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. D

    Mathematica Piecewise even/odd mathematica

    A = Piecewise[{Table[ 8/Pi^2*m*(-1)^m/((2*n - 1)*((2*n - 1)^2 + m^2)), {n, 1, Nmax}, {m, 1, Mmax}],(odd)}, {0,(even)}] What can I do take make this piecewise assignment understand even and odd integer multiplies of n??
  2. J

    Mathematica Maple check of Mathematica code for Puiseux expansion

    Hi, I was wondering if anyone here with Maple could run the algcurve[puiseux] routine to compute the expansion of the algebraic function: f[z,w]=2 w^9+5 w^{10}+20 w^7 z+3 w^8 z+8 w^5 z^{10}+9 w^6 z^{10}+z^{14}+3 z^{15}+4 w^3 z^{15}+w^4 \left(10 z^5-z^6+2 z^7\right)+w^2 \left(3 z^{15}-20...
  3. M

    Mathematica Mathematica plotting with a slightly complicated relationship between variables

    Hi, So here's my latest problem as I get to grips with Mathematica. I will give a simpler version of the one I am actually doing. I started with a closed set of differential equations. Consider the following equations a'(t)=P*b(t) b'(t)=P^{2}*a(t) with known initial conditions and P is a...
  4. E

    Mathematica Mathematica 8.0 - solve two recursive relations

    Hi, all! I have trouble by using Mathemtica to solve the following problem as shown on the attachment. You see that the two recursive relations depend one another. I plan to write a "For" loop to evaluate E, instead of using Rsolve (a build-in function in Mathematica), however, I am very new...
  5. I

    Mathematica Mathematica 8.0 - Generating List of Powers of Matrices/Graphs

    Hello. I'm trying to consider a matrix A and looking at Ak and (Ak)TAk, where T is the usual transpose. This is no big deal. But I'd rather not look at them one at a time--I want to consider some powers k from 1 through as high as I want them. When I try Table[MatrixPower[A...
  6. D

    Mathematica Plotting Mathematica f[r_][x_]: Solving Derivatives & Plotting Lines

    f[r_][x_] := 1 + r*x + x^2; A = Table[ cps[r_] = x /. Quiet[Solve[f[r][x] == 0, x], Solve::ratnz], {r, -5, 5, 0.01}]; I want to then tell mathematica to check the derivative of f with each value from the table, plot the values, but make the lines where there derivative in less than 0...
  7. B

    Mathematica Mathematica: Solving Linear Complex Systems

    Good evening, I am currently trying to use Mathematica to find the symbolic solutions to a set of complex linear equations. I have never used Mathematica for such a task before and am finding it quite difficult. Let me state the problem...
  8. D

    Mathematica Expand cos^5t in Mathematica: Guide & Steps

    How can I tell Mathematica to expand cos^5 t? The command expand doesn't do it.
  9. S

    Mathematica Curve Fitting With Uncertainties

    I have a set of data points \{\{x_1, y_1\}, \{x_2, y_2\} ... \} each with an uncertainty \{\{dx_1, dy_1,\}, \{dx_2, dy_2\} ...\}. Is there any way of fitting a nonlinear model to the data that incorporates the uncertainties on both x and y? I know that you can use the Weights command to...
  10. B

    Mathematica Mathematica - Optimization Over an Elipse

    Hello, I need some assistance with Mathematica. I'm very new to the software, and am not very familiar with the programming language. I guess I'm a little bit lost as to where to go after defining my function. I'm not sure how to apply constraints, or really how to jump in and tackle this...
  11. D

    Difficult improper integral using mathematica

    Homework Statement evaluate $$\int_0^1\frac{Ln(x)}{1+x}\,dx$$ Homework Equations I know the way to solve most improper integrals; replacing 0 or the bound causing the issue with a variable and have the limit of the integral as the variable goes to infinity. My question is using...
  12. K

    Mathematica List of system of differiential equations in mathematica

    Hello, I have a system of DE involving two variables depending on the parameter t. To solve it I need to specify x(0),y(0),x'(0),y'(0). I know how to solve it with NDSolve, (analytical solution doesn't work), and I want to make a list of different solutions with different initial conditions. I...
  13. J

    Mathematica Mathematica: Delete constant term of f(z,w)

    Hi, I have a messy expression as a polynomial in z and w: a+bz+czw+dz^2w+...+kz^n w^m How can I delete the constant "a" term? Here's the function. The constant terms are dispersed throughout the expression. I know I can extract the coefficient list first in w then in z to actually get...
  14. T

