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0
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1answer
32 views

Trying to calculate 5 simultanious equations in Mathematica

$\def\1{x_1}\def\2{x_2}\def\3{x_3}\def\f{f(\1,\2,\3)}\def\bs{\bigskip}\def\b{\begin{pmatrix}}\def\e{ \end{pmatrix}}\def\le{\left}\def\ri{\right}\def\g{g(\1,\2,\3)}\def\l{\lambda}\def\n{\nabla}\def\x{\...
1
vote
1answer
102 views

Why is a complex number plus infinity equal to infinity?

Why is $$2 + 3 i + \infty = \infty$$ according to Mathematica and Wolfram Alpha? Shouldn't it be: $$2 + 3 i + \infty = \infty + 3 i$$ ? After all: $$2 + 3 i + 10 = 12 + 3 i$$ and not: $$2 + 3 i ...
1
vote
0answers
27 views

Computer Code Friendly Books On Differential Equations?

When I need a differential equation for this or that application I generally search (by hand) through old paper and ink books written by mechanical or electronical (electrical) engineers. Sometimes my ...
3
votes
0answers
359 views

SAGE vs. Mathematica for Lie algebras / groups?

What math software is better for working with Lie algebras and Lie groups, SAGE or Mathematica?
0
votes
0answers
587 views

Complex exponential integral: Mathematica and MATLAB give unexpected results

I currently compare analytical vs. numerical evaluation of the complex exponential integral and find mismatches: The imaginary part differs by $\pm \pi$ and the real part has a large error when ...
2
votes
2answers
53 views

Help finding a summation using CAS

While approximating an integral by midpoint rule, I ended up with $$\iint_R f(x, y)\hspace{1mm}dA\approx \dfrac{1}{n^2}\sum_{i=0}^{n-1}\sum_{j=0}^{n-1} f\left[\dfrac{1}{2n}+\dfrac{i}{n},\hspace{3mm} \...
1
vote
1answer
89 views

Solution to second order differential equation

I'm reading a paper in which the authors solve the following equation: $\frac{d^{2}}{dz^{2}}\hat{p}$($\bf{q}$$,z)$-$q^{2}\hat{p}$($\bf{q}$$,z)$-$\frac{iq_{y}}{(2\pi)^{2}}\delta(z-z_{2})$=0 here $\bf{...
1
vote
1answer
92 views

Conversion of Hypergeometric functions from Maple to Mathematica

After a calculation I found in Maple an expression of the kind: $$f(x)=hypergeom\left(\left[\dfrac{a}{b},1\right],\left[c,d\right],h\right)$$ What is the equivalent notation in Mathematica which I ...
3
votes
4answers
95 views

indefinite integral computation $dx/(e^{-x}-x)$

Hi i'm trying to carry out the following indefinite integral: $$\int \frac{1}{e^{-q} - q} \, dq$$ mathematica is not helping me, and i think it is not solvable by substitution method. any idea on ...
1
vote
1answer
65 views

Reduced Residue System in Mathematica

How can I create the standard reduced residue system modulo $m$ in Mathematica for a given positive integer $m$? For example, if I input $10$, I would like it to give me the list $\{1,3,7,9\}$. Thanks....
2
votes
1answer
116 views

Fourier series of oscillation in form $\cos(2 \pi \frac{k}{T}+\phi)$

I would like to calculate the fourier coefficients of $\cos(2 \pi \frac{k}{T}+\phi)$ where $T \in \mathbb{N}$ is the period and is arbitrary but fixed, $k \in [1, N-1]$ is the number of oscillations ...
4
votes
7answers
600 views

Best Math Plotting Software for Electrical Engineering

I am an electrical engineering undergrad. I would like to learn a math plotting software which would be helpful in visualizing topics in advanced calculus (my immediate need). It would also be helpful ...
1
vote
0answers
53 views

Can nodes of Gaussian quadrature shift range?

I used my Python program to generate Gaussian's nodes and their weights. My python program could generate nodes as default in rage of (-1, 1). And my friend used Mathematica to generate them also but ...
6
votes
1answer
185 views

Odd Mathematica series result

I asked Mathematica to evaluate $$\sum_{i=1}^{\infty} \cos(i a)\cos(i b)$$ where $a$ and $b$ are unspecified real numbers, and it told me the answer was simply $-\frac{1}{2}$. This is clearly wrong, ...
4
votes
0answers
57 views

Algorithm for FindSequenceFunction

What algorithm might Mathematica be using to compute FindSequenceFunction? Does anybody know if there is any online material on this topic?
4
votes
4answers
251 views

A limit question (JEE $2014$)

The following is a JEE (A national level entrance test) question: Find the largest value of the non-negative integer ( a ) for which: $$ \displaystyle \lim_{x \to 1} \left( \dfrac{-ax + \sin(x-1) + ...
0
votes
2answers
194 views

Is this computation erroneous?

