Questions tagged [calculus-and-analysis]
Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
5,381 questions
3
votes
2
answers
226
views
Solving a coupled 2nd order differential equation numerically using NDSolve
I would like to solve the following system of differential equations numerically for two one-dimensional functions $R(x)$ and $\phi(x)$:
\begin{eqnarray}
c_1 \left(R''(x) - (\phi'(x))^2 R(x) \right) - ...
- 93
0
votes
1
answer
171
views
How does Mathematica define the indefinite integral $\int f(x) dx$? [closed]
How does Mathematica define the indefinite integral $\int f(x) dx$?
For example, if you input into Mathematica Integrate[Sin[x], x] it will return $-\cos(x)$ and ...
- 1
2
votes
1
answer
116
views
Integration of function involving ArcCsc with assumptions returns wrong answer
When I ask Mathematica (version 14.1) to do the following symbolic integration:
...
- 1,073
6
votes
1
answer
234
views
Is it valid for DSolve to return Indeterminate as a solution to a differential equation?
In V 14.3
Quit[]
ode=2*y[x]*D[y[x],{x,2}]==1+D[y[x],x]^2;
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
Gives
Is it valid for DSolve to return ...
- 156k
3
votes
2
answers
250
views
How to obtain this book solution for first order ode. Initial condition at infinity
This is problem 150, page 54, Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983.
...
- 156k
4
votes
1
answer
148
views
How to implement a 2x2 operator in Mathematica?
I am trying to write a Mathematica program to compute the following:
For a given Hermitian matrix $\rho$, the operator $L_\theta$ with respect to a parameter $\theta$ is defined as:
\begin{equation}
...
- 867
6
votes
3
answers
368
views
Pure functions from pure functions
I study the behavior of spatial curves and it is very convenient to write curvature and torsion as pure functions (PF).
It is often necessary to obtain their combinations, integrals and differentiates ...
- 2,590
2
votes
1
answer
90
views
Definition of inverse Laplace transform [duplicate]
Although there is a ready-made code for the inverse Laplace transform in Mathematica, I want to manually write the code to define the inverse Laplace transform so I can modify it.
This is my attempt:
<...
- 109
3
votes
2
answers
204
views
Converting hypergeometric function to Struve form
In my question on MathOverflow, I was looking for a closed form result of the following sum:
$$\sum _{k=0}^n \frac{(-1)^{n-k} x^{2 k} (2 (n-k)-1)\text{!!}}{(2 k)\text{!!}}.$$
Someone suggested me to ...
2
votes
0
answers
92
views
How to define the derivative of variables inside an expression so chain rule can be correctly applied to the full expression
I don't use Mathematica as much and only use it for some specific tasks from time to time (mostly simplifying expressions and calculating integrals and derivatives).
Lets say I have an large ...
5
votes
2
answers
314
views
NDSolve exceedingly slow
I the following ODE with parameters
\begin{align}
B_e\: \theta''(s)+2(s-1)\cos\theta(s)=S_e\: f\left(\theta(s)\right),
\end{align}
with $0\leq s\leq 1$ and
\begin{align}
\theta(0)=0\:\:\:\text{and}\:\:...
- 806
1
vote
1
answer
145
views
Why DSolve gives solution to $y'=0$ with IC $y(0)=t$ as $y=t$?
I was trying to see if I can trick DSolve for the ode $y'=0$ which has solution $y=c_1$, so all solutions are constant lines (horizontal lines).
But then I asked it ...
- 156k
1
vote
2
answers
163
views
Finding leading order behaviour of an integral
There is an integral whose leading order behaviour in terms of $p$ is what I want.
$$I(p) = \int_0^{D(p-1)} \log(1-Q^2e^{-x}) \, \mathrm dx,$$
where $D$ is really large and $p$ tends to 1.
For the ...
- 13
5
votes
1
answer
367
views
How to determine if ode is linear or not in Mathematica?
Mathematica does not have builtin function to determine if ode is linear or not.
Currently I use the code below, but it can give false negative. For example, the ode $\frac{1}{y'(x)} = x$ is linear ...
- 156k
2
votes
2
answers
205
views
Differential forms in integrals
I'm working on a big integral which I want to define in terms of a wedge of differential forms. I had been using D[x] as a substitute for dx, but I can see based on ...
- 31