Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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5
votes
1answer
287 views

Calculate max value

Update Using ...
0
votes
0answers
43 views

Store results of inequality [duplicate]

I eveluated some values using Reduce commend and I store them in a Table ...
2
votes
1answer
117 views

Solving problems with the floor function

I've got the following problem: If I want to calculate the following equation, ...
2
votes
2answers
162 views

Plotting double inequality only for integer values

RegionPlot is plotting for all values. And using ListPlot I can only evaluate one inequality. How can I plot this type of ...
2
votes
3answers
274 views

Solve the system of equalities and inequalities

I have a system of expressions, in which each expression is an equality or inequality expression of the following form: Var = Var1 + Var2 Var $\odot$ number Var $\odot$ Var1 $\odot$ = $\leq | \geq | ...
1
vote
3answers
124 views

Discrete inequality plotting

I have an equation like this: $${20 \choose k}\cdot \sum_{i=0}^k {k \choose i}\cdot i \leq 1+f$$. I want to plot this inequality as the dependency between k and ...
0
votes
3answers
97 views

Reduce of a table [duplicate]

I have a table for example: t = Table[k,{k,5}] which returns {1,2,3,4,5} and for every element in this table I want to check ...
0
votes
0answers
95 views

Assigning the answer of Solve to a variable [duplicate]

If I enter Solve[(x-2)(x+2)==0,x] then the answer comes up as {{x -> 2}, {x -> -2}} I want to make two variables ...
3
votes
0answers
159 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
1
vote
1answer
131 views

Solve returns a wrong answer

I'm afraid the following is rather localized questions, but I don't know how to simplify and generalize it. I have the following two points (in the real plane): ...
3
votes
3answers
254 views

How can I calculate a combination of limit and sum?

How can I solve the above problem? I enter it as: Limit[Sum[Sqrt[1 + i^2/n^2]/n, {i, n}], n -> Infinity] but this is not working:
1
vote
1answer
130 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
0
votes
3answers
280 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 ...
0
votes
0answers
82 views

Reduce - Most efficient expression - Using FullSimplify

I am trying to solve complicated inequalities using Reduce, in order to determine whether certain mixed equilibria in game theory are stable. My first question ...
2
votes
2answers
189 views

Check if integer has even number of digits

I want to check if a number has an even or odd number of digits. 10 would be even because it has 2 digits 300 would be odd ...
10
votes
3answers
364 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
4
votes
5answers
382 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
2
votes
1answer
143 views

How can I exhibit the evaluation of formulas in a Mathcad-like way?

How can I create a function F that works like this: x = 2 f1 = x^2 + 3 f2=x+5 F[f1] x^2 + 3 = 2^2 + 3 = 7 ...
0
votes
1answer
173 views
1
vote
0answers
230 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
6
votes
1answer
525 views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
1
vote
0answers
204 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
0
votes
1answer
136 views

Small problem at equation solving

I have $2$ equations in $2$ parameters which involve integrations. The limits of the integrals can not be defined analytically. They also require equation solving and eventually I couldnt incorporate ...
2
votes
1answer
102 views

Plotting the solution of a 2nd order equation

I have got to solve a second order equation, where the coefficient depend on the parameter $k$: $$(A_k - \omega) (D_k- \omega) - B_kC_k = 0$$ so that also the solution $\omega=\omega(k)$ will depend ...
1
vote
1answer
189 views

Solving System of Inequalities Relatively

I have been trying to figure out how to solve a system of inequalities relatively. I don't care about values, I just want all possible ordering. An example system might be:$${b > r,\; p > r,\; c ...
0
votes
1answer
170 views

NDSolve + FindRoot for Bessel Zeros

I am trying to use a solution given by Michael E2 in this topic: ...
1
vote
2answers
133 views

Symbolic matrix equation

I am looking to a system of equations of the form $\pi =\pi P$, the one encountered in Markov chain theory. My $P$ variable is: ...
3
votes
2answers
373 views

How to solve a “tensor equation”?

I am trying to solve equations which looks like this: $$ T_{ab} - T_{bc} = a_1 T_{ab} + a_2 T_{ac} + a_3 T_{bc}, $$ where $T_{xy}$ are tensors. I want to get the $a_i$'s (in this simple example ...
1
vote
1answer
82 views

How do I get Nsolve to work with hyperbolic functions?

