What is Mathematica: Definition and 1000 Discussions

Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow symbolic computation, manipulating matrices, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica.

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  1. B

    Expanding Mathematica code from 2 dimensions

    I have this mathematica code to solve a variation of the 2 Dimensional Poisson's equation using the finite difference method. xo = .5; yo = .5; \[Sigma] = .05; q = 1; Gen[x_, y_] := -q*E^-((((x - xo)^2) + ((y - yo)^2))/(2*\[Sigma]^2)); GridNum = 300; Hstep = N[1/(GridNum + 1)]; GridPts...
  2. L

    Mathematica Integration of Numerical Solution Mathematica

    I am kind of new to mathematica, and have checked the documentation but can't seem to find an answer. I have solved 3 coupled differential equations using NDSolve. I wish to integrate the solutions over a range but I'm not sure how to do it - the documentation seems to deal only with...
  3. P

    Mathematica Mathematica®: performing a varying number of multiple integrals

    Hello everyone. In Mathematica® I want to numerically integrate a function of k variables (k varies) with respect to all of them. Does anyone of you know a way to do that? I tried the following simplified example. k = 5; int[x_] := x[[1]] + x[[2]] + x[[3]] + x[[4]] + x[[5]] ; (* My...
  4. K

    Mathematica Mathematica: working with Module for 2 variables.

    Dear all, Iam running a code which has only 2 main variables, i.e. m and n using Module. I have tried to run the code as attached but it is not working. Please help me to improve the code so that I would be able to get qmatrix[m,n]. Perhaps, is there any other better method to use or...
  5. Y

    Mathematica Solve matrix differential system and asymptotic solution in mathematica

    hi i want to solve equation d/dt(A)=B which A and B are n by n matrices. the matrices variable is t which is time. 1-how i can solve this equation? 2-how i can obtain asymptotic solution for time=infinite? i use some help of this topic but i get error in mathematica...
  6. W

    Mathematica Local max/min of Mathematica data sets.

    Is there a way in Mathematica to find the local maxima of a set of points? I have a fairly fine data set, and I can clearly see several peaks in it that I would like to know the numerical value of (as in, the highest point- I don't need a spline approximation or anything too fancy like that). I...
  7. N

    Mathematica Solve matrix differential system with mathématica

    hello , I need to solve a differential system with mathematica that has the form : B'=A*B knowing that B and A are (12,12) Matrix and with initial conditions B(0)=I Can you help me please Thanks
  8. N

    Mathematica Multi scale analysis using mathematica

    I am doing multi scale analysis while solving a particular nonlinear PDE. I am trying to check a solution I have for a particular set of boundary conditions and governing equation, to a given order. Is there a simple way to sort scales on Mathematica? For example, if our small parameter is...
  9. W

    Mathematica Strange postfix quotes in mathematica output

    Hello. I am using the Smooth.m mathematica package on a large set of paired data points. Occasionally, instead of getting a number in my output array, I end up with something like this: 1. (0.861515 + (58 "")/2379) In the output window, the quotes are not visible, but when I copypasta it...
  10. Z

    Mathematica Mathematica: ContourPlot3D without Frame.

    I don't find any option to remove the frame from a ContourPlot3D graphic in Mathematica. Can anybody help? Thank you.
  11. T

    Plotting Inequalities with Mathematica

    I have an equation and some inequality constraints, for example, f(x,y)=0 and g(x,y)>0 I want to see the region (values of x and y) in a graph where both the constraints are satisfied in Mathematica. Any help will be greatly appreciated. Thanks!
  12. B

    Mathematica Mathematica: Graph for a single vector instead of vector field?

    Hi guys, I would like to construct 2 vectors on a coordinate grid.(or a vector field for only one t) of the forces between 2 point particles on a certain moment t. Can I do that? When I try the VectorPlot function and insert all values instead of also inserting a variable it gives the error that...
  13. R

    Mathematica Hey guys,So I have been playing with LogLogPlot in Mathematica and

    Hey guys, So I have been playing with LogLogPlot in Mathematica and it seems to me that PlotRange->{a,b} does not work. I also tried Show[%,PlotRange->{a,b}] but somehow my axes got cut off. Anyone knows how to do it if I want to display a certain area of a log-log plot?
  14. K