    Mathematica Fitting Data Imported into Mathematica from Excel

    Can you fit data that is imported into Mathematica 8? I am just using the Import command, and I cannot figure out how to work with this data. I would really like to fit my curve. This is the code I used to import the data: Import[datafile.xlsx"]
  15. P

    Mathematica Mathematica: Help with NDSolve Error

    Mathematica: Help with NDSolve Error! Hello All, I am attempting to set up a model of an experiment I am running, but I keep getting the following error: "NDSolve::ibcinc: Warning: Boundary and initial conditions are inconsistent." However, I have checked all of my boundary...
  16. D

    Mathematica Fitting Curve to Data Points using Mathematica

    I am trying to use Mathematica to fit a curve to these data points ListPlot[{{2*Pi/(1 - 0^2/16), 5 (3 - Log[2])}, {2*Pi/(1 - .05^2/16), 10 (3 - Log[2])}, {2*Pi/(1 - .1^2/16), 15 (3 - Log[2])}, {2*Pi/(1 - .15^2/16), 20 (3 - Log[2])}, {2*Pi/(1 - .2^2/16), 25 (3 - Log[2])}...
  17. D

    Using Mathematica to plot PDEs

    You can find problems with downloadable notebooks now http://www.mathhelpboards.com/f49/engineering-analysis-notes-2882/. If one boundary is insulated and the other is subjected to and held at a temperature of unity, we wish to determine the solution for the transient heating of the slab. The...
  18. D

    Mathematica Heat and Laplace Mathematica Notebooks

    Mathematica notebooks that will numerical solve for eigenvalues, density plots, Fourier coefficients, and a few other options as well. There are 7 files for 1-D and 2-D. I would like to upload them but the forum says they are invalid file types. I believe the MHB community would greatly...
  19. P

    Mathematica Using an If loop in Mathematica

    Dear all, I have a list of pairs say Li={{a,x},{b,y},{c,z}...}. I want to eliminate from this list all pairs that have their second part i.e the x, y, z...>1 and I was thing of using an If loop. Can anyone tell me how please... Thanks...
  20. S

    Nested for and lists in mathematica

    Hello, I'm new using Mathematica and actually can't understand what's the problem in this code l = {} For[k = 1, k < 3, For[j = 1, j < 3, t1 = RandomInteger[{1, 10}]; t2 = RandomInteger[{1, 10}]; t = (t1 + t2)/2; j++; ] l = Append[l, t]; k++; ]...
  21. fluidistic

    Mathematica Evaluating an integral in Mathematica, analytical form

    So I've several huge integrals to solve by hands and I would like to check my result with Mathematica. However I don't really know how to do so. Here is one of the several integrals I must solve: \int \frac{1}{2\pi \sigma _x \sigma _y \sqrt{1-\rho ^2 }} \exp \{ \frac{-1}{2(1-\rho ^2)} \left (...
  22. P

    Mathematica returns non-numerical integrand while minimizing

    Homework Statement I need to minimize the function Etrial[a] trial[x_] := E^(-a*x^2) Etrial[a_] := NIntegrate[1/2*D[trial[x], x]^2 + x^4*trial[x]^2, {x, -\[Infinity], \[Infinity]}]/ NIntegrate[trial[x]^2, {x, -\[Infinity], \[Infinity]}] Homework Equations The Attempt at a...
  23. 7

    Mathematica Printing only integer values for some equation using MATHEMATICA.

    Hello every one, I need help on some mathematica run program. Suppose the following: 1) 2=<t=<1000 2) r=3+2Sqrt[2] 3) k=(r^t+r^(-t)-20)/4 4) n=2k+4 5) x=n/2-(r^t-r^(-t))/2Sqrt[2] I need to run the program For[t=2,t=<1000,t++ and only print if it found any...
  24. F

    Mathematica Solving systems of nonlinear ordinary equations in Mathematica.

    I'm trying to solve a system of five nonlinear equations (degree 7) in Mathematica: Solve[{q (a^2 + b^2 (3 q^2 + r^2 + 8 t^2)) ((e - q)^2 - R^2 - 4 T^2)^2 + q ((e - q)^2 + R^2 + 4 T^2) - 2 (e - q) (r R + 4 t T) == 0, R (a^2 + b^2 (3 R^2 + (e - q)^2 + 8 T^2)) ((e - q)^2 -...
  25. 7

    Mathematica Count from MatrixForm in mathematica

    Count from "MatrixForm" in mathematica! Hi every one, I really need help on this task.. how do I Count only the zeros elements from a MatrixForm in MATHEMATICA Suppose I have a Matrix 100X100 full with numbers and I just need to know how many zero is there on this matrix thanks
  26. B

