1
Junior Member
Joined
Sep 2009
From
Delaware
Posts
37
Linear Equations - I Need Someone to Check my Work
Hello. I was wondering if someone would be so kind as to check my work on some linear equations. I think I am getting ... | 4 | [
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Doppler Shift
Doppler Effect
Contents
Introduction
Albireo, β Cygni, at the head of the Swan, is a beautiful object, a double star that appears in a small telescope or binoculars as a topaz and a sapphire, 34.4" of arc apart. The brighter star,
spectral type K3, is magnitude 3.1 and described as yellow or golden, wh... | 4 | [
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0.0166015625... | 8,625 | 8625 | |
satisfying axioms to 'prove' vector space
April 29th 2010, 05:20 AM
mathchickie
satisfying axioms to 'prove' vector space
hello there!
I need some clarity on the following please:
The question asked that it be shown that the following set is not a vector space:
'The set of all triples of real numbe... | 4 | [
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0.0... | 8,626 | 8626 | |
Partial Derivatives and Gradient
Date: 12/12/98 at 02:27:21
From: alfredo
Subject: Partial and directional derivative, gradient
I don't understand the definitions of partial and directional
derivatives and gradients. Could you explain the meaning and relations
between them?
Thank you.
Date: 12/12/98 at 07:39:54
F... | 4 | [
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Posts about polynomial on Lucky's Notes
Proofs involving the Remainder theorem
March 24, 2010
The Remainder theorem, sometimes called the Little Bezout theorem states the following:
If $P(x)$ is a polynomial function, then the remainder of $P(x)$ when divided by $x-k$ is equal to $P(k)$.
Example
Say we wanted ... | 5 | [
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0.06640625,
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0.0537109375,
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0.03125,
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0.0390625,
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-0.0419921875,
0.0556640625,
0.02... | 8,628 | 8628 | |
Basis for the space of Harmonic homogeneous polynomial in N variables.
up vote 7 down vote favorite
3
Hello,
Does someone know an explicit basis of the space of harmonic homogeneous polynomial in N variables.
When $N=3$, if I'm not mistaking Legendre polynomial allow to write an explicit basis.
Is there a known exp... | 5 | [
-0.068359375,
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0... | 8,629 | 8629 | |
Divergence Theorem Cylindrical Co-ordinates
May 9th 2011, 10:47 AM #1
Senior Member
Joined
Oct 2008
Posts
393
Divergence Theorem Cylindrical Co-ordinates
$F = {x}^{2 }i + {y}^{2 }j+{z}^{ 2}k$ S the cylinder $0 \leqslant {x}^{2 } + {y}^{2 } \leqslant 4, 0 \leqslant z \leqslant 4$ , including the top and b... | 4 | [
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0.07666015625,
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0.01177978515625,
-0.0771484375,
-0.00... | 8,630 | 8630 | |
Points of bounded height in a number field
up vote 9 down vote favorite
3
Let $K$ be a number field of absolute degree $d$, let $B$ be a positive real number, and write $S(K, B) = \{x \in K : H(x) \leq B\}$. Here $H$ is the absolute multiplicative height of an algebraic
number. A result of Schanuel asserts that $|S(K,... | 4 | [
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0.06396484375,
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Modules of invariants?
