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)

17
votes
1answer
687 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
21
votes
2answers
284 views

Backslide of Limit

A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] This sample calculates well in v8.0.4: but not in ...
0
votes
0answers
39 views

Integration problem: lrgexp

I want to calculate the following integration but it gives the error PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD. The code is: ...
1
vote
2answers
63 views

Derivative of Continuous and Differentiable Piecewise function is indeterminate

I'm attempting to analytically stitch together two linear functions with two quadratic functions. The function I'm considering, then, is a piecewise function consisting of 4 parts. Below are the ...
1
vote
0answers
98 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
2
votes
3answers
168 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. ...
2
votes
0answers
43 views

Computing an inexact derivative with some terms preserved in exact form

I am beginning to learn Mathematica and have the following question: How can I return a derivative with exact numbers instead of one involving numerical approximations? My original, single variable ...
12
votes
1answer
340 views

Why is this infinite series wrongly computed by Mathematica?

Could you let me know if Mathematica (newer versions) is able to correctly compute this one? Sum[(-1)^(n + 1) Cos[3^n x]^3/3^n, {n, 1, Infinity}]
1
vote
1answer
106 views

Limit of a fractional integral

I am trying to find the limit for λ -> 0 of the integral listed below, but Mathematica give me only a ConditionalExpression ...
1
vote
2answers
86 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 ...
6
votes
3answers
178 views

Speed up derivative evaluation

I'm trying to calculate the normal vectors and the tangent vectors at the discrete points of a suface. For example: ...
1
vote
1answer
129 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 ...
2
votes
0answers
50 views

Does DynamicModule cure Problem with Manipulate?

Hopefully, this is a final cure for the Problem with Manipulate introduced on A problem with Manipulate and then continued on Continuation of a Problem with Manipulate. Michael E2 suggested on the ...
1
vote
2answers
248 views

How to numerically integrate this integral?

I want to integrate a function (spherical coordinates): $$\int _0^{2 \pi }\int _0^{\pi }\frac{r^2 \sin (\theta ) e^{-\lambda \sqrt{\rho ^2+r^2-2 \rho r \cos (\theta )}-2 r}}{\pi \epsilon ...
1
vote
1answer
68 views

Integral not being evaluated

I'm trying to do the following integral, but Mathematica won't evaluate it - it just spits out the actual symbolic integral. $$\frac{e^{-\frac{(k-d)^2}{2 a^2}} \left | \frac{-d+\frac{c ...
16
votes
5answers
414 views

Mismatch between numerical and analytic evaluation of an integral

I evaluated the following integral $$\int_0^1 \sqrt{r} \left | \cos \left(\left(k+\frac{1}{2}\right) \pi r\right)\right | dr$$ ...
-2
votes
1answer
128 views

Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: $$ \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } $$ That is: ...
1
vote
1answer
72 views

Continuation of a Problem with Manipulate

For the beginning of this discussion, see: A problem with Manipulate. Now, the final use of the Initialization command doesn't protect the Global workspace. What I am discussing is not a single ...
36
votes
6answers
2k views

Generating evenly spaced points on a curve

In the KnotData package a simple command such as points = Table[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi, 0.1}]; will ...
14
votes
3answers
2k views

How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
0
votes
1answer
115 views

Replacement of terms/Pattern matching involving products of derivatives of a function

In delving into Ramanujan summation, I'm trying to get a hold of the relations of the form $$\sum_{n=0}^\infty f(n)=\dfrac{h\frac{d}{dx}}{{\mathrm{e}^{h\frac{d}{dx}}}-1}\int_{0}^\infty ...
3
votes
1answer
1k views

Convolution of two distribution functions

I have two functions; f[x_] = (1/k) Exp[-x/k] ; g[x_] = (1/p) Exp[-x/p] ; How I can convolve them? In Mathematica for convolving two functions we have this ...
6
votes
1answer
940 views

Convolving/integrating problems

Let's say I want to convolve two functions (f and g), a gaussian with a breit-wigner: ...
6
votes
2answers
361 views

Convolve does not get the correct answer

Convolve[Sinc[x], Exp[-x^2], x, X] (* E^-X^2 π *) is obviously false, but why? Any suggestions ?
2
votes
1answer
99 views

