## Numerical Analysis and Simulation

Parent Category: Math and Arithmetic
The study of algorithms for problems related to continuous mathematics

## Subcategories

will get back to you after asking my professor
234=(1)128+(1)64+(1)32+(0)16+(1)8+(0)4+(1)2+(0)1: 111010102   0.365=(0).5 + (1).25 + (0).125 + (1).0625 + ...= 0.0101...2    1.11010100101110101110000101..._2×27 (see link)
Let L(t) be the instantaneous average rate of occurrences per unit time, at time t. So, for the ordinary Poisson distribution with parameter L, we just have L(t)=L for all t.    Let I be the integral of L(t) dt over a certain time interval [0,T], say.    Then, assuming that L(t) is...
The geometric distribution is: Pr(X=k)=(1-p)k-1p for k=1, 2 , 3 ... A geometric series is a+ ar+ ar2, ... or ar+ ar2, ... Now the sum of all probability values of k=Pr(X=1) + Pr(X=2) + Pr(X=3) ...=p + p2+p3 ... is a geometric series with a=1 and the value 1 subtracted from the...
In numerical analysis finding the roots of an equation requires taking an equation set to 0 and using iteration techniques to get a value for x that solves the equation. The best method to find roots of polynomials is the Newton-Raphson method, please look at the related question for how it works.
 ==Answer==  when a probability experiment is repeated a large number of times, the relative frequency probability of an outcome will approach its theoretical probability.
Error propagation in numerical analysis is just calculating the uncertainty or error of an approximation against the actual value it is trying to approximate. This error is usually shown as either an absolute error, which shows how far away the approximation is as a number value, or as a relative...
  Cos (aX)=1 + bX, give value of X in terms of a and b.   Practical Problem at site: An arc shape insert- plate of which R was 1250 and D was 625mm and thus S=2618 (chord length (L)=2165), has been damaged and flattered. And site staff gives feedback that it is now D=525 instead of 625...
The answer depends on what information you have. Given only one number, all that can be said is that the base is larger than the largest digit appearing in the number. Equations will not help if there are no "carries". For example, For example, 10 + 12=22 is true in any base greater than or...
This is gonna turn into a long answer, please bear with me. If you already know the algorithm's just skip to the examples. Iterative techniques for solving a linear system Ax=b, where A is a square matrix with non-zero diagonal entries, start of by first rearranging the system into a form x=Tx+c...
it is really impossible to get the model question papers but indiastudycentre has certain question papers for the B.Sc degrees, you can check there
A Taylor expansion is a way of representing a function in terms of  a sum of its derivatives. Please see the link.
The probability that 12 randomly selected people from a group of 12 men and 18 women will all be women is (18 in 30) times (17 in 29) times (16 in 28) times (15 in 27) times (14 in 26) times (13 in 25) times (12 in 24) times (11 in 23) times (10 in 22) times (9 in 21) times (8 in 20) times (7 in 19)...
Approximately 7.34847, rounded to 5dp. The square root of any number can be found through the Newton-Raphson and Secant fixed point iteration methods. See links below for more info. 7.3484692
Since the questioner didn't specify which shooting method was being used, I'll explain the linear shooting method. First off, the shooting method is used to solve boundary-value problems, or BVPs, where instead of being given 2 initial conditions to solve a problem, we only have the value of the...
When things expand, it can block certain things out like a machine
If the book is currently available as an online ebook in regards to a class, then one should be capable of downloading it from the virtual library in regards to the school requiring it. Otherwise, a teacher may hand it out on a flash drive at the beginning of class rather than as a download for...
Assuming a diameter of 40mm and assuming hexagonal closest packed, 625 balls would fit in a cubic foot. Boeing's website lists passenger volume for 747-400 as 31,285 plus cargo. 5536+835=37656 cubic feet An estimate would be the number of balls in a cubic foot times volume=23.5 million balls....
A poisson process is a non-deterministic process where events occur continuously and independently of each other. An example of a poisson process is the radioactive decay of radionuclides. A poisson distribution is a discrete probability distribution that represents the probability of events ...
The pythagorean theorem states that a2 + b2=c2.This means that in a right triangle, both legs squared will add up to the hypotenuse squared.To see if a triangle is a right side, add up the two legs squared and see if it equals the hypotenuse.
the Egyptians-----------------------------------------------------------------------------------To be a little more detailed, the base-10 number system that we use is based simply off of our fingers. We have 10 fingers, and so when civilization was developing the concept of counting, it was easiest...