up vote 2 down vote favorite
Let $G \subset SL(V, \mathbb{C})$ be a finite group and $R=(\operatorname{Sym}\[V\])^G$ is the ring of polynomial invariants, $W$ some irreducible complex representation of $G$. I want to know is
there any methods (or at least examples) of computing generators and re... | 4 | [
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0.1201171875... | 8,632 | 8632 | |
Recurrence Relation for a Pell Equation
Date: 11/09/1999 at 22:18:14
From: Steve Cash
Subject: Pell Equations
Can you help me with the following:
I need to find a recurrence relation for generating solutions to the
Pell equation x^2 - 5y^2 = 1. I can't remember much about Pell
equations or recurrence relations from... | 5 | [
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0.019775390625,
-0.049560546875,
-0.097167... | 8,633 | 8633 | |
16. Elliptic Functions
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
16. Elliptic Functions
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
16.1 Introduction to Elliptic Functions and Integrals
Maxima includes support for Jacobian elliptic functions and for complete an... | 4 | [
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Topic: Simple question about irrationals, with a short no... | 5 | [
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0.08984375,
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0.0238037109375,
-0.07177734375,
0.0095214843... | 8,635 | 8635 | |
Dolbeault Cohomology of $\mathbb{P}^1$
up vote 5 down vote favorite
3
So from the $\overline{\partial}$-Poincare lemma, there is a short exact sequence of sheaves on $X = \mathbb{P}^1$
$$0 \to \Omega \to A^{1,0} \to Z^{1,1} \to 0$$
where $\Omega$ is the sheaf of holomophic 1-forms, $A^{1,0}$ is the sheaf of (1,0)-fo... | 5 | [
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-0.094726562... | 8,636 | 8636 | |
rray
This is a brief introduction to array objects, their declaration and use in scipy. A comprehensive list of examples of Numpy functions for arrays can be found at Numpy Example List With Doc
Basics
Numerical arrays are not yet defined in the standard python language. To load the array object and its methods into ... | 5 | [
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Simple DE
(This problem is from the chapter Substitution methods and exact equations.) Find the general solution of $(x+y)y'=x-y$.
Ok, let me give it a shot. Let $x+y=v$. $1+\frac{dy}{dx}=\frac{dv}{dx}$ $\frac{dy}{dx}=\frac{dv}{dx}-1$ Substituting, we get $v\left(\frac{dv}{dx}-1\right)=x-(v-x)=2x-v$ $v\frac{dv}{dx}=2x... | 5 | [
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0.022... | 8,638 | 8638 | |
The Way Things Fall
and so on. This is modified by the resistance of the air, which becomes important at higher speeds and usually sets an upper limit ("terminal velocity") to the fall velocity--a much smaller limit for
someone using a parachute than one falling without.
The distance covered by the ball can be shown t... | 4 | [
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0.0517... | 8,639 | 8639 | |
2nd Derivative
July 22nd 2009, 11:01 AM #1
Newbie
Joined
Mar 2009
Posts
21
2nd Derivative
How do you solve the 2nd derivative of this problem?
[LaTeX ERROR: Convert failed]
I know you have to use the quotient rule and chain rule. I just don't know how to get to the answer correctly. I keep screwi... | 5 | [
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0.00628662109375,... | 8,640 | 8640 | |
I
9.3. NUMERICAL INTEGRATION
This section under major construction.
Midpoint rule. Goal: given continuous function f(x) of one variable, compute ∫ f(x) dx over interval from a to b. Estimate integral by M = (b-a) * f(c), where c = (a + b)/2.
Trapezoidal rule. Goal: given continuous function f(x) of one variable, c... | 5 | [
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0... | 8,641 | 8641 | |
Efficiently Implementing Dilate and Erode Image Functions
Dilate by One
Motivation
Dilate
Dilate is a function that accepts a black and white image. It is also known by the names "grow", "bolden", and "expand". It turns on pixels which were near pixels that were on originally, thereby
thickening the items in the im... | 5 | [
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Green's Functions, how does one go about solving this?
August 9th 2009, 03:41 PM #1
Newbie
Joined
May 2009
Posts
20
Green's Functions, how does one go about solving this?
f" + 2af' + (aČ + bČ)f = g(x)
Boundary conditions: f(0) = f(1) = 0, and a and b are constants
Last edited by kiwijoey; Augu... | 4 | [
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Is There a 'Discriminant' for a Quartic Equation?
Date: 01/12/2005 at 16:57:52
From: Romain
Subject: Quartic equation
Hi,
My question is about quartic equations. I know how to find the roots
but I would like to know if it is possible to predict the kinds of
roots only with the coefficients.