Missing zero in the CoefficientList

The following list has a length only 10 (not 11) CoefficientList[Series[ArcTan[x]/(1-x^2),{x,0,10}],x] {0, 1, 0, 2/3, 0, 13/15, 0, 76/105, 0, 263/315} It should ...
18
votes
4answers
824 views

A bug in Integrate

Integrate[(1 + 16 Tan[2 x - y]^2)/(1 + 4 Tan[2 x - y]^2), {x, 0, 2 π}] Mathematica (wrong) output is (tested under versions 8 and 10.0, took ~ 1 minute of CPU ...
0
votes
1answer
85 views

Numerical integral speed

I have the following code to calculate a numerical integral for any given a, however it takes a very long time, even with adaptivemontecarlo, which is not accurate enough: ...
0
votes
0answers
57 views

Bug (?) in Mathematica in Derivative of function with Abs [duplicate]

I encountered a weird problem with Derivatives in Mathematica, see the following code: ...
20
votes
2answers
1k views

Why does Mathematica give the wrong answer when integrating?

I integrate Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}] Mathematica gives: 2 I Pi BesselJ[1, 1] Which is indepedent ...
4
votes
2answers
136 views

definite integration very slow

I have to perform definite integration of function of this kind : ...
7
votes
2answers
226 views

Why does Mathematica say $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$?

Mathematica 9 says that $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$ and $\int_0^1\int_0^1\int_0^1\frac{1}{xyz}\,dz\,dy\,dx=0$. ...
2
votes
1answer
160 views

How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
6
votes
1answer
215 views

Find exponential generating function from the first few terms

The function FindGeneratingFunction computes the ordinary generating function of a sequence, given a sufficient number of initial terms. I have two questions in ...
0
votes
1answer
52 views

Problem with 'time dependent' functions [closed]

I'm just trying to make $\frac{dx}{dt}$ where $x= \rho \cos\theta \sin\phi$ where $\theta, \phi $ and $\rho$ are time dependent functions. ...
4
votes
4answers
2k views

Numerical differentiation methods

Is it possible to write code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
0
votes
0answers
48 views

Multidimensional integration does not work

I am trying to solve an integral over Cubic Birillioun Zone, but after taking a long time Mathematica give nothing in return and just repeating the integral form, here is my integral, ...
0
votes
1answer
37 views

Plotting partial sums of Taylor Function

I need to plot the partial function: $T_f(x)=\log 2+\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{2^kk}(x-2)^k$ for $n=2$,$n=4$ and $n=6$ on the same plot over the interval $[-\frac{1}{2},4]$ and also the ...
2
votes
1answer
210 views

How can I evaluate surface integral in Mathematica?

$$\iint_{S^+}x^3dydz $$where $S$ bottom part of $$ \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$ $S^+$ - outer side of $S$ $$\iint_{S^+}P(x,y,z)dydz = \iint_{S}P\cos\alpha dS,\ \; normal : ...
12
votes
3answers
383 views

How can I obtain an asymptotic integral expansion at infinity?

I want to find the asymptotic expansion at $x \to \infty$ of the following function: $$ I(x) \equiv \int_0^{\pi/2} e^{-xt^3 \cos(t)} dt.$$ To do this I defined ...
-2
votes
1answer
52 views

Need help to solve this math question when x reach 0 [closed]

My son can home and ask me to help him with this equation: lim ((x-2)/(2x-1))^(1/x) x→0 I try to use /www.symbolab.com but its too complicated to solve this. Thanks with the help
0
votes
1answer
116 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
1
vote
1answer
96 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
5
votes
1answer
295 views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
0
votes
0answers
37 views

Series Expansion of Differential Operators [duplicate]

We know about the possibility of series expansion of a function in Mathematica. Same as below, where a function f[a x] is expanded around zero up to 5th order. ...
3
votes
3answers
98 views

Factoring a separable integral with a product of independent integrands

I would like to input someFunction[Integrate[p[x] p[y], {x, -1, 1}, {y, -1, 1}]] and to get the following output ...
0
votes
0answers
65 views