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.

Filter by
Sorted by
Tagged with
0
votes
1answer
25 views

How should one evaluate this integral

How does one go about evaluating such an integral where E and V are constants? $\int\sqrt{E-Vx^8}dx$
0
votes
1answer
49 views

How can I calculate this integral?

I would like to calculate the integral in equation pol[x] if the quantity is positive or negative. ...
0
votes
1answer
31 views

step-by-step solution unavailable (( possible intermediate steps ))

When using the (( WolframAlpha["integrate 1/(2+Sqrt[1-x]+Sqrt[1+x])"])) function to find integration steps, this message appears to me what is the explanation and ...
1
vote
1answer
46 views

Limit at Infinity of Arbitrary Functions [closed]

Here I have the code that takes the limit of an expression Limit[(-I E^(I x) f1[y])/(g2^\[Prime]\[Prime])[y], x -> \[Infinity] ] and the returned output is <...
0
votes
0answers
52 views

How to get the step-by-step derivative of this?

I'm very newbie to Mathematica, and wanted to use it to help me solve some questions that I don't have the math backing to help me solve on paper. I would like to take this equation and have it be a ...
1
vote
0answers
29 views

Partial differentiation of a tensor

I'm currently struggling with an optimization problem. My objective is to find the rotation $X$ that minimize the $l_1$ norm of $Q_{ijk}$ defined as: $\tilde{Q}_{ijk} = \sum_{p,q,r = 1}^{N} X_{pi}Q_{...
0
votes
0answers
74 views

Problem in solving system of equations using “Solve”

I have an equation in its normalized form as: $\frac{v(x)}{V_{cc}}=C_1\cos qx+C_2\sin qx+1+ \frac{q^2}{1-q^2}.\frac{V_R} {V_{cc}}\sin (x+\phi)$ Where $$q=\frac{1}{\omega\sqrt{LC}}$$ With the ...
0
votes
0answers
19 views

Using NCAlgebra for Matrix Calculus

I have the following expression: $$ F = \| \mathbf{1} \text{diag}(G)^\top P S+(\mathbf{1} \text{diag}(G)^\top P S)^\top - 2 S^\top P^\top G P S - D \|_F^2 $$ where $S\in \mathbb{R}^{M\times N}$, $P\in ...
0
votes
2answers
153 views

How to understand that integrals with DiracDelta? [closed]

Mathematica up to version 12.1 performs ...
0
votes
0answers
22 views

Numerical solution of Triple Integration of a Region with Variable Bounds?

I am asked to calculate the mass of the region bounded above by the plane (2x + 3y - z = 2) and below by the triangle on the xy-plane with vertices ...
3
votes
3answers
252 views

Trouble with the derivative of the delta function

I am trying to evaluate the following integral with Mathematica: \begin{align} I = \int_{0}^{\infty} da \, \frac{e^{-\frac{a ^2}{4s^2}} }{a^2} \mbox{sinc}\left(\tfrac{w}{2} a \right) \delta' \...
0
votes
1answer
26 views

Find parameter value for which sharply-peaked constrained 3d-integral equals 1

I want to find the value (desirably to high-precision) of the parameter $i$ for which the constrained 3d integration ...
0
votes
0answers
34 views

I don't know how to type this problem to get a correct answer

I have the task of finding a partial fraction decomposition for (11x^3+109x^2+346x+350)/(x^4+14x^3+71x^2+154x+120). I was told to use the Apart command, but I receive an answer that is not correctly ...
0
votes
0answers
39 views

Integrals with conditional result

I am trying to get Mathematica to evaluate integrals such as the well-known Fourier orthogonality relations $\int_0^L \sin \frac{2 m \pi x}{L} \sin\frac{2 n \pi x}{L}\,\mathrm{d}x=\begin{cases}0& ...
2
votes
0answers
29 views

How to handle Units when Integrating?

I have some functions defined, which are to use units. Now another function is used to integrate over those, with the integration variable also quantified and the input to said function. I better just ...
0
votes
0answers
68 views

Why Mathematica can't return the answer for this integrand?