For example, in a quadr... | 5 | [
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[plt-scheme] Implementing Rabin-Miller
From: Paulo Jorge O. C. Matos (pocm at mega.ist.utl.pt)
Date: Tue Oct 15 16:09:36 EDT 2002
Hi all,
I've been sometimes confronted with some messy situations in scheme. Two
are of special importance. Sometimes while implementing algorithms
(usually specified in an imperative pse... | 4 | [
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prove sqrt(3) is irrational
October 7th 2012, 03:53 PM #1
Junior Member
Joined
Sep 2012
From
halo
Posts
48
prove sqrt(3) is irrational
proof:
Assume sqrt(3)= a/b where a,b are integers and b cannot equal 0. (sqrt(3)=(a/b)^2 turns 3=a^2/b^2 and 3b^2=a^2. We know that 3|a^2 iff 3|a. Using this theo... | 4 | [
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0.05810546875,
-0.006195068359375,
-0.035888671... | 8,646 | 8646 | |
number of divisors of a number which are not smaller than another number
up vote 2 down vote favorite
Is there any efficient way to find the number of divisors of a number (say n) which are not smaller than another number (say m). n can be up to 10^12. i thought about sieve algorithm & then find the
number of divisors... | 5 | [
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... | 8,647 | 8647 | |
finding.the.value.of a trigonometric ratio
November 25th 2012, 01:20 AM
Tutu
finding.the.value.of a trigonometric ratio
Hi I am wondering about my answer..Given that cosA-sinA=1/3,find the exact value of cosAsinA. I got (2sqrt(5))/9 but the answer is 4/9.. Really appreciate this thanksa. Lot!!
November 25th 201... | 4 | [
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Perturbation in C*-Algebra
up vote 6 down vote favorite
2
Let x be an element in a C*-algebra A, is it true that if x approximately commute with every element in A, then x is near the centre of A? More precisely, I want to know whether the following is true
： Let x be an element in a C*-algebra A with norm 1. Then for... | 5 | [
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0.000265121... | 8,649 | 8649 | |
pre-calc--parabolas
April 19th 2007, 05:26 PM #1
simplytrite
Guest
pre-calc--parabolas
Hey, I have a huge test tomorrow and I haven't been there in awhile so I don't know anything! Here's a typical problem that has been troubling me...
Find the vertex, focus, and directrix of the parabola
x^2 + 4x + 6y ... | 4 | [
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... | 8,650 | 8650 | |
Probability Question on jointly distributed function
May 18th 2009, 07:20 AM #1
Newbie
Joined
Jan 2009
Posts
20
Probability Question on jointly distributed function
I'm having problems figuring out the limits for this. The exponential is e^-(x + y) apologies about the lack of clarity on it.
Hello,
... | 5 | [
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... | 8,651 | 8651 | |
archery
Originally, in the Newtonian formulation of classical mechanics, equations of motion were determined by summing up vector forces (à la free body diagrams). Is there a different way to find the
equations of motion?
In place of drawing a free body diagram, we can represent a system more rigorously by... | 4 | [
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0.0603027343... | 8,652 | 8652 | |
[SciPy-user] Maximum entropy distribution for Ising model - setup?
[SciPy-user] Maximum entropy distribution for Ising model - setup?
James Coughlan coughlan at ski.org
Sat Oct 28 12:18:45 CDT 2006
Martin,
Hope this makes sense. If not, why don't we take this discussion offline.
Best,
James
1.) "I want to find a ... | 4 | [
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0.034423828125,
0.06396484375,
0.0207519531... | 8,653 | 8653 | |
finding the parametric equation of a line
November 8th 2009, 09:44 PM #1
Senior Member
Joined
Jun 2009
Posts
251
finding the parametric equation of a line
question: Find the parametric equation of the line through the points (0,.5,1) and (2,1,-3)
work:r=r_0+tv the vector parallel to the line is <2-0... | 4 | [
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-0... | 8,654 | 8654 | |
derangement problem
May 28th 2013, 03:03 PM
Yuuki
derangement problem
At a party, n people are seated in a room with n+1 chairs. They go to another room for supper; when they return and sit down again, it is found that no one occupies the same chair as before. Show
that this can occur in precisely D[n] + D[n... | 4 | [
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0.05126953125,
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0.0279541015625,
-0.036376953125,
-0.00994873046875,
-0.057861328125,
0.07470703125,
0.00... | 8,655 | 8655 | |
Series
January 1st 2008, 03:25 PM
slevvio
Series
Show that, for all $\theta \in \mathbb{R}$,
$\frac{cos\theta}{2} + \frac{cos3\theta}{2^2} + \frac{cos5\theta}{2^3} + \ldots = \frac{cos\theta}{1 + 8sin^2\theta}$.
