Regular Definition and 251 Threads

Hello, I am trying to understand the definition of regular point, regular singular point and irregular point for example, the ode. what would be the r,rs or i points of this? x^3y'''(x)+3x^2y''(x)+4xy(x)=0 dividing gives the standard form y''+(3/x)y' + (4/x^2)y=0 So...

I am currently studying a great text Elementary Differential Equations and Boundary Valued Problems 9th edition; and we have come to chapter 5 and are studying Ordinary Points, Singular Points, and Irregular Points. (get the point?) Anyway, I did see these mentioned,, this...

Homework Statement A floor tile has the shape of a regular polygon. If the tile is removed from the floor and rotated through 50◦ it will fit back exactly into its original place in the floor. The least number of sides that the polygon can have is? I don't know what are the theories that i...

I am thinking about doing Honors Physics. Is getting the major in math as well a good idea?

[SIZE="3"][FONT="Times New Roman"]Homework Statement α(t) = (sint, cost + ln tan t/2) for α: (0:π) -> R2 Show that α is a smooth, parametrized curve, which is regular except for t = π/2 The Attempt at a Solution I am familiar with the definitions of smooth and regular, which I have...

I'm trying to create an rss feed from a html table on the main page of a web forum. I want to do this because the table displays the new posts. I use yahoo pipes and you can see my attempt here: http://pipes.yahoo.com/pipes/pipe.info?_id=0e72fee43090386fddbc9191f5cddc86 The pipes work up...

Homework Statement Let X by a completely regular space and let A and B be closed, disjoint subsets of X. Prove that if A is compact, then there is a continuous function f : X --> [0,1] such that f(A) = {0} and f(B) = {1}. The attempt at a solution Let {U} be an open covering of A, U_1...

Hi, I read the following theorem in a book: If {A_n} is a sequence of nowhere dense sets in a complete metric space X, then there exists a point in X which is not in any of the A_n's. But what if I say X={1,1/2,1/3, ...} \cup {0} with the regular metric d(x,y)=|x-y|, and A_n={1/n,0}. Why...

A "concentration" degree vs a "regular" degree Good afternoon everyone. I'm new here and it's great to be here. I have a very large interest in Physics and plan on getting a degree in said field. I do have one big question; Is there a big difference between having a BS in Physics and a BS in...

Help: Perpendicular project is regular surface?? (edit found a better way of showing this) Homework Statement Hi I have this problem here which is causing me trouble. Show that the perpendicular projection of the center (0,0,0) of the ellipsoid \frac{x^2}{a^2} + \frac{y^2}{b^2}...

What is the general solution of x^2y''+xy'-y=0 i tried a series solution y=\sum_{n=0}^{\infty} a_n x^n and whitteld it down to \sum_{n=0}^{\infty} (n^2-1) a_n x^n=0 but this isn't getting me anywhere secondly how do i show that x=0 is a regular point of...

How many decibels does a regular apartment wall cancel out?

Hi: This problem should be relatively simple, but I have been going in circles, without figuring out a solution: If f:X->R^2k is an immersion and a is a regular value for the differential map F_*: T(X) -> R^2k, where F(x,v) = df_x(v). Then show F^-1 (a) is a finite set...

Homework Statement Given a parameterized curve \alpha:(a,b)\rightarrow \mathbb{R}^2, show that this curve is regular except at t = a. Homework Equations I know that according to the defintion that a parameterized curve \alpha: I \rightarrow \mathbb{R}^3 is said to be regular if...

Through my learning of calculus, I have come under the impression that there is an important difference between the derivative of a variable with respect to another, and the partial derivative of a variable with respect to another. For example: I think that \frac{dy^2}{dx} = 2y\frac{dy}{dx}...

Homework Statement What is an algorithm which decides whether a context-free language is actually a subset of a regular language? That is, given CFL and RL, how do we decide whether CFL is a subset of RL?

Hello, firstly, what does the regular expression "\\+" do? Would that literally match up "\+". Could I possibly get some recommendations on some software to try regular expressions with as well actually please? and secondly, I've been fiddling around with the cacls command and I've noticed...

Homework Statement I have this pole with mass M and length L which is on a flat table with no friction. Another particle, which has the same mass M hits him on its edge with velocity V, which is vertical to the pole. then, the particle sticks to the pole and they move together. I need to...

Is there an algorithm for converting DFA (or NFA) into regular expressions?

Hello guys, I just bought TI-Nspire CAS+ graphing calculator, and I am wondering what are the differences between CAS+ and normal CAS. What are pros and cons? Thanks in advance, Jan

The two dimensional regular polygon series, the triangle, square, square, pentagon etc. is infinite. If for some reason, it was finite, what would our universe become? especially the dimensions of length and breadth.

Suddenly I'm curious what other uni physics students do and I am studying the physics curriculum of another local uni just now, but it seems there're a lot of differences between the two top uni here...we took a-level here so it's a 3-year program. The core courses are: 1 year on some...

Homework Statement A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let R be the region outside the hexagon, and let S = \{ 1/z |x \in R} . Then the area of S has the form a \pi...

And, just a few minutes ago, I realized I forgot to square a constant in solving for rho in spherical coordinates in determining the limits of integration for a triple integral. I got cosine of phi as 1/2, which gives phi as pi/6, but since I forgot to square the two, it actually is pi/4. :mad...

