Items tagged with equations

How do I find a point in every region defined by a system of linear equations? I have a system of eight linear equations of the form Ai.x+Bi.y=0 (i=1..8) Ai and Bi are numerical values. If I plot all eight equations on one graph then I get numerous bounded regions defined by three or more of the equations and numerous unbounded regions defined by two or more of the equations. (It is possible – though unlikely - for two of the solutions to be parallel or collinear. ) My aim is to find one point – any point does - within every bounded region and one in every unbounded region. It is easy to do this by inspection.
Hi guys, i wrote this fairly simply routine, to basically generate n equations, generate relations between those equations, then attempt to solve them by comparing coeffients, upon which i group together the information about the coefficients, for example i could have the equation ax+by=4x, so from that x=4,b=0 The equations in question are Dx=[x,Dy]+[Dx,y], when D is a map which maps x and y to A, where x and y span A's basis. so Dx and Dy would be a linear combination of x and y. This would be for the 2 dimensional case, for the n dimensional case x and y would extend to n variables.
I have a procedure that contains a loop, solving a set of simultaneous equations for each increment of a known variable (k) and two unknown variables (beta and N_bar). What I would like to do is populate a Maple spreadsheet with the solution to each iteration of the loop, creating three columns of data for each iteration (k, beta, and N_bar). The attached worksheet will create the spreadsheet and loop through a set of equations, but I don't know if there is a way to populate the spreadsheet in the format desired. Thank you for your suggestions and help.
The attached file is an example of a set of equations that define a gearbox composed of 4 planetary gearsets. The first 4 equations are the kinematic constraints. Where "r" indicates the size the sun or ring gear and "w" is the speed of the sun, ring, or carrier. The next 4 equations simply define new parameters (R_n) for the ratio between the size of the ring and sun gears. The last 5 equations define how these gears are connected. My question is how can I (or is it possible) to complete this worksheet in a generic way to solve for the speeds of any of the nodes in terms of some defined list of nodes and the parameterized gearbox sizes? In this example, there are 3 degrees of freedom so I might wish to solve for w[R3] (a dependent variable) in terms of w[R1], w[S2], w[S4] (independent variables), and all the parameters. The generic part comes from needing to be able to change the last 5 equations (including adding or subtracting equations) and perhaps the list of dependent and independent variables.
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Hi, I am trying to create a sheet to show the derivation of 2nd and 4th-order function derivatives as part of a 5-point finite difference scheme for a 1-D model (a continuous beam on an irregular foundation). I have isolated 2 simultaneous equations by using Taylor polynomials and would like to cast these in matrix form and then solve for each of the D-operators symbolically. Is there a simple way to do this or do I have to work with the ops manually? thanks for any help, Neil
Hi, I'm trying to complete two questions. One question is using maple 'to solve the following systems of equations': y=2x-5,y=2x^2+2x-21 I have entered the following code: solve({y=2*x-5,y=2*x^2+2*x-21},{x,y}); The output I get is this: {x = 2*RootOf(-2+_Z^2, label = _L14), y = 4*RootOf(-2+_Z^2, label = _L14)-5} I have no idea what this means apart from the fact that it's wrong but i'm not sure where I have gone wrong. The other question involves expanding the bracket (2x-3)^5 I've input: expand(2*x-3)^5; The output I get is: (2*x-3)^5 Surely this is wrong???!
Hi Folks, I have to believe this is an easy one, but it stumped me anyway. I'm trying to plot an ideal binary VLE curve for two components, and I have equations that describe both my x term and my y term as a function of temperature and pressure. Using the normal plot command, I can get x and y vs. T (if I specify pressure), but how do I get x vs. y (specifying pressure) and either plot T on a second Y axis or ignore it. Thanks in advance. I have my simple worksheet available... Fred Vie
I had a few questions that I need help with: 1) I'm trying to write a procedure to solve a system of equations. To be specific, we are given 2 n x n matrices, say A and B by the user. We have two generic vectors in R^n, write them as x = [x1, x2, ..., xn] and y = [y1, y2, .., yn]. I want to solve for each of the yi's in terms of x'js for the equation A.x = B.y - how would I go about doing this? 2) So I get some answer to 1), say something like y = [x1-x3, x1+x2-x4, x1+x2, x3+x4] (n=4 for ease) . How could I easily take the coefficient matrix of the transpose of this vector? So, my final matrix would look like:
i need to solve a set of linear equations of size 7000x7000 using 128 digits, the system is sparsed. which of the "options" in LinearAlgebra[LinearSolve) is the the most efficient? is there more efficient builtin procedure for such computations? thank's
Hi I have constructed a do loop to represent an epidemic described by 3 equations. I have plotted these using the initial conditions given. If i want to identify the values of S[k], I[k] and R[k] at k=60 how do i enter this? And how do i find out the exact point where the epidemic reaches its peak?
> p:=x->log[b](x); p := x -> log[b](x) > o:=x->b^x; x o := x -> b > fsolve( p(x) = o(x) , {x,b} ); Error, (in fsolve) number of equations, 1, does not match number of variables, 2 I need to find the location (x,y) where they touch each other, thanks for the help.
In trying to answer the second question in How to determine the order of an ODE? I have unsuccessfully tried to use select to filter out the appropiate parts of the differential equations. In these attempts I have hit upon a behaviour of select I do not understand: In my opinion each of the following two code lines (or at the very least the second line) should return the differential expression itself:
But they do not; each line returns diff(y(t)), where the variable t with respect to which is being differentiated is missing. Why? Is it just me having fundamentally misunderstood something?
Although this question might seem silly to Maple experts, I cannot help asking, since despite a long search through Maple Help and Maple Guides I was not able to come across the answer. What I mean is this: > eq1 := diff(y(t),t)-y(t)^2+y(t)*sin(t)-cos(t) = 0; > # here I want some command that would return the order of eq1, i.e. 1 > something(eq1); > eq2 := diff(y(t),`$`(t,2)) = y(t)*u(t) + diff(u(t),t); > something(eq2,y); # this should return 2 > something(eq2,u); # this should return 1 Besides, I would also need the same for recurrent (shift) equations, i.e.
Hi, I'm trying to solve a set of simultaneous equations, and the solutions I get are expressions of _Z. I'd be most grateful if anyone could explain what this means.
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