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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2
votes
3answers
551 views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
5
votes
1answer
73 views
7
votes
1answer
73 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
1
vote
1answer
48 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
0
votes
3answers
254 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
0
votes
0answers
34 views

How to calculate the analytical result of this double integral?

I'm trying to solve this double integral: $I(a,b)=\displaystyle{\int_{-1}^{1}dy\int_1^{\infty } \dfrac{y\left(x^2-1\right) e^{-ax} }{b-\frac{\sqrt{x^2-1}}{x}y} \, dx} \,\, ...
1
vote
1answer
158 views

Mathematica policy for correctness of results [on hold]

Does Mathematica provide any kind of warranty that their calculations are correct? Say I'm running a billion dollar company, and I relied on Mathematica to do calculations, like aerodynamics or car ...
-3
votes
0answers
51 views

instantaneous frequency based on wavelets [closed]

how can we find instantaneous frequency from the phase/maximum modulus of continuous wavelet transform using complex morlet wavelet or mexican hat wavelet?how can we plot wavelet ridges?
0
votes
0answers
39 views

NIntegrate with a parameter in integrand and upper limit [closed]

I want to evaluate NIntegrate[f(x, p), {x, 0, xmax}], where xmax = FindRoot[g(t, p), {t, 1}], and plot the result as a function ...
0
votes
0answers
29 views

Getting NIntegrate::inumr: from NIntegrate [closed]

I tried to numerically calculate the following integral: ...
18
votes
2answers
268 views

Negative probability?

I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
0
votes
1answer
63 views

A problem with “RiccatiSolve::ncsol: Cannot compute a stabilizing solution to the matrix equation ”

I have a SSM ( State Space Model ) and I want to calculate its optimum gains unisng LQOutputRegulatorGains[] command. When I run the code, it solves the equations ...
0
votes
0answers
82 views

Complex Convolution

I am attempting to integrate a convolution variable using the following code. However, the program is taking too long to complete the integration. Does anybody have any coding tips that may make ...
0
votes
1answer
61 views

Integral over geometric region [duplicate]

I'd like to calculate this integral $$ \int_E y\ dydz $$ where $E = \{ (x,y,z) \in R^3 : z^2+6 < y^2 < 5z \}$ By hand i've got $\frac{1}{12}$ but i'm not sure, and i'd like to verify this ...
2
votes
2answers
93 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
0
votes
1answer
77 views

Defining a function that differentiates another function with rule replacement

This question is related to the question I posted here. In that question, I thought I have simplified my original problem into an equivalent concise version, but I found that it is not. So I decided ...
-1
votes
3answers
125 views

Computing integral over explicit region [closed]

I need to integrate $f(x,y)=y^2-2x^2y+6x^3-3xy+2y-6x$ over $\{y\geq 2x^2-2, y\leq 3x\}$ Im using Boole in the following way; ...
-1
votes
1answer
106 views

Finding the maximum of a gradient vector

Im trying to find the maximum of my gradient vector G[x,y], I've tried several options including FindMaximumValue, FindMaximum etc. but i couldn't find it. The full function is shown below, any help ...
3
votes
1answer
118 views

Gateaux (directional) derivatives and higher order differentials of a functional

I would like to calculate the Gateaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
1
vote
1answer
44 views

Plotting a multivariable function [closed]

m[x_, y_] := 0.9*Exp[-((x - 1)^2 + (y - 1)^2)] + 0.5 Exp[-(3^2 ((x - 2.5)^2 + (y - 1.5)^2))] I'm trying to create a 3d plot for the function above. I tried ...
1
vote
1answer
84 views

Generate conditions seems to not work [closed]

I am trying to compute the following integral Integrate[E^(I*k*Omega*t), {t,0,T}, GenerateConditions->True] for which Mathematica returns ...
0
votes
1answer
47 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
0
votes
1answer
47 views

Forcing an integral to be solved in separate terms

Using Mathematica I want to solve an integral over a function that contains both determined and undetermined parts which looks like this: ...
0
votes
1answer
60 views

Integrate and NIntegrate yield different results for double integral

Evaluating a double integral with bivariate normal distribution yileds widely different results depending on the method used. I define a bivariate normal distribution with {10, 3} and {8, 1.5} as ...
1
vote
3answers
142 views

Answer when integrating by partial fractions

Evaluating $$\int \frac{x^2-x+5}{(x-2) (x-1) (x+3)} \, dx$$ Version 9.0.1 gives the following answer $$\frac{1}{4} (-5) \log (1-x)+\frac{7}{5} \log (2-x)+\frac{17}{20} \log (x+3)$$ It seems to ...
3
votes
5answers
104 views

