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

learn more… | top users | synonyms (3)

3
votes
2answers
266 views

Integral converging in M9 but not in M10

Background: Mac OSX 10.9.4, Mathematica 9.0.1 vs. Mathematica 10.0 (both versions are Student Editions). I have a notebook. It used to evaluate fine in Mathematica 9. I upgraded to 10 and, without ...
2
votes
0answers
97 views

Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
0
votes
0answers
51 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as ...
1
vote
1answer
140 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
0
votes
1answer
46 views

Evaluation of integral [closed]

I want to evaluate an indefinite integral using the Integrate command, and I know that the answer can be written in terms of elementary functions (square roots, logs etc.) but Mathematica seems to ...
5
votes
0answers
92 views

Convoluting inverse square root with Gaussian

I would like to convolute the inverse square root on the interval [0,inf] with a Gaussian function, like so: ...
0
votes
1answer
71 views

Integral calculation in Mathematica [closed]

I need to calculate this integral using Mathematica: ∫ t^z * ln(t) dt from x to y with the assumptions that z is an integer and 0 < x < y This is what I'm trying to do: ...
3
votes
0answers
66 views

Symbolic integration of elliptic functions

Is there some clever way to integrate products of elliptic functions $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica? Mathematica seems to be able to integrate functions like ...
7
votes
3answers
257 views

Generating a polynomial that's accurate to within an error of no more than 1/10^5

I'm currently stuck on a question for class that asks... "Find a polynomial p[x] that you can use to calculate 6 ArcTan[x] to ...
2
votes
2answers
103 views

Integrate returns unexpected result

Consider the following function $$g(x,y):= \frac{1}{( (1+y)^2+x^2 )( 1+ax^2y^2 )^2}$$, where I assume that $y\geq 0$ and $a\in (0,1]$ is a parameter. When I try to evaluate the integral $\int ...
14
votes
5answers
314 views

Mismatch between numerical and analytic evaluation of an integral

I evaluated the following integral NIntegrate[Sqrt[r] Abs[Cos[(k + 1/2) Pi r]], {r, 0, 1}] getting as a result 0.413232 for ...
4
votes
0answers
63 views

How to save the result in the Notebook (.nb) and shut down the computer when the calculation is done

I have a notebook(.nb) which its calculation is time-consuming and long. I can not observe it if the calculation is done or not. Therefore, I want to : (1) Save the results in the notebook(.nb) ( I ...
4
votes
2answers
142 views

Integrating a periodic function

I have a periodic function ff: ff := Function[x, Piecewise[{{ff[x - 1], x >= 1}, {2 x, 0 <= x < 1}, {ff[x + 1], x < 0}}]] Plotting it works fine: ...
0
votes
2answers
132 views

Integral with unreliable result

I want to calculate $\int_R^1 \sqrt{r} |\cos((k+\frac{1}{2})\pi r)|dr $ and I get a result from Mathematica. Then I try to check the result putting the value of $k$ and $R$, (k=1 and R=0.5) in the ...
1
vote
2answers
131 views

Higher derivative [closed]

Is there more efficient way to rewrite this code in order to compute 2nd and higher derivatives of r=sqr{x^2+y^2+(z-a)^2}? ...
2
votes
1answer
91 views

a mysterious error in multiple symbolical integration

I am trying to do the following integration: ...
1
vote
0answers
147 views

Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
2
votes
1answer
138 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
3
votes
0answers
73 views

Using Mathematica to help obtain correct analytic formula for logarithm integration

I need to program into my Mathematica code the analytic form for the result of the integral: $$I(a,b)=\int ^1 _0 dx \frac{\ln(x-a)}{x-b}$$ that is valid for all complex $a$ and $b$ (but $\text{Im } ...
8
votes
1answer
125 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 ...
6
votes
4answers
261 views

Conditional Expectation — How can Mathematica find a more general closed form?

Mathematica can't find a solution to this Expectation. ...
2
votes
1answer
93 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 ...
2
votes
1answer
174 views

Mathematica policy for correctness of results [closed]

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 ...
0
votes
1answer
79 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
1answer
107 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 ...
-1
votes
3answers
146 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; ...
0
votes
0answers
94 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
85 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
1answer
128 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 ...
1
vote
1answer
131 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 ...
0
votes
1answer
65 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: ...
2
votes
2answers
209 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 = ...
3
votes
1answer
205 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
115 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
91 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
166 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 ...
4
votes
2answers
232 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
1answer
101 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 ...
3
votes
5answers
120 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
957 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 ...
0
votes
0answers
30 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
73 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
58 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
69 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 = ...
0
votes
1answer
67 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
62 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 ...
2
votes
3answers
289 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
203 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
317 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 ...