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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18 views

Puzzling NDSolve[] behavior for PDE

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
0
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0answers
81 views

How do I select terms by derivative order for integration by parts?

I am trying to calculate derivatives of an integral wrt parameters of the integrand. ...
7
votes
1answer
131 views

Mathematica integration failure - new or old?

Consider the following integral: Integrate[Log[a Cos[x]^2 + b Sin[x]^2], {x, 0, 2Pi}] This takes a LONG time (this is Mathematica 10.0.1 on a Mac), and sometimes ...
0
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0answers
35 views

possibility of predication of next number [on hold]

I am interested to know that possibility of predication of next number in math e.g E O O E E O E E O O E E E O O O E E ? E OR O i am working on number ...
2
votes
2answers
63 views

Integration of piecewise function

I'm trying to understand why Mathematica is not evaluating a piecewise function, while it's able to evaluate each of the regions separately. This fails: ...
6
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5answers
351 views

Find function inverse

I'm trying to find the inverse of a function: (30*x^2 (1 - x)^2) (* where 0<x<1 *) I tried all the following options: 1. ...
2
votes
1answer
89 views

How to solve time dependent Optical Bloch Equations for a three level system?

I am trying to solve the optical block equations for three level system which are time dependent, which i generated using the "Atomic Density Matrix" package. When i use the command to solve this 9 ...
0
votes
0answers
9 views

Cauchy sequences, not converging to zero [migrated]

True or False? If {x_n} and {y_n} are Cauchy and x_n + y_n > 0, for all natural n, then {1/(x_n + y_n)} cannot converge to zero. attempt:False: If both sequences are Cauchy, then they are convergent ...
1
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1answer
32 views

NMaximize not substutiting parameters of objective function [duplicate]

NMaximize is not substituting parameters of its objective function. Is there a way to fix that? I have a three line program that exhibits the problem. ...
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2answers
57 views
2
votes
1answer
103 views

Double integral changing the limits

This integral does not evaluate: Integrate[ Integrate[1/(E^((a - c)^2 + (b - c)^2) ), {c, 0, 1}], {b, -Infinity, Infinity}] However, reversing the integrals ...
0
votes
3answers
54 views

Is there a way to rewrite integrals in Mathematica using u substitution?

In Mathematica, can I give it an integral and a few substitution rules and have it rewrite the integral in terms of those variables?
8
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3answers
293 views

Maximize violating constraints

I have Maximize[{(h*10)/(300*(100 - (l^.5 + d^.4 + H^.6))), (l + d + H + h) == 669, l > 0, d > 0, H > 0, h > 0}, {h, l, d, H}] I believe ...
4
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0answers
151 views

Strange behaviour of MMA in derivatives of some standard functions

There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ...
5
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2answers
170 views

Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...
0
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0answers
33 views

Custom simplification of symbolic definite integral with regards to bounds

I would like to rewrite symbolic definite integrals such that the bounds are always positive. For example : $\int_{-\infty}^\infty f(x) \mathrm{d} x \rightarrow \int_0^\infty \left[ f(x) + f(-x) ...
3
votes
1answer
134 views

How to plot the result of this singular integral?

Please I open a new post here after this one : http://mathematica.stackexchange.com/a/59203/10158 Now I want to plot the function $f(a,b)$ as a function of $b$ for different values of $a$ : $a=0.5$ , ...
1
vote
2answers
121 views

How to calculate the analytical result of this singular integral? [duplicate]

I'm trying to solve this integral: $I(a,b)=\displaystyle{\int_1^{\infty }\dfrac{e^{-ax}}{\sqrt{x^2-1} (1+x\sqrt{1-b^2}) (x-1/\sqrt{1-b^2})} \, dx} \,\, \,\,(a \;\textrm{real>0} \, , 0<b<1)$ ...
1
vote
3answers
120 views

When NSolve fails due to a differential situation?

c = 1.1111; y[x_] = x - c Sin[x] NSolve[y[x] == 0, x] The method has procured no result. Successive derivatives were plotted in an attempt to fix the problem. ...
0
votes
1answer
82 views

Solving Coulomb Integral [closed]

I am trying to solve so-called Coulomb Integral of two Gaussians: ...
3
votes
1answer
81 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
1
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0answers
93 views

Giving hints to Integrate

I working with the integral ...
1
vote
1answer
38 views

Specifying independence of a variable in a function

I am dealing with a function of a finite number of variables and among the operations I wish to do is to differentiate it repeatedly with respect with any of the variables. Now this function happens ...
27
votes
6answers
1k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
5
votes
1answer
179 views

How to find this limit correctly?

How to find the limit Limit[n*Sin[2*Pi*Exp[1]*n!], n -> Infinity] ? Mathematica 10 outputs ...
6
votes
1answer
206 views

Integral of x^p

Can anyone explain why Mathematica does not return a conditional expression that handles the case of p=-1 for Integrate[x^p,x]? ...
0
votes
1answer
80 views

Sum rule in integration not working [duplicate]

I am new to Mathematica and I just tried to play around with some integrals. But the sum rule in integration doesn't work. Here a simple example: Mathematica doesn't recognize that $\int_0^h (1-f(x)) ...
1
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1answer
76 views
0
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0answers
20 views

different values of integral with/without bogus assumptions

I do not understand why I get different answers for the following two identical integrals. ...
3
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1answer
138 views

Fredholm integral equation of the second kind with kernel containing Bessel and Struve functions

I need to solve this Fredholm integral equation of the second kind: f[s]+integrate[f[t] K[s,t],{t,0,1}]=s where ...
1
vote
1answer
95 views

Under what conditions does Mathematica give a natural antiderivative when integrating?

Natural antiderivative is defined as follows, using Fourier transform: $$f^{(-1)}(x)=\frac{i}{2\pi}\int_{-\infty}^{+\infty} \frac{e^{- i \omega x}}{\omega} \int_{-\infty}^{+\infty}f(t)e^{i\omega t}dt ...
1
vote
2answers
632 views

Computing 10-dimensional volume of a 9-sphere [closed]

I'm trying to compute 10-dimensional volume of a 9-sphere with radius r using Monte Carlo. ...
3
votes
2answers
250 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
89 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
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0answers
50 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
125 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
41 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
89 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
68 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
60 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 ...
5
votes
3answers
196 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
96 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 ...
13
votes
5answers
285 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
61 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
91 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
128 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
120 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
82 views

a mysterious error in multiple symbolical integration

I am trying to do the following integration: ...
1
vote
0answers
86 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 ...
1
vote
1answer
130 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 ...