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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8
votes
0answers
101 views

Strange kernel segmentation fault in Integrate

Bug introduced in 8.0 or earlier and persisting through 10.4 Define tointegrate = D[V[y1[t], y2[t]], y2[t]] D[V[y1[t], y2[t]], {y1[t], 2}] and try to find its ...
15
votes
1answer
265 views

Integrate returns imaginary answer for smooth, real function

Bug introduced in 7 or earlier and persisting through 10.4 I'm trying to evaluate the integral: $$\int_0^{\infty} \frac{1}{4 b \sqrt{\pi} r} e^{-(b-r)^2}(e^{4 b r} - 1) \mathrm{d}r$$ with ...
5
votes
2answers
214 views

RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...
7
votes
3answers
364 views

Where did I go wrong with my implementation of the trapezoidal rule?

One method for doing quadrature, called the trapezoidal rule, improves accuracy by connecting the points on the curve corresponding to the points of subdivision with line segments, forming trapezoidal ...
2
votes
0answers
90 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
3
votes
1answer
60 views

Evaluating function

I'm trying to evaluate this function, which is gradient of integral with variable limit of integration: $$ u(x,y,t)=\nabla(\int_{v(x,y)}^\infty \frac{e^{-b(t-\tau-c)^2}}{\sqrt{\tau^2-{v(x,y)}^2}} ...
1
vote
1answer
104 views

Asymptotics of sum of binomials

I would like to find the asymptotics of Sum[Binomial[n,i]*1/i^((n+1)/2),{i,1,n}] I saw Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}] but I ...
23
votes
2answers
541 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...
0
votes
1answer
40 views

Limits at infinity not neglecting added constants [closed]

This is such a simple question that I'm sure it must be answered somewhere, but I haven't had any luck finding an answer. I am trying to simplify expressions of the form: $$f(x) = ...
1
vote
1answer
74 views

How to calculate the derivative at a point of a non-integrable multivariable function?

I want to integrate this function with respect to θ1 and then take the derivative of that function with respect to n. Since the ...
3
votes
2answers
196 views

Use Meijer-G function to represent elementary functions

I want to represent these elementary functions: $x^{2}\sqrt{x}$, $\sin{4x}$, and $x\ln{x}$ as cases of MeijerG. What arguments should I give to ...
1
vote
1answer
70 views

The assumption in integration does not work?

I am new to mathematica. Here is the question. I try to do the following integration with the assumption that k1<0, k2<0 and k1,k2 are real number. However, the result includes \sqrt{k1}? ...
1
vote
1answer
182 views

Derivative of a symbolic matrix

I need to write an elasticity equations as: {{a*∂/∂x,b*∂/∂y},{c*∂/∂x,d*∂/∂y},{e*∂/∂y,f*∂/∂x}}.{{u},{v}} where a,b,...,f are ...
0
votes
1answer
55 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
78 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
2
votes
1answer
78 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
423 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
97 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
348 views
5
votes
5answers
163 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
101 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
77 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
64 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
150 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
177 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 ...
26
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 ...
1
vote
1answer
42 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
159 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
157 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
74 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
101 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
110 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
69 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
96 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
80 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
59 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
62 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
69 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
46 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
-3
votes
1answer
108 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
167 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
88 views

Euler-Maclaurin summation

I want to compute asymptotic approximations to partial sum of harmonic series in Mathematica, using Euler-Maclaurin summation formula. ...