Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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0
votes
1answer
57 views

Same integral gives different results with assumption

b = 1 k = 12560 r = 500 res = Integrate[Exp[I*k*x*Sin[o]]/(r + x*Sin[o]), {x, -b/2, b/2}] resab = Abs[res]^2 Plot[resab, {o, -Pi/20, Pi/20}, PlotRange -> Full] ...
0
votes
0answers
79 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
2
votes
1answer
79 views

How to plot linear term of a function expanded by Taylor seires in Mathematica?

I am quite new in Mathematica and I am trying to plot a linear term of a particular function in Mathematica. I have tried something like this: ...
1
vote
2answers
74 views

Problems in animating graphs and its extrema

I tested to animate 2D graph and its extrema for simple case using Mathematica. ...
7
votes
2answers
428 views

Need help with the Lagrange multiplier method

Well I am new to Mathematica and got really stuck solving this problem. In class, I was ask to use the Lagrange multiplier method to find the maximum and minimum value of $f(x,y) = x^2+y^2$ which ...
0
votes
2answers
99 views

Using Mathematica to find the areas described by polar curves

I am working on a project and I need to find the area of the surface inside the polar-curve $r=2\cos(\theta)$ and outside the polar-curve $r=1$. The graph is pretty straightforward: just two ...
4
votes
2answers
350 views
5
votes
5answers
167 views

How to find the derivative value at $(\pi,0)$ for this implicit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
0
votes
1answer
71 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
1
vote
0answers
41 views

How obtain the n-th derivative of a function with an implicit variable? [duplicate]

I'm interested in obtain the analytical n-th derivative with respect to the variable $x$ of an implicit function like $V(h(x))$ where $h(x)$ is an implicit equation and can not be obtained the ...
1
vote
0answers
102 views

Implicit differentiation dx/dt? [closed]

I am trying to find $\frac{\partial t}{ \partial y}$ as a function of $x$, $y$ and $\frac{\partial t}{\partial x}$ if both $x$ and $y$ depend on $t$ for the function ...
-9
votes
1answer
78 views

How to partially differentiate tu[t]u'[t] with respect to t [closed]

How can I partially differentiate tu[t]u'[t] with respect to t in Mathematica?
-2
votes
1answer
67 views

Wolfram Mathematica ONLINE does not give me the solution for the following integral [closed]

I have some problem in Mathematica and I could not evaluate the following integral. There is a closed-form solution for the following. Can someone please give me the result. ...
2
votes
2answers
152 views

Revolve a non one-to-one function about the y-axis

I am attempting to revolve $f(x)=-x(x-3)(x-2)^2$ about $x=0$. What I have come up with is that I need to redefine each interval between the relative extrema as a separate function, and then treat it ...
0
votes
1answer
44 views

Integrating Poisson distributions [closed]

I'm trying to do the following Integrate[Exp[-λ] λ^k/k!, {k, 0, ∞}] The answer should be 1 but Mathematica is unable to do it. Same story when I try the ...
4
votes
1answer
206 views

Computing the Caputo fractional derivative of a polynomial

In fractional calculus, the Caputo derivative of a monomial has the following form: $$\operatorname{\mathit D}_t^\alpha\,t^\beta = \frac{\Gamma(\beta+1)}{\Gamma(\beta-\alpha+1)}t^{\beta-\alpha}$$ I ...
28
votes
5answers
7k views

Multivariable Taylor expansion does not work as expected

The basic multivariable Taylor expansion formula around a point is as follows: $$ f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot \nabla)...
1
vote
1answer
45 views

Having trouble taking derivative of a function and assigning it to a new function [closed]

I am trying to take the derivative of a function and assign it to a different function name, but I am getting an error message (I think). Here is my Mathematica input: ...
3
votes
2answers
182 views

How to get the training error and the validation error using Classify function with SVM

I am using Classify[] function with Support vector machine model. I need to analyze the quality of results by analyzing the training error and the validation error ...
4
votes
2answers
166 views

Derivative of piecewise function

I tried to find $f'(0)$ of this function: $$f(x) = \begin{cases} x\cdot\sin(\frac{1}{x}) & \text{if $x\ne0$} \\ 0 & \text{if $x=0$} \end{cases}$$ This is what I tried in Mathematica: ...
0
votes
1answer
39 views

Efficient calculation of leading order behavior of rational function under a limit?

Considering a rational function, as for example myExpr=(x+3)(2+5x+6x^2)/(x(x-5)(x+20)) I would like to have a function that tells me the leading order behavior ...
5
votes
1answer
75 views

Behavior of D and Derivative when acting on functions with Rules as arguments

I was (pleasantly) surprised that when a Derivative is taken of a symbolic function for which the last few arguments are Rules, ...
5
votes
1answer
103 views

Somewhat Irreproducible Integrate Results

Backslide introduced in v10 and persisting through v10.3.1. In the course of considering question 102922, I encountered erratic results from a particular integration. It is illustrated as follows. ...
3
votes
1answer
114 views

Mathematica Can Find the Primitive Function But It Cannot Find the Closed Form for Corresponding Definite Integral

Consider the following function f = 1/2 (-3 + 4 u) Sqrt[-u (1 + u) (-1 - u + u^2)] where it is assumed that ...
1
vote
1answer
71 views