When I run Integrate command for an expression it doesn't return nothing, as you can see in the following screenshot. What's the reason? My input: ...
1
vote
1answer
43 views

Solving multiple integral with symbolical limits [closed]

I am trying to solve a double integral, though I am not sure how I could potentially handle the symbolic limits. I have attempted the following code: ...
-3
votes
1answer
67 views

How to solve a PDE problem by Fourier series method? [closed]

I made the following about Fourier series: ...
3
votes
2answers
79 views

Which method should I use for NIntegrate near a singularity?

I am looking at the following integral: $$I= \int_{-\infty}^\infty d\tau_3 \int_{-\infty}^\infty d\tau_4 \frac{1}{(1+\tau_3^2)^2} \Phi \left(\frac{1+\tau_4^2}{1+\tau_3^2},\frac{(\tau_3-\tau_4)^2}{1+\...
3
votes
3answers
271 views

Table of Derivatives looks better on Wolfram|Alpha

I would like to reproduce the table format on the right side of the included image (Wolfram|Alpha) in Mathematica (left side). How best to do this? I copied the Mathematica code from wolfram|...
1
vote
1answer
45 views

Why doesn't this integral return a symbolic result, but when evaluted in Plot returns the correct function?

I have the intgeral $$f(z_{0}) = \int_{z_{0}}^{\infty} |z| \exp(- a z^{2}) \, \mathrm{d}z$$ Which I compute with ...
2
votes
3answers
103 views

Incorrect limit in complex quantity

I have the following quantity $$ f = \frac{\exp(\sqrt{-k^2-i\epsilon}d)}{\sqrt{-k^2-i\epsilon}} $$ and form the limit as $\epsilon\to0$. Mathematica does not produce the correct result. Code: <...
5
votes
4answers
404 views

Derivative with prime for vector-valued function

Consider first the following vector-valued function of a real variable: s[t_] := {Sin[t], Cos[t]} Then this works as expected: ...
0
votes
1answer
40 views

Plot integral expression

Trying to plot in Mathematica with an integral as the iterator Plot[x, {Integrate[1/Sqrt[0.31*x + 0.68*x^4 + 0.01*x^2], x], 0, 10^7}] But get the error that it ...
1
vote
1answer
60 views

Does the order of integration in indefinite integral matters?

I have a function f of four variables. x1, x2, x11 and <...
4
votes
1answer
100 views

Apparent Bug in Calculation of Limit [closed]

Set k=x/Abs[x] Then: when $x$ is set to $0$, $k$ is indeterminate the limit of $k$ as $x\rightarrow 0$ from below is a well-defined $-1$ and the limit of $k$ ...
5
votes
2answers
109 views

Define an $n$-variable function with $n$ undefined?

I would like to define an $n$-variable function with $n$ undefined. For example, I want something like this: $$ f(x_1, \, \dots, \, x_n) = x_1 + \dots + x_n $$ And afterwards I want to take its ...
3
votes
1answer
123 views

Providing Mathematica with a “known” antiderivative

Suppose, I wanted to calculate some definite (or indefinite) integral in Mathematica: $$\int_a^bf(x)\mathrm{d}x$$ Normally, this can be done using ...
0
votes
1answer
51 views

How to get a function from a numerical integration?

I wold like to know how to get a function from a numerical integration. Here is an example: h[y_?NumericQ] := NIntegrate[y*Sin[Sin[x]], {x, 1, 2}] h[2] Then my ...
3
votes
4answers
209 views

Evaluate the defining Integral of the Bessel functions of the first kind

I am trying to evaluate the integrals $$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}(x\sin t - nt)} \mathrm{d}t $$ and $$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}x\sin t} \mathrm{d}t $$ ...
1
vote
0answers
53 views

How to reform a expression to improve numerical stability?

