what is superposition theorem?
109153
The previous answer is correct. There are many superposition theorems. But in mathematics and physics, the typical superposition theorem refers to solutions of a linear equation, say Lx=0. If there are two solutions x, and y so Lx=0 and Ly=0, then the superposition of solutions x and y is their linear combination, so L(x+y)=0 also. \n\nThere is a superposition theorem that exists in circuit design as well (see attached).
213762
Not directly!! You're not going to go work for some company, go to a meeting, and say, "according to the Remainder theroem ..."  However, because those theorems work, other, more advanced theorems work, in Calculus, complex variables, differential equations, advanced algebra, ect.  And those definetly have practical application in virtually all fields.
215087
false position is simply a way of estimating the zeroes of a function. I don't know about matlab, but you can find code for C/C++, java, and others at www.planetsourcecode.com\n\nHowever, if you're trying to solve a problem rather than just code false position, I would recomend secent method or newton's method as they provide a higher order of convergence
312542
Ancient. This is the "Law of Superposition. See\n \nhttp://en.wikipedia.org/wiki/Law_of_superposition
1008113
The Russian mathematician P. L. Chebyshev (1821- 1894) discovered that the fraction of observations falling between two distinct values, whose differences from the mean have the same absolute value, is related to the variance of the population. Chebyshev's Theorem gives a conservative estimate to the above percentage.\n\nFor any population or sample, at least (1 - (1 / k)2) of the observations in the data set fall within k standard deviations of the mean, where k ³ 1.\n\nUsing the concept of z scores, we can restate Chebyshev's Theorem to say that for any population or sample, the proportion of all observations, whose z score has an absolute value less than or equal to k, is no less than \n(1 - (1 / k2 )). For k = 1, this theorem states that the fraction of all observations having a z score between -1 and 1 is (1 - (1 / 1))2 = 0; of course, this is not a very helpful statement. But for k ³ 1, Chebyshev's Theorem provides a lower bound to the proportion of measurements that are within a certain number of standard deviations from the mean. This lower bound estimate can be very helpful when the distribution of a particular population is unknown or mathematically intractable.
1179245
This is an inevitable occurrence; there is actually a theorem by Paul Erdos (I forget who he was working with) that is applicable...  Erdos-Schekeres Theorem, perhaps.  It's the one where they proved that if you take a piece of paper, cover the bottom of a box with it, remove it, wad it up and throw it back into the box, at least one point will be exactly above the same place it was before...  It doesn't take a whole lot of imagination to see a definite isomorphism between the E-S theorem (or whichever one it is) and what you're talking about.\n\nANYHOW, what it boils down to, in your case, is that you will have an experience (whether in dream or in reality is not germain) and it will match a future one.  On the whole, you should expect that to happen once in a while--and if you have a wide enough breadth of experience, perhaps more often...\n\nI'm not sure that this addresses your question.  If it doesn't, here's a shorter answer: It is part of normal life; it isn't a problem; and we all share it to some degree or other.
108399
use binomial theorem, it can be applied to any power.if you don't know this theorem, i'll send it to you.
869774
That's kind of a tall order, mentioning every single definition and theorem related to vector spaces and subspaces.  I suggest you ask your professor for help on this one and read the textbook if you need a thorough explanation.\n\nBut anyway, the main idea is: suppose you have a subset W of a vector space V.  Then W is a subspace of V if W itself is a vector space when using the operations inherited from V.\n\nThen there's this theorem which basically says the same thing:\n\nLet V be a vector space and W a subset of V.  Then W is a vector subspace if and only if\n\n1) W is nonempty,\n2) for every x in W and scalar c, cw is in W, and\n3) for every x, y in W, x + y is also in W.\n\nExamples:\n\nA) Let P3 be the polynomials of degree at most 3.  Then P2 (which is the set of polynomials of degree at most 2) is a vector subspace of P3.\n\nB) Let P3 be as above, and let W = { f in P3 : f(7)=0 }.  Then W is a subspace of P3.\n\nC) Consider R^4 = { (x,y,z,w) : x,y,z,w in R }.  Let U = { (x,y,z,w) in R^4 : x + y = 0, z = w }.  Then U is a subspace of R^4.\n\nNonexamples:\n\nA) Consider R^2 = { (x,y) : x,y in R } and D = { (x,y) : x^2 + y^2 <= 1 }.  So R^2 is the real plane and D is the disk of radius 1 centered at the origin.  D is not a subspace of R^2 since it is not closed under addition or scalar multiplication.  For instance (0,1) is in D, but (0,1) + (0,1) = (0,2) is not.  Also, if |c| > 1, then c (0,1) is not in D as well.\n\nB) Consider P3 as above.  Then the subset S = { f in P3 : f(7) = 1 } is not a subspace.  I'll let you figure out why.\n\n\nYou can verify that all these are subspaces or not using the theorem above.  I hope this helps you out.  Cheers!
