A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
In mathematics, the notion of a number has been extended over the centuries to include 0, negative numbers, rational numbers such as one half
(
1
2
)
{\displaystyle \left({\tfrac {1}{2}}\right)}
, real numbers such as the square root of 2
(
2
)
{\displaystyle \left({\sqrt {2}}\right)}
and π, and complex numbers which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or subtracting its multiples). Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers.
Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is often regarded as unlucky, and "a million" may signify "a lot" rather than an exact quantity. Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. In modern mathematics, number systems (sets) are considered important special examples of more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.
Please help me confirm that I understand this correctly.
Imagine a system comprised of two black holes orbiting each other, which will eventually merge. At any point in time we describe the stress-energy tensor of the system. Assume that we could solve the EFE's for every point (t,x,y,z). This...
Hi,
can somebody explain the spin structure factor (static and dynamic)?
how is it related to the lattice symmetry(I m working with honeycomb)?
How could I implement it easily?
Thanks :)
So I am working on a project where I have a tank, which has a volume of electrolyte liquid inside it. This is coupled to a battery which charges it, and gives it energy. I will have a copperband arround it, so i can measure a potential voltage from the electrical field.
So what I need to...
Hey everybody,
Background:
I'm currently working on a toy model for my master thesis, the massless Klein-Gordon equation in a rotating static Kerr-Schild metric.
The partial differential equations are (see http://arxiv.org/abs/1705.01071, equation 27, with V'=0):
$$ \partial_t\phi =...
Homework Statement
I need calculate the points (##x_i##) and weights (##w_i##) with Gauss Lobatto seven points on the interval [a,b]. With the points and the weights I am going to approximate any integral at this interval.Homework Equations
I have found the relevant points and weights at the...
Hi,
I've computed 512 terms of a power series numerically. Below are the first 20 terms.
$$
\begin{align*}
w(z)&=0.182456 -0.00505418 z+0.323581 z^2-0.708205 z^3-0.861668 z^4+0.83326 z^5+0.994182 z^6 \\ &-1.18398 z^7-0.849919 z^8+2.58123 z^9-0.487307 z^{10}-7.57713 z^{11}+3.91376 z^{12}\\...
Hi folks,
I've got everything I need to write a paper on the effect of constraints on passwords... except the math. I actually could write it, but the math would make it much meatier.
Here is what I know about math. If the answer to a math problem is obvious, it is probably wrong. If the...
Hi PF!
I'm solving an PDE where the analytic solution is called ##F(x)## (unknown). To approximate the analytic solution I made a naive expansion in some small parameter ##\epsilon## such that ##F(x) = f_0(x)+\epsilon f_1(x)+O(\epsilon^2)##, where I know ##f_0(x)## and ##f_1(x)##. I then...
Hello, I have been working on a little movement system in a program called Game Maker: studio.
The code works fine on the programming perspective, but something I did not expect happened:
When I ran the code by adding to the speed while pressing a key, and every step passively subtracting from...
Homework Statement
In this exercise, we are given a discrete Lagrangian which looks like this: http://imgur.com/TL0P61r. We have to minimize the discrete S with fixed point r_i and r_f and find the the discrete equations of motions.
In the second part we should derive a discrete trajectory for...
Homework Statement
I was recently assigned an assignment where my instructor told us to come up with an idea for a numeric classical mechanics problem that is solved by computer methods. Some ideas the instructor gave was to simulate motion of a sun-earth-moon system or simulate the tides of a...
Set hasDigit to true if the 3-character passCode contains a digit.
#include <iostream>
#include <string>
#include <cctype>
using namespace std;
int main() {
bool hasDigit = false;
string passCode;
int valid = 0;
passCode = "abc";
if (hasDigit) {
cout << "Has a digit." << endl;
}...
hey,
need an idea for a paper on differential equations, which can be implemented in two or three days work.
also it will be nice if that paper has graphs on it.
any help would be most welcome
thx
Could use some help figuring out the error
Operand type clash: numeric is incompatible with uniqueidentifier
which points to the specified line below
CREATE PROCEDURE AddPartner
@name NVARCHAR(50), @email NVARCHAR(254), @new_guid UNIQUEIDENTIFIER OUTPUT
AS
BEGIN
SET NOCOUNT ON...
Hey guys, so my professor told me to take a look at an equation, because he thinks that there is a mistake. We are basically talking about exercise 6.3 (on last image). The pictures will show you the text, so that you have all the information, that I have
http://puu.sh/mrNDl/ec19cdff63.png...
I want to clear numeric content(without clear others) in certain range with a button. example: $E$10:$H$26 and $K$11:$Z$15. What macro code should I have? Appreciate your help
Set hadDigit to true if the 3-character passCode contains a digit.
Sample program:
#include
#include
#include
using namespace std;
int main() {
bool hasDigit = false;
string passCode;
int valid = 0;
passCode = "abc";
<student code>
if (hasDigit) {
cout << "Has a...
The topic says it all. I am trying to figure out how to delete unwanted equations out of my TI-89 "numeric solver" app. I consulted the manual...nothing. I have googled and youtubed...nothing. Any help here would be great as I love the numeric solver app but it is becoming hard to find the right...
Hello,
I've been trying to solve a system of equations but I'm getting a lot of troubles when I tried to insert inside a matrix a numeric variable. This is my code. I've tried both schemes, i.e., (1) introducing all elements of the matrix by hand (real numbers) and (2) introducing numeric...