In engineering, we usually have to solve a function numerically, which has no symbolic computation ability and may using a low percision data type like fp32 or even ...
0
votes
0answers
53 views

Indefinite integration giving expression in ArcTanh

I am using Mathematica version 12 and facing a problem which was not present in the previous version. I am performing indefinite integration $(x/((1-x^2)\sqrt{1+a^2 x^2+b^2 x^4}))$ and getting the ...
1
vote
2answers
208 views

Making Integrate find an integral involving logarithms

I need to simplify the following integrand to make it work with Integrate, I've tried to make a substitution with u = x ln(x) ...
-1
votes
0answers
63 views
4
votes
1answer
129 views

DSolve: unable to solve the conditions

I have a second order differential equation with $2$ boundary conditions and want to use the following code to solve it: ...
1
vote
1answer
95 views

Finding derivatives

I'm not sure as to how to solve the following problem: This is what I've done but no luck: Solve[Dt[r Cos[θ]], Dt[x, θ]] Solve[Dt[r Sin[θ]], Dt[y, θ]] It gives ...
1
vote
0answers
94 views

normal derivative for Laplace equation

I am try to evaluate the Neumann boundary conditions for Laplace equation which define as: dy/dn, where n the external normal vector to the boundary, I have: ...
1
vote
0answers
35 views

Interpolation of a eigenvector of a matrix and it's derivative

I have a matrix with two variables and the condition is I can't evaluate it's Eigenvectors analytically. I want to interpolate its numerical eigenvectors and Most importantly get a derivative of them ...
8
votes
2answers
207 views

Unexpected 'switch' of partial derivatives when differentiating InterpolatingFunction

Bug introduced in 11.3 or earlier and persisting through 12.1.0 or later In short, there is a simple initial boundary-value problem for which NDSolveValue produces an InterpolatingFunction ...
2
votes
3answers
102 views

Specifying condition with NIntegrate

I have an integral $$ P_{\frac12 + \mathrm i\mu}(\eta) = \frac{\sqrt{2}}{\pi} \cosh(\pi\mu) \int_{0}^{\infty} \frac{\cos(\mu\tau)}{\sqrt{\cosh\tau + \eta}} \mathrm d\tau, \quad \eta \geq 1, \quad \mu ...
0
votes
0answers
32 views

Construction/good guess of a certain weight for a functional to satisfy given condition using numerics: [migrated]

Consider the following function : $$F(z) = \omega(z)\sin^2\left(\frac{π\Gamma(z)}{2z}\right)$$ Here, $\omega(z)$ is a weight we have to construct The following two condition should meet for $\...
0
votes
3answers
56 views

Taking derivative of solution of ParametricNDSolve

I solved the following differential equation $$\frac{d^2y}{dx^2}+(a^2 (5+4\tanh( x))+b^2)y=0$$ using ParametricNDSolve and I want to use $\frac{d y}{dx}$ in further calculation so I wrote the ...
2
votes
1answer
111 views

Did I or Mathematica make a mistake?

Here is the code, it doesn't make sense. Or did I make a mistake? ...
1
vote
0answers
25 views

Numerical Derivative ND doesn't work [closed]

I have entered the following code from the ND documentation, and get the wrong answer. ...
1
vote
0answers
25 views

FindRoot of Derivative

I want to write a function that takes the derivative of f wrt y1 and then find the root of this derivative when ...
4
votes
1answer
112 views

I am failing to verify an analytical integral with Mathematica

I am trying to use Mathematica to check an integral from a book, and cannot get it done. The book talks about a spherically symmetric mass distribution in $R^3$ of the form $\rho(r)=r^{-\gamma}, \...
1
vote
0answers
23 views

Output with cases. How to interprete the case `True'? [closed]

I am performing the following integration Assuming[{r > 0, s > 0, a == 2}, Integrate[s^(2 - a)/Abs[r - s] s^2, s]] and I get two cases for the output. ...
5
votes
1answer
185 views

Why do the Integrate and NIntegrate give different results?

Bug introduced in 12.0 or earlier and persisting through 12.0.0 or later I'm using Mathematica to calculate the following integral, but I don't know why the result of using ...
4
votes
2answers
77 views

A suitable strategy to estimate numerically a complex integral. How to use “MaxErrorIncreases”?

I am trying to numerically estimate a complex 3D integral. Here is its version considerably reduced for the purposes of the present discussion: ...
0
votes
0answers
48 views

Bessel Function Integration

I am trying (with no luck) to integrate this pdf that has a Bessel function within it... ...

1
2 3 4 5
61