1041583
Godel's theorem is a rather technical result about axiom systems. It is widely misunderstood, so be careful of popular explanations of it.\n\nThe set-up is as follows:\n\nAn axiom system consists of a collection of symbols and a collection of axioms (which are strings of symbols) and rules of deduction (which are ways of taking strings of symbols and obtaining another string of symbols). For Godel's result, there should only be countably many symbols (usually there are only finitely many in practice) and it should be possible to decide whether a string is an axiom via a computer program. There are also rule for deciding which strings are 'well formed'.\n\nMost of mathematics can be done in the context of axiom systems of this sort. For example, Zormelo-Fraenkl set theory is of this type.\n\nGodel's result says that for any axiom system which is strong enough to model the natural numbers there is a well formed formula which can neither be proved nor disproved from the axiom system.\n\nEssentially, Godel's result shows that there is no reasonable axiom system for the natural numbers that can answer every question that arises in that system. For example, with set theory, it is known that the axiom of choice can neither be proved nor disproved from just the ZF axioms. If the axiom of choice is added, it is known that the continuum hypothesis can neither be proved nor disproved from the new axiom system.\n\nProbably, the best way to interpret Godel's result is to say that axiom systems are inherently limited in their ability to answer questions that arise in those systems. If they are strong enough, there will be questions that can't be answered in the system. That doesn't mean the questions are unanswerable because considerations outside the system (aesthetics, for example) may dictate an answer.
672272
I have taken the liberty of calling it the (a+b)^2=a^2+b^2+2ab ; (a+b+c)^2=a^2+b^2+c^2+2ab+2ac+... ; (a+b+c+d)^2=a^2+b^2+c^2+d^2+2a...\n+2cd etc... theorem. A bit long winded but exact.
16666
it called the Cayley-Hamilton Theorem, type it in google and its proved in many places;\n\n\nhttp://delta.cs.cinvestav.mx/~mcintosh/comun/summer99/mcintosh/node9.html  <---this one is good :)\n\nLet B = x*I - A, where I is the identity matrix of the same size as A.  \nLet C be the classical adjoint of B, so that BC = (det B)I. Recall \nf(x) = det(B), by definition. We wish to show that f(A) = 0. It \nsuffices to show that f(A)*e(k) = 0 for 1 <= k <= n, where e(k) is the \nk-th unit vector, so fix a value of k in that range.\n\nNow x = A implies that for all j,\n\n   x*e(j) = A*e(j),\n\n             n\n          = SUM A(i,j)*e(i),\n            i=1\n   \n      n                     n\n   x*SUM delta(i,j)*e(i) = SUM A(i,j)*e(i),\n     i=1                   i=1\n\n    n\n   SUM [x*delta(i,j)-A(i,j)]*e(i) = 0,\n   i=1\n\n    n\n   SUM B(i,j)*e(i) = 0,\n   i=1\n\n           n\n   C(j,k)*SUM B(i,j)*e(i) = 0,\n          i=1\n\n    n\n   SUM B(i,j)*C(j,k)*e(i) = 0.\n   i=1\n\nThen, summing over all j, reversing the order of summation, and using\nthe definition of the classical adjoint,\n\n    n   n\n   SUM SUM B(i,j)*C(j,k)*e(i) = 0,\n   j=1 i=1\n\n    n    n\n   SUM [SUM B(i,j)*C(j,k)]*e(i) = 0,\n   i=1  j=1\n\n    n\n   SUM [det(B)*delta(i,k)]*e(i) = 0,\n   i=1\n\n    n\n   SUM [f(x)*delta(i,k)]*e(i) = 0,\n   i=1\n\n    n\n   SUM [f(A)*delta(i,k)]*e(i) = 0,\n   i=1\n\n         n\n   f(A)*SUM [delta(i,k)]*e(i) = 0,\n        i=1\n\n   f(A)*e(k) = 0.\n\nThis proves that f(A) annihilates all the unit vectors, so must be\nthe zero matrix, and f(A) = 0.\n\n\nsecond one taken off the dr math website, but the link above might be easier to understand.
161194
Biot-Savart Law. Look it up.
958292
I think that the sum converge for all w except w=0. Here is an idea you could try to develop.\nLets define a new serie b(n) like this: b(1) = a(1) + a(2) + ... + a(p1) such that a(1), a(2), ... a(p) have all the same sign and a(p1 + 1) the opposite sign. \nThus b(2) = a(p1 + 1) + .... a(p2) such that a(p1 + 1), ... a(p2) have the same sign and a(p2 + 1) the opposite sign.\nThus b(3) = ....  etc   Note that this construction is possible only if w is different from 0.\nThen, by construction the b serie is an alternating one. It is easy to verify that |b(n)| is a serie which converges to zero. The problem would be ended if we had |b(n+1)|<|b(n)|, but that is not true. Nonetheless, you can make an integral approach to find a majoration of the |b(n)|. [something like a majoration of |integral of cos(wx)/x between pi*n/w and pi*(n+1)/w |]\nI leave you the detail of calculation... this approach should work ...
733754
Simple Harmonic Motion (SHM) is all around us. Indeed, I understand that superstring theory embraces the notion of vibration in harmony. In fact the resonance of the superstrings is what gives rise to the manifestation of matter. Newton's First Law would be better expressed as "Every object moves in a manner dictated by simple harmonic motion."
939642
Counterexample.  Let u(x), v(x) be members of {sin x, cos x}.  Both of those are solutions, but you do not get zero by adding one to the other, or by doubling one of them.
45454
Do you mean the Pythagorean theorem?\n\nIn any right triangle, the area of the square whose side is the hypotenuse (the side of the triangle opposite the right angle) is equal to the sum of the areas of the squares of the other two sides.
379983
Fosters reactance theorem \nThe Foster Reactance Theorem states that the poles and zeros of a reactive impedance function determine the frequency characteristics of the impedance. The poles and \nzeroes must alternate.\n\n\n(try some other sources,this may not b fully reliable)