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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0
votes
0answers
18 views

Not Simplify automatic some expression(values)

I try to calculate $$\text{res}\left(h(z) (\psi ^{(0)}(z)+\gamma )^2,\{z,-4\}\right)$$ the result is $$\frac{1}{6} \left(6 h'(-4)-25 h(-4)\right)$$ the result it is possible to write as $$2 \left(6 ...
8
votes
2answers
691 views

Weird plot with SphericalPlot3D

Taking the equation $x^2-y^2-z^2=1$ and using ContourPlot3D: ContourPlot3D[ x^2 - y^2 - z^2 == 1, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}] Yields the proper image. ...
6
votes
2answers
157 views

Different results of the integrate $\int \frac{\sin (\pi s)}{(s-0.5)^2+90} \,ds$?

Following results are given of big different values. I think NIntegrate's one is right but others are not explained. ...
3
votes
1answer
152 views
2
votes
0answers
55 views

Better to have infinities in limits or integrands (`NIntegrate`)? [closed]

I'm using ListPlot to plot the integral of a function with respect of the function's second variable: ...
2
votes
1answer
151 views

Numerically integrate and plot $f(x;p)$ for a range of the parameter $p$

Suppose we have an integral of the form $$I = \int_a^b dx \, \sin(px), \tag{1}$$ where I've take $f(x;p) = \sin (px)$ to be specific. I want to plot this integral for a range of values of the ...
7
votes
2answers
377 views

How much time should one give Mathematica for an integral evaluation?

Sometimes when I do integrals in Mathematica (M), it keeps thinking and thinking and I have no idea what is going on inside M. For how long should one wait or how does one know whether M has not got ...
1
vote
0answers
42 views

Which type of integrals are better for Mathematica [closed]

Is it in general better to type in a integral with its limits, or is it better to type an indefinite integral into Mathematica? With better I mean: Likelihood that Mathematica can solve it, ...
0
votes
1answer
76 views

repeat calculate [closed]

I want to calculate the below program x[t+1].But I can only calculate t=0,1. please tell me how to calculate t = 0 to 10. ...
9
votes
1answer
413 views

Laplacian and DiracDelta

It is known that: $\nabla^2 \dfrac{1}{|r-r'|} = - 4 \pi \delta^3(\vec{r}-\vec{r}')$. If I do that with Mathematica, I find: ...
6
votes
1answer
261 views

Traces of the level surface $z=4x^2+y^2$

I came up with this method to plot the traces of the surface $z=4x^2+y^2$, in this case for $z=1$, 2, 3, and 4. ...
0
votes
2answers
134 views

Given integral, how to plot

I want to use mathematica to visualise some plots, this would help me understand my calculus course. My problem is this: Given that x^2 + y^2 <= a^2 Find ...
6
votes
3answers
297 views

Derivative of contour in ContourPlot

Sorry to bring this question up again, since there are many similar questions on the site. I use to think this is a easy job to do, because for the worst case I can follow the answers on this site. ...
12
votes
2answers
417 views

Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
5
votes
1answer
257 views

Fitting a Parametric Curve

I apologize if this question is obvious or simple. I'm in high school and have started playing around with Mathematica only recently. For my Calculus Final, I am supposed to use rotation about the ...
2
votes
1answer
112 views

Meaning of Pattern at derivatives of arbitrary functions

I want to derivate some general functions like D[F[x[r_, p_], y[r_, p_]], r] or this simpler one D[F[G[x_]], x] . When I ...
0
votes
0answers
85 views

Using Manipulate to determine intersection of two surfaces

Here is what I have done thus far: ...
2
votes
2answers
229 views

Strange Boundary NDSolve Problem

Mma10.1 doesn't work with the following boundary problem: ...
10
votes
6answers
815 views

Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
10
votes
2answers
248 views

Volumes of Revolution with detailed diagram

All, In calculus I have to do images such as the following in helping explain technique to students. This one is by rotating $y=\sqrt x$ about the x-axis, an image copied from Stewart's Calculus ...
1
vote
1answer
86 views

Adding a title that includes angle between two vectors in Graphic in Manipulate

Here is what I have tried thus far: ...
0
votes
0answers
53 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
135 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 ...
0
votes
0answers
122 views

same code different results on different computers

This very simple code: ...
2
votes
0answers
47 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 ...
1
vote
1answer
136 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 ...
0
votes
1answer
181 views

Asymptotic forms of Bessel function

I want to replace Bessel functions by asymptotic forms, so the question is: can I find the best ones with help of Mathematica? And if it's possible, how can I do it? Update How can I get with ...
2
votes
1answer
89 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 ...
6
votes
3answers
207 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
0answers
148 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 ...
1
vote
1answer
89 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 ...
-2
votes
1answer
175 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: ...
0
votes
0answers
130 views
4
votes
3answers
527 views
0
votes
0answers
63 views

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

I encountered a weird problem with Derivatives in Mathematica, see the following code: ...
0
votes
1answer
95 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: ...
19
votes
4answers
918 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 ...
2
votes
1answer
116 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 ...
5
votes
1answer
220 views

Wrong Limit in Mathematica 10.0.0

Bug introduced in 9.0.0 and fixed in 10.0.1 Limit[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n), n -> Infinity] Mathematica (wrong) output: ...
10
votes
1answer
212 views

Wrong Limit with LaguerreL

Bug introduced in 7.0 and fixed in 10.2.0 Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞] Mathematica (wrong) output ...
4
votes
2answers
205 views

definite integration very slow

I have to perform definite integration of function of this kind : ...
8
votes
1answer
146 views

LogisticSigmoid residue bug?

Bug introduced in 10.0 and fixed in 10.2.0 On version 10.0 for arm: Residue[LogisticSigmoid[z],{z,I Pi}] gives 0 not 1. ...
2
votes
1answer
191 views

How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
8
votes
2answers
278 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 $\int_0^1\int_0^1\int_0^1\frac{1}{xyz}\,dz\,dy\,dx=0$. ...
0
votes
1answer
65 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. ...
6
votes
1answer
321 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
0answers
52 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
42 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
54 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
2
votes
1answer
660 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 : ...