For solving a series solution near a regular singular point with the Frobenius method, why is it that the indices of summation derivatives aren't shifted? For example, in my textbook and lecture notes y = \sumA_{}nx^{}n+r from n=0 to infinity y' = \sum(n+r)A_{}nx^{}n+r-1 from n=0 to...

I have a prescription for Wellbutrin, a drug which blocks reuptake of dopamine (strong) and noradrenaline (weak). I got this prescription because my family wasn't keen on my idea of self-medicating with ephedrine (strong noradrenaline response) and caffeine (strong dopamine response). I was very...

1) A vector form of Green's theorem states that under certain conditions, where n is the unit[/color] outward normal to the curve C and D is the region enclosed by C [Now, my question is: must n be a unit vector? Why or why not?] 2) A "regular region" is a compact set S in Rn that is...

Problem on regular language! Homework Statement Homework Equations The Attempt at a Solution Thanks!

So i began reading up on some group theory and I came across an interesting question, what is the order of the group of symmetries on of a n-sided regular polygon? with a square it's 8, triangle it's 4. I feel like I'm missing something with the pentagon because I'm only finding these: the 5...

Homework Statement Balance this redox equation. Homework Equations Ag + H^{+} + NO_{3} ^{-} \rightarrow Ag^{+} + H_{2}O + NO The Attempt at a Solution Using a conventional balancing mechanism I got these coefficients: 1 + 8 + 2 -> 1 + 4 + 2 but the correct...

I am trying to remember the rumor I heard about a new gun shooting design in one of my ap physics class discussions, do you guys now of any new breakthrough designs? anyway i think it has to do with the reloading mechanism. (I know I have asked a question of this type before, so if i sound...

When integrating and differentiating I'm not sure weather to use a lower case delta or just a d. Is there a time when one is more a appropriate then another or does it not even make a difference? Are they to completely different things? I know it might seem trivial but I have no idea which is...

Superimpose concentric regular polygons of equal area with maximal symmetry, starting with the equilateral triangle and sequentually approaching the circumference of a circle. What series can you derive for the fraction of the area not occupied by any successive polygons?

I was reading about what would happen if an Anti-Matter star and Matter star collided. What I read says the collision would make enough gamma rays to sterilize and entire eighth of a galaxy of life. Yet, I thought about something, when the two collide, their surfaces would touch first. (Duh) So...

If possible, could anyone tell me if the clousure of every open connected set always has a regular boundary ? thanks in advance.

How do I approach this problem? give a regular expression for a set containing strings consisting of 0s and 1s where numbr of zeroes is odd... thanks ps: I have tried it with Kleene's theorem, but there is so many possibilities that i get lost

Can anyone help me with this question please... Five points form the vertices of a regular pentagon. What is the shortest distance such that we can go from any of those five points to each of the four remaining points using the minimum amount of lines to join the points? What about 6...

The higher levels of Sugar in chocolate milk, will this mean that it keeps longer? Also the eternal Chocolate vs no chocolate issue? Should we make value judgements based on the consumption of chocolate even in less obvious forms? :smile:

I have seen two different definitions of "completely regular" (one in my class and online, and the other in my textbook). I am having trouble seeing how these definitions are equivalent. A space S is said to be completely regular if for every closed subset C of S and every point x in S-C...

Hi All, I'm looking for the conformal mapping (using complex functions) that maps the unit circle (or the upper half plane) into a REGULAR polygon with n vertices. I know the Schwarz-Christoffel transformation for an ARBITRARY polygon, but that doesn't help me because the expression is way...

Show that the only regular figures that fills the plane are the triangle, the square and the hexagon.

I heard one of the problems with quantum computers is there is not a certin output for each input, meaning there is some randomness in their computations. Can this randomness some how be reduced until it becomes negligible? My question is basicly can a quantum computer perform most of the...

What are the distinguishing characteristics of Fascism that make it different from any other Dictatorship out there? I mean, I hear "Hitler and Moussolini were Fascist", but being that nearly everything I know about those two comes from the American Public School system and the History Channel...

Hi, I have a question regarding group theory. For the cyclic group C2 with elements e and a, what are the matrices of the regular representation? How do you find this? How would I reduce this representation into irreducible representation? Lastly, how do I find a matrix which brings the...

I've been intrigued by regular polyhedra for years, and have oft tinkered with them. Can someone provide the "textbook definition" of a regular polyhedron?

My dad just bought a car and he decided to use a premium gasoline instead. The car uses regular at the moment, if premium is mixed into it would it somehow ruin the engine? long term wise is this a bad thing?

Hey ppl, Could anyone help me with this: what is the ratio of the areas of the circumscribed and inscribed circles of a regular hexagon? how do I go about working it out from first principles? Cheers, joe

How do i show that a group of symmetries of a regular quindecagon has order |G| = 30 ? And how do i describe the elements of G and classify them by their order? Thanks

Archived thread "Volumes of Regular Icosahedron and Regular Tetrahedron" Hi, The above-referenced thread is at this url address: https://www.physicsforums.com/archive/t-3876 I have something to add, having worked with this structure, in a bit of a different way, however, than is spoken...

A friend at work asked me to calculate the central angle of a regular dodecahedron. I think he was trying to stump me. :smile: Just to be sure we are talking the same thing, he was referring to the angle between any two radii drawn from a vertex of the dodecahedron to the center. At any...