This is a rather simple numerical solution, but it simply doesn't work. Does anybody have a solution? NSolve[x - Sinh[x] - 1 == 0, x] NSolve::nsmet: This ...
-1
votes
3answers
799 views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
1
vote
1answer
205 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
1
vote
1answer
377 views

Solving a nonlinear system of recurrence equations

I am having two problems regarding Mathematica, and both of them are happening because it does not accept such inputs: ...
0
votes
1answer
72 views

Find the point that holds a given property

I have a normal distribution with mean 106, and a standard deviation of 8. I'm being asked to find the point that has the property that 25% of these values have this value or lower. What I've ...
0
votes
1answer
185 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
2
votes
1answer
222 views

FindRoot giving false roots with Bessel Functions

I have read in some places about the errors associated with FindRoot, but the closest thing I can find on this website seems to be due to the imaginary unit. I am dealing with what should be a ...
-2
votes
2answers
292 views

Solving a system of nonlinear equations? [closed]

I'm relatively new to using Mathematica so I'm not sure if this is really even possible, but I figured it may be worth a try. In my Physical Chemistry class today, we were learning about acid/base ...
6
votes
2answers
225 views

Using NSolve in the complex plane

I am trying to find numerical values for $\Im\ e^{\frac{1}{2} +i\ y} = \Im\ \zeta(\frac{1}{2} +i\ y)$ for a given range. I have tried: ...
12
votes
2answers
768 views

How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
-1
votes
1answer
127 views

Efficient Table Generation & NDSolve Error

I'm currently working on solving an SEIR model with data from the CDC. I've created a function to calculate the Square difference for the model and want to create a table of values for the 4 variable ...
1
vote
0answers
240 views

Solving asymptotic equations

Let's say I have several equations that have solutions given as a negative series $$y(t,x)=\sum_{n=-1}^\infty a_n(t) x^{-n}=a_{-1}x+a_0+a_1x^{-1}+\mathcal{O}(x^{-2})$$ My equations look like ...
1
vote
0answers
80 views

Simple Solve example fails: why? [duplicate]

Solve is an amazing tool, but sometimes it doesn't work in the way I expect it to. The particular instance that is confusing me right now is this: ...
0
votes
1answer
156 views

Plotting a function only non-zero for discrete values of argument

I have a function like: $$ f(E)= \Sigma_{n=0} \Sigma_{\ell=0} \, \delta\left(E+\frac{\ell+2n+2} {R\sec{\rho}}\right) w(n,\rho,\ell)\,, $$ i.e. the function is zero unless $$ ...
1
vote
1answer
198 views

Gram Schmidt inner and outer products

I know the Gram-Schmidt orthogonalization generates an orthonormal basis from an arbitrary basis. I need help with: Write a program that inputs a list $\{b_1,\dotsc,b_n\}$ of linearly independent ...
2
votes
1answer
160 views

Numerical errors/inaccuracies in ProductLog

Context In cosmology, a fairly accurate model to describe the gravitational potential, $\psi(r)$ of dark matter halos is given by $\psi( r)=\log(1+r)/r$. ...
0
votes
0answers
68 views

Parallelising the solving of polynomials

I'm working on finding solutions to a, not so very nice, system of equations. They are all polynomials of degree $4$ with $5$ parameters and all terms are of even order. I'll post the code on request, ...
1
vote
1answer
91 views

Solve failing and not clear why

I define the function: w[q_, n_, a_] := q/(4 Pi n r^2) (1 - Exp[-2 r/a] (2 (r/a)^2 + 2 (r/a) + 1)) I then want to solve: ...
5
votes
2answers
275 views

Intersection of two splines

I have a collection of sets of points, each set defining the segment of a (nice) curve on the unit sphere $S^2 \subset \mathbb{R}^3$. The points are computed numerically. I now want to compute the ...
2
votes
2answers
137 views

Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...
0
votes
1answer
62 views

Issues FindRootPlot command

I've had some fun playing around with FindRootPlot for a simple system of equations: ...