I understand that this has something to do with a geometric series however taking $\frac{a_... | 5 | [
-0.1796875,
-0.0810546875,
0.01202392578125,
0.07275390625,
0.019287109375,
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-0.0257568359375,
0.11474609375,
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0.02734375,
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0.00616455078125,
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0.00396728515625,
-0.08056640625,
-0.0... | 8,656 | 8656 | |
Trig equation
March 2nd 2010, 02:31 PM #1
Trig equation
Hi there,
I'm having a little trouble solving the following equation for $-\pi <x\leq 2 \pi$:
$sin^2(x)cos^3(x)=cos(x)$
I've rearranged it into the form:
$cos(x)\left [sin^2(x)cos^2(x)-1\right ]=0$
So where $cos(x)=0,\ \ \ x= \pm\fra... | 4 | [
-0.06591796875,
0.0036163330078125,
-0.018798828125,
0.0908203125,
-0.0966796875,
0.041259765625,
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-0.00262451171875,
0.061767578125,
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0.0228271484375,
0.04736328125,
0.056884765625,
-0.011962890625,
0.0888671875,
-0.02001953125,
0.09130859375,
-0.... | 8,657 | 8657 | |
maximize and minimize
April 14th 2009, 12:33 PM
Abbas
maximize and minimize
A wire 20 m long is cut into two pieces. One piece is bent in the shape of
an equilateral triangle, and the other is bent in the shape of a circle. How
should the wire be cut to maximize the total area enclosed by the shapes?
... | 4 | [
-0.00543212890625,
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0.08251953125,
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0.04345703125,
0.07421875,
0.00604248046875,
0.033447265625,
-0.000698089599609375,
0.031982421875... | 8,658 | 8658 | |
\varphi^{(4)}-\lambda\varphi=0
March 7th 2011, 10:14 AM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
\varphi^{(4)}-\lambda\varphi=0
$\varphi^{(4)}-\lambda\varphi=0, \ \ 0<x<L, \ \ \varphi(0)=\varphi'(0)=\varphi(L)=\varphi'(L)=0$
$m^4=\lambda, \ \ r=\lambda, \ \ \theta... | 4 | [
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0.0439453125,
-0.0... | 8,659 | 8659 | |
Help with an Inverse Equation
November 18th 2011, 09:22 AM
rpgnick85
Help with an Inverse Equation
I am really stumped on this homework question and I am trying to better understand how to find the inverse, domain, and range.
The equation g(x) = -2x/(-7x-3). I feel like I am not going about getting the inve... | 4 | [
-0.09521484375,
-0.056884765625,
0.00921630859375,
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-0.019287109375,
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0.03564453125,
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... | 8,660 | 8660 | |
bernoulli equation/partial fraction
October 14th 2009, 07:02 PM #1
Member
Joined
Oct 2008
Posts
93
bernoulli equation/partial fraction
so i know this question can be done both way
y' = 3y - y^2
<=>
y' = y(3-y)
alright so i dont think i can do it by bernoulli because i dont have two v... | 5 | [
-0.034912109375,
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-0.02294921875,
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0.00653076171875,
-0.0184326171875,
0.0830078125,
0.020751953125,
-0.04614257812... | 8,661 | 8661 | |
Euler's divergent series sum n!*(-1)^n: what is known about the resulting constant?
up vote 10 down vote favorite
3
Much of the theory of continued fractions has been developped by Euler in the 18th century. The little survey "Euler: continued fractions and divergent series (and Nicholas Bernoulli)", mentions
towards ... | 5 | [
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-0.052490234375,
0.012573242187... | 8,662 | 8662 | |
problem on A.P/G.P
Please solve the problem for me Find the sum of the series 3+7+14+27+52+...................up to nth terms
The nth term in the series is given by the recurrence relation $a_n = 2 a_{n-1} - n + 3$ with $a_1 = 3$. This does not define an Arithmetic Sequence or a Geometric Sequence. So I don't know why... | 5 | [
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... | 8,663 | 8663 | |
Need help re-arranging an equation!