The solution to $\lim_{n\to\infty}\frac{n^{100}}{2^{n/100}}$ should be $\infty$ because $n^{100}$ grows much faster than $2^{n/100}$ But if you input ...
4
votes
1answer
111 views

Finding the period of the solution to $y'(x) = y(x) \cdot cos(x + y(x))$ with Fourier transform; how to interpret complex result?

A question elsewhere on this site asks about detecting the frequency of oscillations in a system defined by differential equations. The equation is $y'(x) = y(x) \cdot cos(x + y(x))$. The solution ...
1
vote
0answers
50 views

How to evaluate Bessel functions $K_{i x+\frac{9}{4}}(2\pi)+K_{i x-\frac{9}{4}}(2\pi)$ with $x>1.5*10^8$ in Mathematica 7?

I am trying to evaluate Bessel functions $K_{i x+\frac{9}{4}}(2\pi)+K_{i x-\frac{9}{4}}(2\pi)$ with $x>1.5*10^8$ in Mathematica 7. This function is the first Polya approximation to Riemann $\xi(s)$...
0
votes
1answer
224 views

Partition a set into n subsets with elements with sum equal to m

For example, given the set $a_n = \frac{n}{20}$ for $\,n \in \{1,\,2,\,\dots,\,19\}$, I would like to get all possible partitions of this set in 4 subsets such that the sum of their elements is always ...
1
vote
0answers
53 views

Plotting in Mathematica

I'm new to mathematica. How would I plot the following functions in the polar complex plane? $$ \phi={-k\over 2\pi r}\cos(\theta_0-\theta) $$ and $$ \psi={-k\over 2\pi r}\sin(\theta_0-\theta) $$ ...
1
vote
0answers
147 views

What is the Fourier series of $e^{\mu\cos\theta}$?

Motivation: I want to solve this convolution problem on the circle: find $f$, given $g$ and $$ g(\theta) = \int_{S^1} e^{\mu\cos(\theta-\phi)}g(\phi)\ d\phi. $$ To do this, I want to find the Fourier ...
0
votes
3answers
88 views

Plotting a region in $3D$ space

I would like to know if someone knows of a software where I can plot the following region $$ D = \{ (x,y,z) \in \mathbb{R}^3: 0 \leq x \leq 1 , \; x^2 \leq y \leq x, \; \; 0 \leq z \leq x \} $$ ...
1
vote
0answers
86 views

Roots and Weights

I use a Mathematica package to compute roots and weights (and other things) but the package gives me only the expression of the roots in $\omega$-basis (basis of fundamental weights) and in the $\...
4
votes
1answer
63 views

How does the base of a group determine the “sort” of the elements in the group

I'm trying to study groups in Mathematica, and I've asked a question on Mathematica.SE that perhaps only someone from Math.SE could answer. Related: How does ...
5
votes
3answers
126 views

Find min of $\frac{\left( \sum kx_k \right) \left( \sum x^2_k \right)}{\left( \sum x_k \right)^3}$

With $n \ge 2$ and $x_1,\ x_2,\ \dots,\ x_n > 0$. Find the minimum of: $$ M = \frac{(x_1 + 2 x_2 + ...+ nx_n)( x^2_1 + x^2_2 +...+x^2_n)} {\left( x_1 + x_2 +...+ x_n \right)^3}$$ For specific $n$...
1
vote
0answers
179 views

Which symbolic programming language for manipulation of nonlinear equations?

I have a set of (multivariate, nonlinear) equations which I want wo modify according to my own rules, i.e. not in a standard ways such as matlab's simplify function. I am looking for a mathematical ...
1
vote
1answer
51 views

Mathematica DSolve input

I'm trying to solve this differetial eqation. dy/dx=3y^(2/3). This is my input: DSolve[{y'[x] = 3 y[x]^(2/3), y[2] = 0}, y[x], x] This is my output: DSolve::deqn: "Equation or list of equations ...
0
votes
2answers
61 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
0
votes
1answer
75 views

Mathematica Homework Question [closed]

I had a mathematica assignment the other day that was fairly simple. I thought I did it correctly, but I guess not. Question: Write a single Mathematica Command which will display (plot) both $y = x\...
1
vote
1answer
210 views

Good software package to help Maths learning

I'm a mature student enrolling at a Maths degree course soon at the university. I'd like to be able to use some software package to help me visualize equations, graphs, play around with variables with ...
0
votes
1answer
312 views

How to Expand $f(x) = \sqrt{x^2-y^2}$ about $x=y$

How would one go about expanding $f(x) = \sqrt{x^2-y^2}$ about $x=y$? You can't do a Taylor series, because $f'(x=y)$ diverges. I tried a few other things, but to no avail. Interestingly enough, ...
2
votes
1answer
427 views