    Mathematica Mathematica: Summation in the Do-Loop

    Dear all, Iam trying to get the right codes so that the summation could be done in the Do-Loop function using Mathematica. The problem is that I could not get the summation for sumU1 and sumV1 to start from 1 using my codes as attached (Summation2.nb). Please help me to improve the...
  15. A

    MATLAB Matlab and Mathematica can't do this integration

    Hello, While doing a research, I obtained the following PDF: f_{Z}(z)=\frac{1}{2\pi\sigma^{2}_{1}\sigma^{2}_{2}}e^{-\frac{1}{2} ( \frac{\mu^{2}_{1}}{\sigma^{2}_{1}} + \frac{\mu^{2}_{2}}{\sigma^{2}_{2}})}\int^{2\pi}_{0}ze^{-\frac{1}{2\sigma^{2}_{1}\sigma^{2}_{2}}\{...
  16. N

    Mathematica Plotting Log as part of an equation in mathematica

    Hello I'm trying to plot log as part of an equation in mathematica and it does not seem to be working for me. for example I'm using Plot y = 25x / log10 (x) - 50x I'm just experimenting with different numbers and formulas to see what happens to the log curve...
  17. M

    Mathematica Mathematica: Export sequence of MatrixPlots

    I've constructed a visualisation of the solution of an equation over time as a sequence of MatrixPlots and I'd like to export this as a movie for use in a presentation, but whatever file extension I try, I either get an error message (e.g. "The Export element \!\(\"GraphicsList\"\) contains...
  18. A

    Mathematica Mathematica help - simplification

    Hello, I'm trying to find out how I can let Mathematica know what is a variable and what is a parameter when asking it to simplify an expression. For example: if I have the following expression \[Beta] \[CapitalOmega] ((1 - \[Gamma] y) \[Xi] \[Sigma] + (x - \[Xi]) \[CapitalOmega]) + a...
  19. W

    Mathematica Adding many functions in mathematica

    Hello. Can someone tell me what I can do to the following code fragment: sigma = {2,4,6,8} mu = {1,3,5,7} gauss[x_, mu_, sigma_] = (1/(2*\[Pi] * sigma^2))* E^-((x - mu)^2/(2*sigma^2)) lorentz[x_, m_, gamma_] = 1/(\[Pi]*gamma*(1 + ((x - m)/gamma)^2)) spec1 = Apply[Plus, gauss[x, mu...
  20. K

    Mathematica Mathematica: how to avoid replacement from taking the previous outputs

    Hi all, Please help me with regard to my problems about replacement syntax. Iam looking for a method such that Mathematica won't use the previous output as an input for the subsequent cells or codes. Instead, I wish Mathematica express the replacement in terms of expressions for the...
  21. S

    Mathematica Calculate r^2*q Faster in Just 1 Click: Tips and Techniques

    hye everyone...i would like to ask question. i just wonder how to calculate question faster without solving one by one.for my equation given.i want to know if r increase by=1,2,3,4,5 and value of s are not change,how can i do without fill r by 1,2,3,4,5 one bye one.(q is fixed value).example...
  22. K

    Mathematica How to make a simplified general code for repetitive formulations in Mathematica

    Hi there, I have altogether 17 formulations or expressions which are repetitive and have link from each other. My question is that how to make these formulation or expressions in a simpler form. In another word, how to make the codes or syntax become shorter due to these repetitive...
  23. G

    Mathematica Curve fitting in Mathematica with FindMinimum function

    Hello, I attempt to fit experimental data using FindMinimum function with Levenberg-Marquardt (LM) method. I know that the problem can be solved with FindFit function (or other methods of finding minimum), but I really have to use FindMinimum function and LM method. Therefore, I would...
  24. D

    Mathematica Is Mathematica Worth the Cost? Pros and Cons

    I realized that Mathematica is extremely expensive, and I want to ask users whether it is worth the money (considering that there are other CAS such as Maxima)?
  25. K

    Mathematica How to make the positions of eigenvalues consistently in Mathematica

    Hi there, Iam just wondering that at different values of m and n, the position of eigenvalues are always varies accordingly. I mean, the outputs positions of eigenvalues are not consistent given by mathematica. Please see attached file for reference. My question is that how to fix this...
  26. J