I'm an EE/applied physics student (probably interested in an academic path involving signal processing, programming, computation, mathy stuff) with a hole in my upcoming schedule. The choice is basically between these two courses - numeric linear algebra and a course called "neural networks and...
dear friends
when I run my code in MATLAB , some expressions like:
"8763559185889905/20769187434139310514121985316880384"
appear in my result, so if I want MATLAB to give the numerical value of these sentences, what shouls I type?
for example in mathematica I know that I must write ...
A while back, I dug out a topic I worked on many years ago after taking a course in ordinary differential equations and I was left with an unanswered question, which I thought I would post here. While my question arose from studying numeric methods for approximating the solutions to ODEs, I feel...
I'm trying to write a python program that is able to numerically execute functions of the form:
y(t) = exp(Integrate[A(x),x]) within the bounds of 0 and t
I tried using quad from scipy.integrate but it seems not to be able to evaluate expressions of this form.
Any other suggestions on...
Hi,
I am searching for a smart way of calculating all numbers in a special matrix kind of game.
The game board consist of numbers between 1 and 9 in a 4x4 matrix.
Swiping over numbers will either add up (swiping left or right), subtract (swiping up or down) or do nothing (diagonal...
Hey,
So I am fairly new to Mathematica (and the physics forums too). I am having a problem with mathematica not calculating the numeric result to an very complex integral. My question is, how do I force it to evaluate the integral as a number? I'm assuming that the integral of a square root...
Hello,
I'm trying to (numerically) solve the equation y''*y=-0.5*y'^2 in Mathematica.
I know there's an analytic solution (and I know how to calculate it), but I want to modify this equation and thus need to verify that the numerical solution for the original equation is exact.
I'm using...
Hello,
EureKalc 3 is an environment for numeric and symbolic calculation, dedicated to solving problems in the field of physics and engineering... It's a free and opensource MathCad like application running on Mac OSX. I developed it primarily for solving physics problems at the level of...
Hello,
my problem is to numerically count "lambda" from that kind of equation:
(\lambda ^2 \check{A} + \lambda \check{B} + \check{C}) \vec{v}=0
which means that:
det(\lambda ^2 \check{A} + \lambda \check{B} + \check{C})=0
where A, B and C are n x n matrices, v is unknown vector and "lambda" is...
Homework Statement
I am posting for my son, who needs the full readout for a formula, more than what a small graphing calculator can do. Is there such a program for that? Am I in the right place to get an answer for this?
I would appreciate any help in this for my mathmatical skills are...
I am posting for my son, who needs the full readout for a formula, more than what a small graphing calculator can do. Is there such a program for that? Am I in the right place to get an answer for this?
I need the numeric result of "2 times the inverted sign of 1 minus the inverted sign of...
hey,
I'm trying to use MATLAB to simulate a simple RC low pass filter. I have an array of data that represents the signal I want to filter, and I have the s-domain representation of the filter circuit. I'm pretty new to this type of analysis, but I'm pretty sure I should be taking the fft...
Dear all,
Im trying to solve the following ode:
y'' = -0.12*y + 0.4/sqrt(y^2 + 5.76) , y=y(t) , t: [-50,50]
y(-50)=2.3 , y'(-50)=0
i changed it to a set of two first order ode using z=y'
and solve it with finite differences.
note that the right side...
That is to say, how does one go about it for a non-separable partial differential equation?
Let me preface by saying that I am not asking for an answer of perturbation theory, variational theory, mean-field theory, or some sort of self-consistent guess-and-check method (i.e., coupled...
I'm trying to fix a problem with a computer system and I'm not sure where to go next.
My office manager said that her numeric keypad wasn't working, though the keyboard was otherwise fine. I replaced her keyboard but to no effect: the new keyboard worked fine except for the numeric keypad...
Full-size keyboards take too much space when you're on a small desk. But a minimal keyboard that I got turned out to be cap, I ended up making more typos and was unable to type fast.
So does anyone know of a decent small-size keyboard? With standard-depth, decent keys like those of a normal...
hi,
i am in the final yr aerospace engg...i am trying to write a program on MATLAB to calculate the lift distribution over a wing using the numerical estimation based on the classic(prandtl) lifting line theory...however, due to my relatively limited exposure to MATLAB i am having trouble...
In a playground, two slides have different angles of incline theta1 and theta2 (theta2 > theta1). A child slides down the first at constant speed; on the second, his acceleration down the slide is a. Assume the coefficient of kinetic friction is the same for both slides. (a) Find a in terms of...
the purpose of this thread is to be a placeholder for discussion about the performance of Java in Numerical Computations.
Started as a discussion between CRGreathouse and me about weather or not Java can be used effectively in doing computations.
The plan we have:
Phase 1:
Solve a...
Using the suggested algorithm steps of the University Physics extra http://wps.aw.com/wps/media/objects/877/898586/topics/topic01.pdf" I want to make Maple (ver. 10) output values for coordinates, speeds and accelerations (as described in the linked PDF).
I've reached the 5th step, which is...
Hi,
It has been a long time, and I do not remember how to set up a probability calculation with the following variables -
take a lottery that draws 12 numbers, values 0-9 only, from a hopper that replaces the number after it is drawn, i.e. probability of each number appearing remains...
I couldn't find a forum section on numerical analysis, so I'm writing this here.
I'm on the lookout for simple matrix rotation/multiplication methods that can overcome the precision problems associated with poorly conditioned matrices.
In my case I'm trying to simulate the rotational...