June 19th 2012, 05:49 AM #16
Re: Need help re-arranging an equation!
Remember the rule $\frac{a^2}{b^2} = {\left(\frac{a}{b}\right)}^2$? well, if you square both sides of the equation, you'll remove the square root.
Then, you can rearrange to remove the fraction, and solvi... | 5 | [
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0.052978515625,
0.0123291015... | 8,664 | 8664 | |
LaPlace transforms
January 27th 2011, 10:43 AM #1
Newbie
Joined
Aug 2009
Posts
16
LaPlace transforms
Bear with me here, I took DIFF EQ 3 semesters ago and laplace transforms have come up again in a new class and I need to help
Solve the following using Laplace transforms:
$x''+x'+x=1$ where x $'(... | 5 | [
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0.042724609375,
0.03173828125,
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0.004486083984375,
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-0.029541015625,
0.043212890625,
0.04516601562... | 8,665 | 8665 | |
proof of limy->inf,g(y)ln(ln(y))/ln(y) = 1
April 3rd 2013, 04:55 PM #1
Newbie
Joined
Aug 2012
From
Japan
Posts
8
proof of limy->inf,g(y)ln(ln(y))/ln(y) = 1
Hi everyone,
Stuck on the following proof, any help would be appreciated! (Calculus a Complete Course, Adams, 3rd Ed., Ch3 Ch Review, in cas... | 5 | [
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0.08251953125,
-0.0712890625,
-0.0607910... | 8,666 | 8666 | |
Linear Differential Homogeneous Equations
May 24th 2009, 03:30 AM
fobos3
Linear Differential Homogeneous Equations
If we have $\sum_{i=0}^{n} A_i \dfrac{d^i y}{d x^i} =0$, why does the soloution have the form $e^{z x}$ as suggested by Euler. Is there any proof to that?
May 24th 2009, 07:35 AM
HallsofIvy
... | 5 | [
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-0.044921875,
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0.046875,
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0.021484375,
-0.0169677734375,
-0.057373046875,
0.009521484375,
0.0174... | 8,667 | 8667 | |
Functions
Definition of a Function
Functions are nothing more than equations where you can plug in an input variable \(x\) and get an output variable \(y\) in return. \[ x \xrightarrow{\text{input}}\boxed{function}\xrightarrow{\text
{output}} y \] Functions describe the relations, causalities, and changes between one... | 4 | [
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-0.0732421875,
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0.01312255859375,
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0.010498046875,
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0.08203125,
0.050048828125,
0.060546875,
0.002227783203125,
-0.01904296875,
0.0395507... | 8,668 | 8668 | |
serious trouble finding big O
August 11th 2009, 06:27 PM #1
Newbie
Joined
Aug 2009
Posts
8
serious trouble finding big O
Original statement:
$f(n)=(n^3+4log_2 n)/(n+4)$
I'm sure the n+4 in both the denominator and numerator have something to do with it, but if i make $n$in the denominator a $n^... | 5 | [
0.04638671875,
0.0703125,
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0.056884765625,
-0.01251220703125,
-0.05615234375,
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-0.015625,
0.09912109375,
-0.0439453125,
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0.056396484375,
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0.02197265625,
0.04931640625,
0.0791015625,
... | 8,669 | 8669 | |
first derivative test
February 8th 2008, 02:15 PM #1
Member
Joined
Dec 2007
Posts
80
first derivative test
Hi, thank you for your help.
i have being given this question to do, i have done the first part but am unsure about the nxt parts..
