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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14
votes
1answer
241 views

Why do big-O terms disappear in definite integrals since Mathematica 9?

In Mathematica 8, when I computed the following input: Integrate[Series[Cos[x], {x, 0, 2}], {x, 0, a}] Mathematica returned an expression that had a O[a^4] in ...
1
vote
0answers
42 views

Order of integration resolves “Indeterminate expression encountered.”

Bug introduced in 10.0.0 and fixed in 10.0.1 Today I came across the following integral: ...
1
vote
2answers
84 views

Integration over a (non-parametric) curve defined by indicator function

I want to integrate the real function myFun defined on a 2D plane over the line locus, defined as the solution of a set of ...
5
votes
2answers
176 views

Unexpected Integration Constant [closed]

Why does this integration Integrate[15-30x+6x^2-1/(x+5),x] return 700 as integration constant? If we make a slight modification ...
0
votes
0answers
42 views

Mathematica Integrate implicit assumptions returns a function not defined in some points while NIntegrate performs integration safely

Hi guys i'm performing a standard integration with mathematica routine Integrate, the function i'm integrating is the following: ...
2
votes
4answers
144 views

Problem in finding the numerical maximum

I need to find the numerical maxima of the function $$i(s)=\bigg[ \frac{\sin{50\pi (\cos s+1)}}{\sin{10\pi (\cos s+1)}} \bigg] ^2$$ Or in the mathematica input form: ...
4
votes
2answers
218 views

Limit not giving expected result

I am taking the limit Limit[Sin[π Sqrt[4 n^2 + n]], n -> ∞] the returned answer is Interval[{-1, 1}] I think the right ...
3
votes
1answer
99 views

Problem with series expansion and integrate

I have the following very simple code. A power series in a-parameter, function f[x], is integrated with respect to x, and the ...
0
votes
1answer
84 views

Functions in functions

I have three functions f(x,y) , g(t) , and h(t) and somehow I have to find (d/dt)f(g(t),h(t)) where t = 0. How would I go about writing this in Mathematica? In this equation g(t) is taking place of x ...
1
vote
1answer
89 views

Derivative of an expression containing a symbolic sum [duplicate]

Is there a general pattern for working with symbolic sums in Mathematica? For example here's a derivative I want to compute: ...
5
votes
0answers
152 views

Integrate wrong for absolute value of trig function

I was trying to get $\int_0^1 \lvert \cos(2 \pi k x) \rvert \,\mathrm{d}x$ for $k \in \mathbb{Z}$, and was surprised by the result (using Mathematica 10.0.1.0): ...
2
votes
2answers
71 views

Providing wrong answer on integral $\int_{-\frac{2}{3}}^{\frac{2}{3}} \left(\text{Ln}\left(\cos ^4(x)\right)+1\right) \, dx$ [closed]

I tried to evaluate the following in mathematica $\int_{-\frac{2}{3}}^{\frac{2}{3}}{1+\ln \left( \cos ^{4}\left( x \right) \right)}dx$ and got the answer as $0.91905 - 3.94746*10^{-16} I$. However, ...
3
votes
0answers
54 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
0
votes
0answers
31 views

Plot3D and NIntegrate issues

f[x_, y_] := 2*x - y Plot3D[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] NIntegrate[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] I ...
0
votes
2answers
56 views

Taking derivatives

This is my code: X := g[P] P = a*t R = t*X FOC = Dt[R, t] This is what I get for the last line: ...
0
votes
1answer
64 views

How to differentiate an integral on Mathematica?

I am so new on Mathematica. I try to find the first variation of this function according to $t$ on mathematica but I could not achieve. Here is the function ; ...
8
votes
4answers
305 views

Mathematica complaints that convergent integral diverges

Bug introduced in 10.0.0. Fixed in 10.0.2 Trying to do the integral ...
3
votes
3answers
136 views

Factoring a scalar function out of a vector

I've taken a first and second derivative: ...
-2
votes
1answer
157 views

Mathematica Giving Me Trouble [closed]

I'm new to mathematica and am just learning the basics. I've run into a few things that I can't figure out. The first is this: "Number 11" ...
8
votes
1answer
186 views

Mathematica integration failure - new or old?

Bug introduced in 7.0.1 or earlier Consider the following integral: Integrate[Log[a Cos[x]^2 + b Sin[x]^2], {x, 0, 2Pi}] This takes a LONG time (this is ...
2
votes
2answers
139 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
votes
5answers
448 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
182 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 ...
1
vote
1answer
42 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. ...
1
vote
2answers
60 views
2
votes
1answer
126 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
91 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?
9
votes
3answers
351 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 ...
5
votes
0answers
170 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 ...
6
votes
2answers
184 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
votes
0answers
38 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) ...
4
votes
1answer
148 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
134 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
129 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
111 views

Solving Coulomb Integral [closed]

I am trying to solve so-called Coulomb Integral of two Gaussians: ...
18
votes
2answers
525 views

Symbolic integration error

I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...
4
votes
1answer
113 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
vote
0answers
97 views

Giving hints to Integrate

I working with the integral ...
1
vote
1answer
44 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 ...
29
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
192 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
219 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
101 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
vote
1answer
104 views
0
votes
0answers
24 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
votes
1answer
188 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
131 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
648 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
265 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: ...