    Mathematica Help Plotting Mathematica Functions f(x,y) & sin(exp(xy))

    The goal is to plot both the surface graph of the function and the tangent plane to the surface on one plot. There are two functions I believe I'm having issues with: f(x,y) = cos(x+y)exp(x^2 - y^2) @ point (0.5,-0.5) & f(x,y) = sin(exp(xy)) @ point (1,1) My code for the two are as...
  27. H

    How to plot a function with several constants using Wolfram Mathematica

    How can I plot this probability density function using Wolfram Mathematica Keeping the constants the same. ψ*ψ= A^2 (x^2)exp(-2a(mx^2/h)) ; where m,a,A,and h are constants and I want the graph in terms of them. I tried: Plot[A^2 *(x^2)*exp(-2a(mx^2/h)),{x,-1000,1000}]
  28. D

    Mathematica Construct Contour Plot in Mathematica for Quasi-Linear 1-D Wave Eq

    How can I construct a contour plot in Mathematica for Consider the quasi-linear 1-D wave equation $$ \frac{\partial\rho}{\partial t} + 2\rho\frac{\partial\rho}{\partial x} = 0 $$ with the piecewise constant initial conditions When $x_0 = \pm 1$ $$ \rho(x,0) = \begin{cases} 4, & x < -x_0\\ 3, &...
  29. D

    Mathematica Space time diagram Mathematica

    How can I make a space time diagram in Mathematica for: Consider the quasi-linear 1-D wave equation $$ \frac{\partial\rho}{\partial t} + 2\rho\frac{\partial\rho}{\partial x} = 0 $$ with the piecewise constant initial conditions $$ \rho(x,0) = \begin{cases} \rho_1, & x < -x_0\\ \rho_2, & -x_0 < x...
  30. D

    Mathematica Mathematica 3D plot color function options

    Hi, I have 3D plot used to represent the amount of light that hits a solar panel. Basically what I would like is a way to have say 10% of the data red, the next 10% of the data yellow etc. The 3D plot is at a peak in the centre and then goes to zero by some function based on data, so there...
  31. M

    Mathematica Strange plotting behaviour- Mathematica 8

    I'm confused by Mathematica's behaviour when plotting some functions I've constructed by interpolating functions. I have three graphs (attached). The first is a plot of the family of functions; they're negative, and decreasing to zero. I tried to do a LogLogPlot to look at their behaviour as...
  32. S

    Mathematica To generate and plot random real numbers in Mathematica within a specified time range

    Hi, I'm trying to write a short code in Mathematica that can generate random real numbers in - say 5 secs, and then plot this against any specified range I want. An additional complexity is that the function I'm generating the random numbers for is embedded in an integral. Here's an example...
  33. M

    Mathematica MaxRecursion(/WorkingPrecision?) Error in Mathematica 8

    I'm getting an error message that suggests my attempts to increase the variable MaxRecursion in NIntegrate aren't working. I define f[n_,b_]:=NIntegrate[q*BesselJ[0,q*b]*(-(2/(n (2+n) q^4))+(1-q^2)^(n/2) HeavisideTheta[1-q^2] ((2+n q^2)/(n (2+n)...
  34. F

    Mathematica Implicit function plot in Mathematica

    Hello everyone, I have an implicit equation: -155.034 x^4 ×sin(377 t) = 0.0524166 x^6 × cos^{1.414}(-377t)-(0.0581964+0.0442696 i) x ×cos^4(377 t)+7.09332 cos^5(377 t) I would like to create a plot of this function using Mathematica, but I am not very proficient with this software, and...
  35. M

    Mathematica ExtrapolatingOscillatory integration strategy in Mathematica

    "ExtrapolatingOscillatory" integration strategy in Mathematica A question I can't work out from the "advanced numerical integration" documentation for Mathematica. In http://reference.wolfram.com/mathematica/tutorial/NIntegrateIntegrationStrategies.html it claims that Mathematica recognises...
  36. N

    Mathematica Mathematica: Coupled differential equations

    Hi I am trying so solve a set of coupled ODE's. I have been able to get a solution from Mathematica using NDSolve, but when I change the coefficients an error appears: "NDSolve::mxst: Maximum number of 10000 steps reached at the point t == 0.0000748339914040257`. >>" I have tried...
  37. M

    Mathematica Mathematica 8: indeterminate result of NIntegrate

    Hi all, Yet another post concerning my battle with a family of messy integrals that are standing between me and a scientific publication. I'm defining a function by...
  38. V

