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.
5,384 questions
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Principal value of integrals of piecewise defined functions?
14.2 appears to have trouble with the Cauchy principal value of piecewise defined functions; Integrate is off while NIntegrate ...
- 375
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0
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FullSimplify not utilizing the linearity of integrals when an arbitrary function is involved [closed]
I am having the following issue: I am trying to verify that two expressions that involve an arbitrary function L satisfy a system of partial differential equations.
One of the two functions is defined ...
3
votes
2
answers
281
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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) - ...
- 95
1
vote
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answer
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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 ...
- 11
2
votes
1
answer
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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
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1
answer
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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
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2
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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
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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}
...
- 1,010
6
votes
3
answers
370
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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 ...
- 2,620
2
votes
1
answer
91
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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
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2
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204
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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
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0
answers
94
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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
315
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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
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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
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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 ...
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