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.
5,379 questions
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2
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1
answer
102
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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:
...
6
votes
1
answer
209
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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 ...
3
votes
2
answers
247
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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.
...
4
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1
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142
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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,ドル the operator $L_\theta$ with respect to a parameter $\theta$ is defined as:
\begin{equation}
...
6
votes
3
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365
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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
votes
1
answer
90
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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:
<...
3
votes
2
answers
203
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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
92
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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
313
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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ドル\leq s\leq 1$ and
\begin{align}
\theta(0)=0\:\:\:\text{and}\:\:...
1
vote
1
answer
145
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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,ドル so all solutions are constant lines (horizontal lines).
But then I asked it ...
1
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2
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162
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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.
$$I(p) = \int_0^{D(p-1)} \log(1-Q^2e^{-x}) ,円 \mathrm dx,$$
where $D$ is really large and $p$ tends to 1.
For the ...
5
votes
1
answer
365
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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 ...
2
votes
2
answers
203
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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 ...
1
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1
answer
130
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Real assumption in Mathematica and double integral
Consider the following integral: $$\int_{-27}^{27}\left(9-x^{\frac{2}{3}}\right)dx$$
In WolframAlpha if I assume the real-valued root, the answer is $\frac{972}{5}$.
Now rewrite the above integral via ...
5
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1
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332
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DSolve returns only trivial solution for $t y' = 3y$
WRI CASE:5291279
The textbook says that the differential equation
\begin{align*}
t y' &= 3 y\\
y(0) &= 0
\end{align*}
has a solution $y= c_1 t^3$ for any $c_1$....