Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
6,594
questions
115
votes
2
answers
31k
views
What is the difference between Reduce and Solve?
Solve and Reduce both can be used for solving equations.
Just by working with them, I know there are some differences between ...
- 1,759
85
votes
9
answers
7k
views
Updating Wagon's FindAllCrossings2D[] function
Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
64
votes
8
answers
108k
views
Assign the results from a Solve to variable(s)
I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?
...
- 6,968
53
votes
4
answers
22k
views
How do I work with Root objects?
I want to solve the trigonometric equation :
$$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$
I tried
Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]
It returns the ...
- 4,513
53
votes
5
answers
29k
views
Find eigen energies of time-independent Schrödinger equation
I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation,
$-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$
where U(x) is some potential and Ei is the ...
- 27.6k
51
votes
9
answers
13k
views
About multi-root search in Mathematica for transcendental equations
I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range?
Perhaps ...
- 4,835
41
votes
5
answers
3k
views
Does Mathematica have a built-in tool that allows one to operate on both sides of an equation?
Geogebra has a very neat CAS view that allows one to solve an equation step by step in the following fashion:
$\quad \quad \quad \quad \quad \quad \quad \quad \quad $
You type an equation and can ...
- 5,411
40
votes
2
answers
18k
views
Marking points of intersection between two curves
I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each ...
- 734
40
votes
3
answers
6k
views
Nonlinear FEM Solver for Navier-Stokes equations in 2D
it's me again. I'm trying to obtain a numerical solution to Navier-Stokes equations in 2D in a non-rectangular region. So far, this guide was very helpful, but he is using finite differences, which is ...
- 2,396
38
votes
2
answers
4k
views
The Orbit and Perigee of the Flamsteed comet
Historical context
This year we have the 330-th anniversary of the Battle of Vienna - one of the great formative events of European history, it took place on September 12, 1683.
Kara Mustafa, Grand ...
- 57.6k
33
votes
4
answers
27k
views
Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
- 433
32
votes
6
answers
13k
views
Finding the intersection of a curve with an interpolation function
There are no issues trying to find the intersection points of two defined curves.
...
- 9,308
31
votes
11
answers
3k
views
Plotting the Star of Bethlehem
Christmas is around the corner! In preparation, consider the polynomial
f[x_,y_]:= 1/10 (4 - x^2 - 2 y^2)^2 + 1/2 (x^2 + y^2)
and define $r=(f_x,f_y)$ using the ...
- 1,005
30
votes
1
answer
385
views
Solve slower in versions 9 and 10
With some systems of equations, Solve is much slower in versions 9 and 10 than in earlier versions, apparently because it is doing more simplification of the ...
- 6,221
29
votes
4
answers
11k
views
How to find numerically all roots of a function in a given range?
It is common that I search numerically for all zeros (roots) of a function in a given range. I have written two simple minded functions that perform this task, and I know of similar functions on this ...
- 7,056