I have y=3x^4+4x^3
i had to find dy/dx = 12x^3+12x... | 4 | [
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-0.003936767578125,
0.0027618408203125,
... | 8,670 | 8670 | |
Optimization problem
April 5th 2009, 10:49 AM #1
Member
Joined
Jul 2007
Posts
147
Optimization problem
Dear forum members,
in a problem I was asked to show that when the surface area of a fixed cylinder was at its minimum, the height of the cylinder would be equal to the diameter of the cross sectio... | 4 | [
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0.095703125,
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0.004852294921875,
0.004150390625,
0.04... | 8,671 | 8671 | |
[SciPy-User] raising a matrix to float power
Charles R Harris charlesr.harris@gmail....
Sun Jul 11 17:02:10 CDT 2010
On Sun, Jul 11, 2010 at 2:17 PM, David Goldsmith <d.l.goldsmith@gmail.com>wrote:
> On Sun, Jul 11, 2010 at 10:41 AM, Charles R Harris <
> charlesr.harris@gmail.com> wrote:
>
>>
>> On Sun, Jul 11, 2010... | 4 | [
-0.0634765625,
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-0.000965118408203125,
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0.042236328125,
0.1015625,
-0.07080078125,
0.05810546875... | 8,672 | 8672 | |
[racket] Style and Performance question
From: Matthias Felleisen (matthias at ccs.neu.edu)
Date: Tue May 10 16:25:46 EDT 2011
On May 10, 2011, at 3:40 PM, Matthew Flatt wrote:
> At Tue, 10 May 2011 10:05:35 -0400, Matthias Felleisen wrote:
>> 2. The addition in lieu of the multiplication is consistently the fastest ... | 4 | [
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0.04248046875,
0.061279296875,
0.0644531... | 8,673 | 8673 | |
Which Quadrant in the Unit Circle?
Date: 11/30/98 at 21:57:23
From: Rosalynn
Subject: The Unit Circle
Hello, I'm trying to determine how to do this problem:
"for each value of s, find the quadrant in which C(s) is found."
I've studied the examples in my textbook. One example was:
Find the quadrant in which C(s) i... | 4 | [
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0.068359375,
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-0.07763671875,
-0.0299072265625,
-0.0043334... | 8,674 | 8674 | |
solve these two system of differential equation
#2: I get the following solutions for the respective DE's: $x=C_{1}e^{5t}-\frac{1}{3}e^{2t}-\frac{3}{5}y$ $y=2e^{t}+2xt+C_{2}$ $z=e^{t}+t(x+y)+C_{3}$ Perhaps that is something for you to start with.
i m just not familiar with how to do the second question... would you po... | 5 | [
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0.04443359375,
0.00194549560546875,
-0.04858... | 8,675 | 8675 | |
Stats Problem - Central Limit Theorem
February 18th 2009, 06:37 PM
chrissybee
Stats Problem - Central Limit Theorem
An economist wants to estimate the average hourly wage of waitresses in a large metropolitan area. This will be done randomly surveying 250 waitresses and calculating the sample mean. Find the
... | 5 | [
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0.0238037109375,
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0.0703125,
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-0.06640625,
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0.0142822265625,
... | 8,676 | 8676 | |
Minor point of clarification regarding congruencies
May 30th 2010, 12:39 PM #1
Minor point of clarification regarding congruencies
Hi,
In my book there are many proofs that looks like this in the primitive roots chapter:
$a^{t+k\phi(m)} \equiv a^{t}(a^{k})^{\phi(m)} \equiv a^{t} \equiv 1 (mod \ m)$
... | 4 | [
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-0.053466796875,
0.05419921875,
-0.... | 8,677 | 8677 | |
Real Solutions,
March 28th 2009, 06:04 AM
craigmain
Real Solutions,
Hi,
The graph $y=\frac{2}{x^2}+x^4$ has four real number solutions for values of $y > 3$.
I can draw the graph using my math tools, but this is quite a stinker to try and graph by hand.