Can wolfram alpha compute symbolic vector derivatives

Can Wolfram alpha be used to find out say $$\nabla_x\left(\|y-Ax\|_2\right)$$ What command do I use? I tried some obvious ways, and googled a bit, but didn't find anything.
0
votes
1answer
46 views

fourier transforms with Woflram Alpha

I'm studying Fourier transform at the moment and I've noticed some weird irregularities between my textbook and Wolfram Alpha's answers. Say I ask Wolfram the following: fourier transform delta(...
3
votes
1answer
134 views

Fourier series for $e^x$

I'm trying to teach myself partial differential equations from Strauss' book. I have run into a very bizarre problem - I cannot figure out what is the Fourier series of $e^x$! And not even Google has ...
0
votes
1answer
206 views

Solving an ODE with Mathematica, using Lagrangian mechanics

Question: The velocity of light above a hot surface decreases with the height from that surface. The velocity is given by $v=v_0(\frac{1-y}{\alpha})$ where $y$ is the vertical distance above the ...
0
votes
1answer
109 views

Using Mathematica to know the number primes that are contained in a given interval

So I want to know basically how to determine how many prime numbers (integers that can only be divided by 1 and themselves) are contained in a given interval. Thank you.
0
votes
1answer
176 views

Solving a nonlinear system of differential equations in MATLAB or Mathematica

Is it possible to solve the system $$\dot{W}=A\left(k-\frac{M}{W}\right)$$ $$\dot{M}=B\left(k-\frac{M}{W}\right)$$ with initial conditions $$W(0)=w_0$$ $$M(0)=m_0$$ in MATLAB or Mathematica? If so, ...
23
votes
8answers
4k views

LaTeX/TeX Vs. Mathematica for Typesetting [closed]

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regard to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that I ...
1
vote
3answers
8k views

How to plot a phase portrait for this system of differential equations?

I beg your help.. I'd like the phase portrait for this system. I don't know how to use Mathematica/Matlab ... :( If anyone can make this portrait and post a print screen here, I would thank you ...
1
vote
1answer
41 views

inequality, complex number [closed]

let $b>0$, $y:[0,b]\rightarrow\mathbb{C}$ and $y(0)=0$, where $\mathbb{C}$ denotes the space of complex numbers. Is the following inequality true or not? $$|y(x)|\le \max_{\tau\in[0,b]} |y'(\tau)| ...
3
votes
2answers
225 views

Graphing a function f(x,y) on a restricted set of values for (x,y)

I'm having a hard time with this certain problem. Suppose that $S=\{(x,y): x^2 + y^2\leq 4\}$ and define $f:S\rightarrow\mathbb{R}$ as $f(x,y)=-x-2y-2y^2+cos(x\pi /4)$. How can we produce a (3d) ...
3
votes
1answer
75 views

Why these integrals are evaluated differently? $\cos(x)/(a-b\cos(x))$

In attempt to solve electrostatics problem I came up to this integral that I am trying to integrate: $$\int_0^{2\pi}\frac{\cos(x)}{a-b\cos(x)} \, dx$$ where $a>b$ and both are real numbers. For ...
0
votes
2answers
80 views

How plot $f(x,y) = \frac{x}{1-y}$ with $x^2+y^2<1$?

How do you plot $$f(x,y) = \frac{x}{1-y} \text{with}~ x^2+y^2<1$$ in Mathematica or Maple?
1
vote
1answer
248 views

Mismatching Results - Keno and Probability

In Keno, a player picks from 1 to 70 (at least in this version), 20 of these numbers are drawn, and the payouts are based on the number of matches. What I have tried to do is to check that the Swedish ...
1
vote
2answers
196 views

Newton's Method in Mathematica? [closed]

Which code should I use it for? FindRoot? or Plot? I am actually new to this program... and I would appreciate if you could tell how to mention the precision. Thanks! Solve the nonlinear ...
1
vote
2answers
96 views

Fraction Cross Multiply

Students first learning about fractions are often taught to "cross-multiply" when dealing with fraction with non-like denominators, however, in Mathematica, with the function ...
4
votes
0answers
192 views

How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?

How would you integrate $\left(1 + \ln\left(x\right)\right)\, \sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$ using the Risch algorithm? I want to know this because Mathematica is using the Risch ...
2
votes
2answers
736 views

How to fit a sinusoidal function through 2 points with known slopes?

I can define my sinusoidal function as $y(x) = A\sin(B x+c) + D$ or as $y(x) = A \sin(B x) + C \cos(B x) + D$ Now, I have two points with known slopes that I must fit this sine wave to, thus my ...
0
votes
2answers
315 views

Concerning the general solutions to linear ODEs Y'=AY when A has multiple eigenvalues

Given linear ODES Y'=AY, where Y is a column vector, A is a 6*6 square matrix. Clearly A has 6 eigenvalues, namely r1, r2, r3, r4, r5, r6. Herein we assume r5=r2, r6=r3.That is, r2 and r3 are two ...