Unfortunately I can't find any freely available information about the concept/theory/derivation of the Everett formula, I can find the equation fine but none of the theory related to it, and it's not covered in any of my text books that go well beyond my university course where I have also taken all...
 #include<stdio.h>     int main()     {     double matrix[10][10],a,b, temp[10];     int i, j, k, n;     printf("Enter the no of variables: ");     scanf("%d", &n);     printf("Enter the agumented...
There are 10 digits in our number system. The symbols 0,1,2,3,4,5,6,7,8,and 9 are the digits used to create numbers.
about the distance between the two lines below |..........|
The rate of convergance for the bisection method is the same as it is for every other iteration method, please see the related question for more info. The actual specific 'rate' depends entirely on what your iteration equation is and will vary from problem to problem. As for the order of...
The fact that this number has been on your mind for the past six years is very likely to be a symptom of obsessive compulsive disorder. Please seek professional counseling as soon as possible, for your sake and the sake of those around you (which could be me).
The sum of the series a + ar + ar 2 + ... is a/(1 - r) for |r| < 1
It is quite complicated, and starts before Fourier. Trigonometric  series arose in problems connected with astronomy in the 1750s, and  were tackled by Euler and others. In a different context, they  arose in connection with a vibrating string (e.g. a violin string)  and solutions of the wave...
If "Jack" is "Izbj" in a code, then a likely candidate for that code is a trivial "rotate left one position" code. "Mary", in the same code, would be "Lzqx".A=Z, B=A, C=B, etc.
There are several that are especially important:    integers: ..., -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1,  2, 3, 4, 5, ...  rational numbers: ie, numbers that can be written as quotients  of integers, such as 1/2, 7/8, etc.  irrational numbers: ie, numbers that cannot be written as ...
it works exactly the same as it does with linear equations, you don't need to do any differentiation or anything fancy with this method, just have to plug in values of x, so it shouldn't make a difference if the equation is linear or nonlinear.
The number system now in commonest use worldwide is positional.  Consider a number such as 924.37. The position of each  digit in the number indicates how significant it is. The digit 9  represents 100s, the 2 10s, the 4 1s, and so on.    The Roman number, or 'numeral' system, is non...
A harmonic frequency is a multiple of the fundamental. If the frequency is 60Hz, then the 2nd harmonic is (2 * 60) 120 Hz, the third is (3 * 60) 180 Hz, etc.
The probability mass function (pmf, you should know this) of the Poisson distribution is    p(x)=((e-λ)*λx)/(x!), where x=0, 1, ........ Then you take the expected value of exp(tx), you should always keep in mind to find the moment generating function (mgf) you must always do ...
Application in String theory in Quantum Mechanics
==Answer==  I don't know why there should be 4 laws (=axioms) specifically. In mathematics you can choose whatever system of axioms and laws and work your way with those. Even "logic" (propositional calculus) can be redefined in meaningful ways. the most commonly used system is Zermolo...
You are given a system of n or more simultaneous linear equations  involving n unknowns. Pick one of the unknowns, called the pivot  variable. Find an equation in which it appears, called the pivot  equation.
actually montecarlo is based on random selection (of cours randamness is expected to be random means to cover tjhe whole interval so the more the better )along the CDF(cumilative distribution function ) to extract the input that expected to keep the original distribution to some degree. in latin...
==The Point of Homeschooling==  Now that is a good question!   The "point of homeschooling" stems from your worldview. The concept of world view is central to the current firestorms surrounding education because it forms the basis for one's idea of a good life.   It is impossible to talk...
Convergence of telecommunications
Poisson distribution shows the probability of a given number of  events occurring in a fixed interval of time. Example; if average  of 5 cars are passing through in 1 minute. probability of 4 cars  passing can be calculated by using Poisson distribution.     Exponential distribution shows...
In Sri Lanka, there are less facilities than in England, but good behaviour and better rules ,where the children grow up with good manners..
 If you mean properties of numbers such as 'six is triangular'  and 'seven is prime' then I would offer number theory as an  answer.  If you mean that a certain subset of integers derived from the  integers by taking remainders modulo a prime form a field then I  would offer abstract algebra....