I was wondering how you would find the four ... | 4 | [
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0.0703125,
0.11474609375,
-0.00567626953125,
... | 8,678 | 8678 | |
Coordinated Geometry
September 14th 2006, 06:09 AM #1
Newbie
Joined
Sep 2006
Posts
6
Coordinated Geometry
Given that A is the point (0,11), B is the point (8,5) and O is the origin , calculate
How to find the,
a) the coordinates of M , the mid point of AB,
b) the gradient of OM,
c) the le... | 4 | [
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0.0042724609375,
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0.10107421875,
-0.032470703125,
0.006... | 8,679 | 8679 | |
numerical solution to differencial equation
May 8th 2007, 06:25 PM #1
Newbie
Joined
Dec 2006
Posts
9
numerical solution to differencial equation
dy/dx = y' = f(x,y(x)) = 2e^(-x^2)
Solve this differential equation using Heun's method and plot solution over -5 < x < 5. You'll need to derive the approp... | 4 | [
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0.00469970703125,
-0.0... | 8,680 | 8680 | |
Topological space with some conditions
up vote 3 down vote favorite
Can one give an example of non-compact space $X$ which satisfies the following conditions:
• the countable union of compact subsets is relatively compact,
• for every closed noncompact subset $A$ of $X$ there is a positive lower semicontinuous f... | 5 | [
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0.002243041992... | 8,681 | 8681 | |
Inverse Trig Functions
September 20th 2009, 12:49 PM
horsepower.850
Inverse Trig Functions
I'm having trouble understanding this:
tan[arc cos (square root of 3 / 2) = square root of 3 / 3
How does this answer come to be?
September 20th 2009, 01:17 PM
artvandalay11
This question is saying what is t... | 4 | [
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-0.06103515625,
-0.031494140625,
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-0.01043701171875,
0.068359375,
-0.041748046875,
-0.01123046875,
-0.000331878662109375... | 8,682 | 8682 | |
Winning the Game
Date: 09/21/2000 at 14:29:49
From: Ryan Lane
Subject: Mathematical Expectation
In an equitable game of coin tossing, I have x dollars and my friend
has y dollars. I win a dollar if I choose correctly after each flip,
but my friend loses a dollar, and vice versa. What is the probabitity
that my frien... | 5 | [
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Finding the maximum
November 3rd 2009, 08:22 AM #1
Junior Member
Joined
Oct 2009
Posts
36
Finding the maximum
How would you find the maximum value and smallest +ve value the maximum occurs at for f(x) = -cosx + sqrt3sint ?
I've got as far as
f'(x) = sqrt3cosx + sinx
but I'm not sure where ... | 4 | [
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0.014404296875,
-0.0240478... | 8,684 | 8684 | |
Why is this limit true...?
October 29th 2009, 02:15 PM #1
Member
Joined
Nov 2008
Posts
121
Why is this limit true...?
I've just seen this:
$\{x_i\}_{i=1}^\infty \ \sum _i ^\infty |x_i| < + \infty \rightarrow lim_{+\infty} x_i = 0$
why is this true?
$Put\,\,S:=\sum\limits_{i=1}^\infty|x_i... | 5 | [
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Integration/Differentiation help.
Can someone please explain how I would differentiate this: (1-e^(-x^2))(1-e^(-y^2)) and integrate this: 24y(1-x-y) Regards.
Apologies TES. Differentiating w.r.t x and a double integral dydx.
So for the first question if you have $f(x,y)=\dfrac{1-e^{-x^2}}{1-e^{-y^2}}$ The partial der... | 5 | [
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Class number of PGL_2
up vote 8 down vote favorite
1
Hello.
Let $K = F_q(x)$ be the rational function field and let $G = \textbf{PGL}_{2,K}$. For any finite and non empty set $S$ of valuations of $K$, we refer to the subgroup of the adelic group $G(\Bbb{A})$:
$$ G(A_S) = \prod_{p \in S} G_p(K_p) \times \prod_{p \not... | 5 | [
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0.... | 8,687 | 8687 | |
peakdet: Peak detection using MATLAB
Here's a problem I encounter in several fields: Find the local maxima and minima in some noisy signal, which typically looks like the following graph:
The local maxima and minima are plotted as red and green stars on the graph. To the eye it's so obvious where they are, but making... | 5 | [
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0.02038574... | 8,688 | 8688 | |
Why is a Telescoping Series Called Telescoping?