Using Mathematica to find a Derivative

I am given a system first order differential equations: $x'=y$ and $y'=6x^2-a/2$, where $a$ is a constant and $'$ denotes $t$-derivatives. I then make the substitution $(x,y)=(x_1y_1,y_1)$. This ...
8
votes
8answers
628 views

Finding maximum or minimum of implicit functions

is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ...
4
votes
3answers
222 views

Function given exact arguments returns hugely different value than it returns when given equivalent inexact arguments

I was trying to compute the probability that a coin is from a particular underlying distribution given that a particular set of tosses was observed. (I know this can be done in a different way, but I ...
1
vote
0answers
65 views

How can I compute a functional derivative of a composed function? [closed]

Thanks in advance! Given: v[Log[x_]] := Vm*Log[x]/(Km + Log[x]) How can I compute the first order derivative of ...
1
vote
1answer
89 views

Using Mathematica to find Derivatives

I am given a system first order differential equations: $x'=y$ and $y'=6x^2-a/2$, where $a$ is a constant and $'$ denotes $t$-derivatives. I then make the substitution $(x,y)=(x_1y_1,y_1)$. This ...
2
votes
2answers
664 views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
0
votes
0answers
29 views

How to calculate this derivative? [duplicate]

Can Mathematica do the following simple calculation? $$F(x_0, x_1, x_2, ...) \equiv \sum_n x_n^2$$ I want to do the symbolic calculation: $$ \frac{\partial F}{\partial x_m} = \sum_n 2 x_n ...
1
vote
1answer
57 views

Integrating a function forcing parameters to be real and positive

I'd like to integrate the function $f(x)=x^{a-1}e^{-b x}$ over the interval $[0,\infty)$. f[x_] := x^(a - 1)*Exp[-b*x] Then: ...
0
votes
0answers
49 views

Computing integrals with differential operator

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...
-3
votes
1answer
61 views

Finding integral bounds

i have this integral shown below is equal to 1, and i need to find "a" on mathematica, but I'm not sure how. integral (from 0 to a) sqrt((-50.8938 sin(8.4823 t))^2+(4-11.3097 sin(11.3097 t))^2) dt = ...
1
vote
3answers
175 views

Marking specific points on a 3D curve

Here is the curve below. (written as a position vector) r = {Cos[7 Pi*t], Cos[6.2*Pi*t], 2.5*t} ParametricPlot3D[r, {t, 0, 2}] I want to know how I can mark ...
0
votes
1answer
55 views

Integrating function can't be epressed? [closed]

Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ...
0
votes
0answers
43 views

A regularized hypergeometric function related question

I'm interested in finding a way (if possible) of expressing this specific value of the regularized hypergeometric function in terms of known constants. How might I use Mathematica to check this ...
9
votes
3answers
2k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
17
votes
2answers
224 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
122 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
1
vote
2answers
213 views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
2
votes
3answers
166 views

Manipulate fails with f[x]=x^k/(1+x^k)

I have this code: Clear[f] f = Function[x, x^k/(1 + x^k)]; Manipulate[Plot[f[x], {x, 0, 5}], {k, 1, 10}] But nothing draws as I move the slider. Am I missing ...
0
votes
2answers
39 views

Problem with using the chain rule [closed]

I have the functions w[x_] := x*Cosh[x] and x[a_] := n/k*a. I take the derivative ...
0
votes
0answers
58 views

Evaluating an indefinite integral at the boundaries

I have the following expression i need to integrate over $\alpha$ from 0 to 1 and $x$ from $x1$ to $\infty$ ...
0
votes
1answer
84 views

Help with Computation-heavy triple integration

I'm Trying to use Mathematica to symbolically integrate a function with respect to x, y, and z. For some reason, this computation either takes about, 60s and returns the input, or takes many hours ...
1
vote
0answers
82 views

Help wanted in evaluating an integral

Trying to evaluate an integral. To be specific, I'm trying to find the expectation value of $x^2$ for the ground state of hydrogen. Here is the code I used: ...
0
votes
1answer
42 views

Derivative of the composition of two functions

Background, this seems to work (This is manually transcribed from the program, beware of errors): J1[f_, i_] := DifferenceDelta[f[i], i]^2 D[J1[f + t v, i], t] ...
1
vote
0answers
54 views

Working with abstract vectors

I often need to compute derivatives or integrals involving N-dimensional vectors (where the dimension could be equal to 2 or 3 but is not particularly relevant for the sake of the derivation). The ...