    Mathematica Mathematica: Transistor Harmonic Derivations

    Hello, I am trying to derive the harmonic content of a signal passing through a transistor's transfer function. After a Taylor expansion in Mathematica 7, I have the expanded equation and the next step is to reduce everything to first order Sine/Cosine functions. In Mathematica, if I have a...
  39. M

    Mathematica NIntegrate w/ MaxErrorIncreases in Mathematica 8

    MaxErrorIncreases option for NIntegrate in Mathematica 8 Hi all, I'm trying to do the following integral numerically in Mathematica 8 (defining a function of the parameter b): \int^{\infty}_0 dq q J_0(b q) \left(\left(1-q^2\right)^{3/2} \theta \left(1-q^2\right) \left(\frac{3 q^2+2}{15...
  40. S

    How to solve the attached differential equations using Mathematica

    Hello everyone, I am making use of Mathematica to solve differential equations developed by Lagrange method, I have met some problems in solving the equations, I cannot obtain the correct result even though I have set "t" and "MaxSteps" both as "Infinity". I have run the program for 7...
  41. S

    NDSolve problems in Mathematica (differential equations)

    Hello everyone, I am making use of Mathematica to solve differential equations developed by Lagrange method, I have met some problems in solving the equations, I cannot obtain the correct result even though I have set "t" and "MaxSteps" both as "Infinity". I have run the program for 7...
  42. J

    Complex Arithmetic - Mathematica agrees with me, textbook says I'm wrong.

    Mathematica agrees with my second solution (not the first one though). The back of my textbook says: "\sqrt[4]{8}[\cos(\frac{5\pi}{8}) + i\sin(\frac{5\pi}{8})] and \sqrt[4]{8}[\cos(\frac{13\pi}{8}) + i\sin(\frac{13\pi}{8})]" Edit: The second z in my picture should be |z|, the modulus...
  43. M

    Mathematica Mathematica - using NIntegrate within NDSolve

    Hello, I am computing orbits of constant energy in a gravitational potential of a complicated planet (sth like a torus). I need to solve a system of 2nd order differential equations, that look something like \ddot x=-\frac{\partial \phi}{\partial x} and the same for y and z. The problem is...
  44. M

    Mathematica Evaluate limit relation between variables in Mathematica

    Hello. How do I evaluate, in Mathematica, limits like this: "X+Y" when X is much bigger than Y, i.e., when Y/X->0. The unswer should be X+Y->X. Regards.
  45. M

    Mathematica Problem in Eigensystem in Mathematica

    Hello. In Mathematica, I'm trying to find the eigenvalues and eigenvectors of a 10x10 matrices that is diagonalizable for sure. The matrix ix: {{0, 0, 0, 0, -2 t, -2 t, -2 t, -2 t, 0, 0}, {0, 0, 0, 0, -t, t, -t, t, 0, 0}, {0, 0, 2 U, 0, -t, t, -t, t, 0, 0}, {0, 0, 0, 2 U, -2 t, 2 t...
  46. N

    Mathematica Need Help Integrating w[x] with Mathematica

    Hi! I hope this is the right forum... I am having trouble with Mathematica: Maybe someone could help out of his experience ? I created w[x]:=RandomReal[NormalDistribution[0,1],x] I got it's plot. Now I want to integrate it: I wish to receive another graph, which is the plot of the...
  47. M

    Mathematica How to put a matrix in its block diagonal form (Mathematica)

    Hello. I got a 10x10 matrix that I know that has a block diagonal form. How can I put it in that form, using Mathematica? Regards, Marcus.
  48. Y

    Mathematica Mathematica help union/intersection of 3d plots

    I want to do the following: Say I have 4 RegionPlot3D plots, namely A1 A2 B1 and B2. Each of those four plots are region plots so they occupies some kind of region inside the same 3d space. First I want to find and display union of A1 and A2, call it A. Then find and display union of B1...
  49. M

    Mathematica Interrupting Mathematica in mid calculation

    Hi all, I've left Mathematica running on a set of calculations that I thought should take about 5 hours, and after 5 days I need to stop it. Is there any way I can actually extract useful information about what it's been doing? I know that I can enter a "subsession" via the panel that comes...
  50. A

    Mathematica Collecting denominators together with Mathematica

    Hi all, I have a very simple issue, but can't get round of it. I have a long sum of rational functions, which is in the form for example \frac{n_{1}}{d_{1}}+\frac{n_{2}}{d_{1}}+\frac{n_{3}}{d_{1}}+\frac{n_{4}}{d_{1}}+\frac{n_{5}}{d_{2}}+\frac{n_{6}}{d_{2}}+\frac{n_{7}}{d_{1}\cdot...
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