Associated Topics || Dr. Math Home || Search Dr. Math
Why is a Telescoping Series Called Telescoping?
... | 4 | [
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-0.022827148437... | 8,689 | 8689 | |
Quadratic Application
October 12th 2007, 01:03 PM #1
Junior Member
Joined
Sep 2007
Posts
60
Quadratic Application
1.) The sum of a number and its reciprocal is $\frac{29}{10}$. Determine the integers.
So i figure, let $x$ be a number,
let $\frac{1}{x}$ be the reciprocal.
Now i got the equat... | 4 | [
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-0.02856... | 8,690 | 8690 | |
solve inequality
Log(base x)[5/2 -1/x] > 1 [5/2 -1/x] > x^1 2.5 -1/x > x Multiply both sides by x, 2.5x -1 > x^2 --------no change in sense of inequality since x is positive x^2 -2.5x +1 < 0 2x^2 -5x +2 < 0 (2x -1)(x
-2) < 0 x < 1/2 -----------(1) or x < 2 -----------(2) And, since there are no real logs of negative nu... | 5 | [
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-0.1... | 8,691 | 8691 | |
Cross Product
In this final section of this chapter we will look at the cross product of two vectors. We should note that the cross product requires both of the vectors to be three dimensional vectors.
Also, before getting into how to compute these we should point out a major difference between dot products and cros... | 5 | [
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0.07226562... | 8,692 | 8692 | |
Simple question about linear functionals
May 16th 2012, 02:04 PM
Mazerakham
Simple question about linear functionals
Hi everyone. Paul Halmos asks a seemingly-innocuous question in Finite Dimensional Vector Spaces: let V be a vector space over a field F and let y and z be linear functionals from V to F.
Supp... | 5 | [
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extrem
Extrema
Idea
In general, a maximum is a top element, a minimum is a bottom element, and an extremum is either. However, these terms are typically used in analysis, where the order theory is secondary. One also
usually speaks of extrema of a function, meaning a top or bottom element of the range of the function... | 4 | [
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-0.05786132812... | 8,694 | 8694 | |
[SOLVED] Integration by Parts
May 1st 2009, 04:59 AM #1
Newbie
Joined
May 2009
Posts
4
[SOLVED] Integration by Parts
I've having trouble integrating this expression by parts:
The first expression is the one I want to solve by using the second equation.
I've tried solving it by parts but I can... | 5 | [
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0.065429... | 8,695 | 8695 | |
Triangle Series
Date: 07/09/99 at 14:55:40
From: Simer Singh
Subject: Triangular Series
Dear Dr. Math,
I am doing a project on a formula that calculates the sum of the nth
row of the following triangle:
1
2 3
4 5 6
... | 4 | [
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-0.0223... | 8,696 | 8696 | |
Find volume of cylindrical tank
August 12th 2005, 06:29 PM
Steves5a
Do not know geometry
Find the volume. Use 3.14 as pi
1. water storage tank is shaped like a circular cylinder with half of a sphere at each end. what is the volume of the tank if the cylindrical section is 100cm long with a 40cm diamerter. ... | 4 | [
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-0.0737... | 8,697 | 8697 | |
Homeomorphism and identity
October 18th 2012, 04:36 PM #1
Newbie
Joined
Oct 2012
From
Chile
Posts
4
Homeomorphism and identity
Let $(M_1,d_1),\ldots,(M_n,d_n),$ and $M=M_1\times\cdots\times M_n.$ Prove the following:
$1_M : (M,d_e)\to(M,d_m)$ and $1_M :M,d_e)\to(M,d_s)$ are homeomorphisms, where... | 5 | [
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Tannakian description of a semi-direct product
up vote 7 down vote favorite
3
Let $H$ and $K$ be affine group schemes over a field $k$ of caracteristic zero. Let $\varphi:H\to Aut(K)$ be a group action. Then we can form the semi-direct product $G = K\ltimes H$.
Problem: Describe the tannakian category $Rep_k(G)$ in ... | 4 | [
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