Product derivative on derivative [closed]

this is a silly question, probably. How to product derivative on derivative in Mathematica. I mean for example how to achieve this result: Just more explanation. I need this for solving task with ...
1
vote
0answers
99 views

Product of two Meijer's Function

I want to evaluate an integral $I_1$ defined in $Eq.(1)$ as \begin{align} I_1=\int_{0}^{\infty}\frac{x\exp(-\beta x)K_1(\alpha x)}{1+x}dx\tag{1} \end{align} Where $\alpha\geq0$, $\beta\geq0$, and $...
0
votes
1answer
81 views

How to evaluate the integral of exponentials

I want to evaluate the following integral wrt $\phi$ from 0 to $2 \pi$: ...
0
votes
1answer
60 views

Plotting a function based on complicated integral

I have this function : f[Lambda_] := K Integrate[x Exp[- x^2-Lambda x] HypergeometricU[-Lambda,1/2,(x+ Lambda/2+2)^2],{x,0,Infinity}]; where ...
0
votes
1answer
64 views

Improper Integral Difficulty [closed]

Trying to do the problem $$\int_0^{\infty}e^{-sx}\cosh(ax)\,dx.$$ where we have the assumption that $s>|a|$ and everything is a real number. We tried: ...
1
vote
1answer
73 views

NIntegrate::inumri: error [closed]

I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ...
1
vote
1answer
49 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
-3
votes
1answer
113 views

How to symbolically integrate 2D exponential function? [duplicate]

Is it possible to symbolically solve a 2D integral of the following form $$\int d \vec{r}e^{-\frac{\left| \vec{r} - \vec{r}' \right|^2}{2c}}e^{-i \vec{k} \cdot \vec{r}} $$ where $\vec{r} = (x,y)$ and $...
2
votes
1answer
229 views

Existence of an analytical form for integral

Can the following integration be performed with an analytical output? ...
2
votes
2answers
171 views

Symbolic vs numerical integration

This is related to a question that I asked before but didn't resolve quite well. I want to obtain the solution of the following expression analytically: ...
1
vote
0answers
30 views

Hidden assumption in Mathematica integration [duplicate]

If I do Integrate[Exp[I*omega*t],t], it gives me $\frac{1}{\omega} e^{i \omega t}$, as expected in most of the cases, except when $\omega$ is 0. Mathematica seems ...
3
votes
1answer
89 views

Euler-Maclaurin summation

I want to compute asymptotic approximations to partial sum of harmonic series in Mathematica, using Euler-Maclaurin summation formula. ...
2
votes
1answer
58 views

Why do Wolfram Alpha and Mathematica give different answers? [closed]

I've just got my hands on Wolfram Mathematica and tried to see if I can figure out how to use it by myself. I've plugged in an integral $\int \frac{dx}{(1-x^2)^{2/3}}$, knowing that the result is $\...
2
votes
1answer
111 views

Problem with Volume [closed]

A bug probably. This should give the volume of the unit sphere: vol = Volume[{1. r, th, ph}, {r, 0, 1}, {th, 0, Pi}, {ph, -Pi, Pi}, "Spherical"] but it gives: ...
17
votes
3answers
382 views

How to efficiently find moments of a multinormal distribution?

Update: Starting from V10.0 the build-in Moment is fast enough for practical use. I have a multinormal distribution with covariance matrix $\sigma$ and zero mean....
2
votes
2answers
141 views

Confirmation of a nice closed form

Can Mathematica 10 confirm a nice closed form for ...
1
vote
2answers
118 views

How to get the $0$ result for this limit?

Consider the following series: $$\sigma (\text{x$\_$})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the ...
4
votes
1answer
106 views

Finding Euler spiral convergence point for powers other than 2

I'm playing around with Euler spirals, using a variable power to see how the plot changes, $ \left\{\begin{matrix} x = \int_0^s \cos \left ( s^n \right ) ds \\ y = \int_0^s \sin \left ( s^n \right ) ...
1
vote
1answer
70 views

Wrong Limit[…] for inexact expressions

I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) parameter,...
9
votes
1answer
139 views

Non-rectilinear integration of InterpolatingFunction

Bug introduced in 7 or earlier and persisting through 10.3.1 [CASE:3487737] I have a 2-d array that I would like to resample into a different coordinate system and integrate along one of the new ...
2
votes
2answers
133 views

A simple question: Input problem

I have a simple problem. First I define the value of variables, then I calculate the expression as the following: Code 1: ...
15
votes
3answers
2k views

How to evaluate the $0/0$ type limit in Mathematica?

When I use Limit to evaluate the limit $$\begin{align}\lim_{k \to 0} \frac{ (k+2)(\alpha^2 - \sqrt{\alpha^4 + k}) + k}{\alpha^2 - \sqrt{\alpha^4 + k} + 2 k}\end{...
0
votes
0answers
35 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
4
votes
1answer
89 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
0
votes
0answers
16 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
1
vote
2answers
154 views

Is there a way to do a cyclic convolution analytically in Mathematica?

Let's say I want to convolve a Gaussian function Pulse[t_] = Exp[-(t - Mid)^2/(2 sig^2)]; with an exponential broadening function ...