    Mathematica Small quantities in mathematica

    "Small" quantities in mathematica Hi, I'm doing a calculation in which I have a small parameter \epsilon floating around, and I want to automatically remove terms of order \epsilon^2 and higher. Is this possible to do?
  27. N

    Mathematica Error explanation in the function NDSolve in mathematica 8

    Hello , I have tried to solve a system of differentiel equations with mathematica that is presented as follow X[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] , x7[t], x8[t], x9[t], x10[t], x11[t], x12[t]}; system = MapThread[#1 == #2 &, {X'[t], A.X[t]}]; where the matrix A is...
  28. P

    Mathematica Mathematica: take derivative in terms of original function

    Hello, Let's say we have f[x_,y_]:= whatever then we say expr1 = D[f[x,y],x] which is some complicated expression. How can we get the answer in terms of f[x,y]? That is, how can we get expr1 to look like: expr1 = f[x,y]*this term + pi*Sqrt[f[x,y]] + et cetera? Thanks Gurus
  29. M

    Mathematica Tables/Matrices in Mathematica

    Hi, I'm trying to make a table/matrix in mathematica to describe a system of differential equations that I have. At the moment, what I want is a table with the first column reading (A*v*(1-v)*(1-a)-w-w0)/e and the second column reading v-g*w-v0 and I want to be able to arbitrarily...
  30. N

    Mathematica Solving a differential system with mathematica 8

    I need to solve a differential system with mathematica that is presented like this : eqns = { X1'[t] == A[[1]][[1]] X1[t] + A[[1]][[2]] X2[t] + A[[1]][[3]] X3[t] + A[[1]][[4]] X4[t] + A[[1]][[5]] X5[t] + A[[1]][[6]] X6[t], X2'[t] == A[[2]][[1]] X1[t] + A[[2]][[2]]...
  31. Orion1

    Mathematica How Can You Extract Numerical Values from Output Box Data in Mathematica?

    \text{In}[1]:=\text{Solve}\left[\partial _{\theta } \text{Sin}[\theta ]==0,\theta \right] \text{Out}[1]:=\left\{\left\{\theta \to -\frac{\pi }{2}\right\},\left\{\theta \to \frac{\pi }{2}\right\}\right\} Is there a Mathematica source code command that can read a specific numerical value...
  32. K

    Mathematica Solving simultaneous equations with big matrices using Mathematica 7

    Hi all, Please help me to solve my problem in Mathematica that involves simultaneous equations with large matrices. The code is provided in the attached file, Exercise1.nb the errors say like this " General::unfl: Underflow occurred in computation. >> General::unfl: Underflow occurred...
  33. A

    Mathematica Rasterized density plot + countour plot in Mathematica (to solve EPS issues)

    Dear All, I am plotting a density and a contour plot of the same function in order to have a smooth shading in the background of the contour lines. I do this using "Show[DensityPlot[...], ContourPlot[..., ContourShading->None]", like the following example given by Mathematica help files...
  34. A

    Mathematica Help with Mathematica: Transforming Image Pixels to Natural Numbers

    Hi, I am trying to do a transformation on an image with the program Mathematica in the same way stated in the following scientific article : http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.0021v1.pdf I would like to associate each pixel of the picture with a pair of natural numbers. I used the...
  35. R

    Feasible to export and manipulate Mathematica animations in Powerpoint?

    Hi PhysicsForummers! I'm working to export some dynamic animations from Mathematica to Powerpoint but found that the only way is to export into a video file before inserting into Ppt. This makes the picture blur and i wonder is there any way i can export without dramatic loss in quality...
  36. C

    Mathematica Mathematica: Putting an expression in terms of a specific variable

    My problem is this: I have an algebraic expression, and I want to express it in terms of one variable divided by another. It's a fairly large expression, and I'd like to do it in mathematica before attempting it by hand. I've tried Simplify, FullSimplify and Solve, but none of these have done...
  37. A

    Mathematica How to make my own color scale (ColorData) on Mathematica

    Dear All, I started to use Mathematica to make some plots I usually did with gnuplot. I know it has some great color schemes, but I would like to be able to use the same I was using in gnuplot. The question is: how could I create a color scheme? In gnuplot I just used the following command set...
  38. R

    Mathematica How to plot 3D vector field in spherical coordinates with Mathematica

    I want to graph this vector field -^r/r^2 but I don't know how to do. Any help would be appreciated.
  39. M