There are two digits in the binary number system. 0 and 1
First of all you need get the access to the figure properties . this is done by gca () command. and then you need to change the data_bounds .    a=gca() ;//get the current axes  a.data_bounds=[0,-1;10,1.5];
Yes, there is one. And your question is ... ?
In the USA more than 40 million people play some form of baseball.This takes into account all ages and gender. Mens slow pitchsoftball accounts for up to 18 milliion players participating insome league each year. These numbers make baseball/softball the #1played in US. compared to basketball at...
By x3 I assume that you mean x3. In which case f(x)=x3-2x+1, and f'(x)=3x2-2. Therefore our iteration formula is: xn+1=xn- (xn3-2xn+1)/(3xn2-2) Starting with x0=0 we get: x1=0.5 x2=0.6 x3=0.617391304 x4=0.618033095 x5=0.618033988 x6=0.618033988 Starting with x0=0.9 we get: x1=1.065116279 x2...
Hindu-Arabic numeral system
There is no last or final number. The real number system is  designed in such a way that the numbers go on indefinitely.
Irrational Numbers, Rational Numbers, Integers, Whole numbers, Natural numbers
==Answer==  Harmonics are multiples (thirds, fifths, etc) or divisions of frequencies. In radio, harmonics can be used carry additional signals on a single base frequency. It is the harmonics of an audio frequency that make a musical instrument unique. By damping a string at a half or third...
I can solve this question . But i think it is better to hold on . I want to register my finding with my name.
If X and Y are i.i.d Poisson variables with lambda1 and lambda2 then, P (X=x | X + Y=n) ~ Bin(n, p) where p=lambda1 / lambda1 + lambda2
It could be divergent eg 1+1+1+1+... Or, it could be oscillating eg 1-1+1-1+ ... So there is no definition for a sequence that is not convergent except non-convergent.
Multiplicative means pertaing or related to the mathematicalopration known as multiplication.
Two pennies stamped from the national mint, indistinguishable from each other.
 economists  statisticians  various kinds of scientists and engineers plus technicians and  technologists  people programming computer numerically controlled machine  tools  financial and compensation analysts, and similar  physical model makers  mathematical model builders    ...
There is no four digit number where the ones is twice the tens, the hundreds is five less than the ones, and the thousands is the sum of the tens and hundreds. int ones, tens, hundreds, thousands; for (thousands=1; thousands<10; thousands++) { /**/ for (hundreds=0; hundreds<10; hundreds++) ...
this was very easy to do.but you should know how to divide a number by 2. Eg:- 46/2=23 -023/2=11 -111/2=5 -15/2=2 -12/2=1 -01/2=0 -1Answer=101110
You would have to use the Regula Falsi Method formula to prove that  the answer is 1. There are two different types when it comes to the  formula; simple fast position and double false position.
On object falling under the force of gravity (9.8 m/s2) would, in a vacuum, fall a distance of 706 metres in 12 seconds. In a non-vacuum, i.e. air, the object would fall less distance in the same time due to drag.xt=0.5 (9.8) t2
Probably the movement on a swing can be approximated by assuming that the magnitude of each swing will be a certain percentage of the previous swing (because of lost energy).
The decimal representation of numbers is shorter. Binary number require approx 3.3 times as many digits.
The correct formula is: 1.5 x (N-1) +1 where N is the score on a 7 point scale.
Make a mark on the ground. Starting back from that mark walk toward  it, and then starting with it walk normally for ten paces. Make  another mark showing the place where the tenth pace occurred.  Measure the distance between the first and tenth pace, divide by  ten. Divide 25 by this distance...
Let's ignore 'triangles' with sides of length zero. I assume that  you mean triangles with sides of whole-number length; otherwise,  the possibilities are infinite.    The sides have to add to five. There are only two ways of doing  this:    1 + 1 + 3   1 + 2 + 2    Both of...
Simply because the Maclaurin series is defined to be a Taylor series where a=0.
The answer to this question depends on many factors: the skill of  the archer, the hardness of the first arrow's shaft, wind direction  and condition, and so on.
It takes more values of the integrand into consideration in forming  its estimate. Simpson's uses just three values in the domain of  integration. Romberg's uses as many as required to achieve the  desired accuracy. Please see the links.