    Mathematica Mathematica: Find Maximum Value of Interpolating Function

    Hi everyone, I'm pretty new to Mathematica, and I'm trying to find the maximum value of an interpolating function. I'm looking at Fitzhugh-Nagumo dynamics and below is what I have so far. My 'fitz1' gives me 4 variables each described as an Interpolating Function, and I would like to find...
  40. M

    Using Mathematica to solve 2nd order system of nonlinear ODE's

    Hello, I've started learning how to numerically integrate ODE's and I've run aground when i posed a 2nd order system for mathematica. Here is my initial code: NDSolve = [{x'[t] == -y[t] - x[t]^2, y'[t]==x[t], x[0]==1, y[0]==0.5},{x,y},{t,0,30}] and i get an error message saying the...
  41. B

    Mathematica Hessian optimization through Mathematica

    I know by default that Mathematica will use the BFGS method when you request "FindMinimum[Function]" but I am curious for a hint towards a pseudo-code for the following problem: I have a collection of functions, say F = {f1,f2,...,fN} and I want to transform them as linear combinations of one...
  42. V

    Please help me to work out this Mathematica pendulum problem Thanks

    Write a program in Mathematica that makes a plot of the period of a simple pendulum vs. its amplitude, as the amplitude (the initial angle from which the pendulum is released from rest) ranges from theta = 0 to theta = Pi/2. Use the built-in function NDSolve to solve the exact differential...
  43. ChristinaJ

    Mathematica Mathematica - Label plot ticks using strings

    All, I have a ListSurfacePlot3D graphic and wish to label the tick marks using strings. For example if I have X={x1,x2,x3} I would like to label each tick mark at that point with a string, i.e. x1="a", x2="b" etc. I would also like to know how to take a list of strings and distribute them...
  44. T

    Mathematica Mathematica eigensystem incorrect?

    I'm trying to compute the eigenvalues and eigenvectors of a 4x4 matrix using mathematica. The problem comes when I try to check the values using the commands: {vals, vecs} = Eigensystem[m] TrueQ[m.vecs[[1]] == vals[[1]] vecs[[1]]] Which should return "True"; instead it returns "False" I...
  45. A

    Mathematica Import and plot multiple data sets in Mathematica

    I have a dat file with multiple data sets, with the following structure: # t = 0.0 , ... -10.000 0.00001 1.000001 ... -9.000 0.00002 0.900001 ... ... 10.000 0.00005 1.000001 ... # t = 0.2 , ... -10.000 0.00301 1.000203 ... -9.000 0.02222 0.900043 ... ... 10.000 0.00025 1.000551...
  46. A

    Mathematica Mathematica repeating commands

    Hi, I have the following simple code in Mathematica: a=1; step=0.5; b=2; y=a^2-5 -4 What I need to do, is make Mathematica calculate the value of y each time for a different value of "a" ranging from the initial value of 1 to "b"(=2) in "step" increment (=0.5), and remember previous...
  47. Hepth

    Mathematica Mathematica : Log Handling/Simplification

    I'm having a simple problem with simplifying of logs. Given the input : FullSimplify[8 Log[m1] - 8 Log[m2] + 4, m1 > 0 && m2 > 0] FullSimplify[8 Log[m1] - 8 Log[m2], m1 > 0 && m2 > 0] I get out: 8 log(m1)-8 log(m2)+4 8 log(m1/m2) So for the second command it combines the logs...
  48. F

    How do I write and manipulate a vector equation in Mathematica?

    Homework Statement Alright I searched all over Mathematica on Google and I can't find the answer. How do you write out a vector equation and then do a bunch fancy stuff to it? (Like if it was a parametric surface or line, how do you graph it? Find the derivative? Integrate it?) For...
  49. A

    Mathematica Partial differential equations with mathematica

    hello, i just want to ask if mathematica 7 can solve nonlinear second order partial differential equations. i tried solving it with DSolve but it kept on giving me the question back as the output...please is there any way or syntax for solving it on mathematica 7?...thanks for any suggestions.
  50. F

    Mathematica Problem in derivative of big eqaution in mathematica

    i want to put this equation in mathematica to have derivative i always have error please tell me how to write it in mathematica to get the derivative also to solve the equation i attache the equation in word file
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