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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3
votes
1answer
441 views

Normal and Tangent of Acceleration in 3D

I need to figure out how to find the Normal and Tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal ...
2
votes
1answer
393 views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
11
votes
1answer
167 views

Keeping Integrate from making unnecessary assumptions

I would like to evaluate the integral $\int_{-\infty}^\infty \mathrm{d}x \, \exp\left(- a x^2 - x^4\right)$ for any real value of $a$. Mathematica 8.0.4 gives the following result: ...
2
votes
1answer
271 views

Multi-dimensional integral in the complex plane with poles and essential singularity

I've passed the last week searching a way to numerically integrate this multi-dimensional integral in the complex plane at the poles and avoiding the singularity at z=0: $$ \oint_{C}\oint_{C\ auound\ ...
0
votes
0answers
90 views

Non-Solvable PDE?

I would like to know whether this PDE is solvable and if yes, for which values of $a$. ...
0
votes
0answers
87 views

recurrence relations

If I write f[i_] := Expand[FunctionExpand[x^(i/5) LerchPhi[x, 1, i/5]]] for any i < 5, the result is a linear combination ...
6
votes
1answer
240 views

Mathematica 9 can't integrate this function but earlier versions could

Integrate[ ArcTan[x]/(1 + x) Log[(1 + x^2)/2], {x, -1, 1}] I used Mathematica 9.0.1 on Windows7 32bit, Mathematica 9 cannot compute this, but Mathematica 8 gives ...
3
votes
2answers
294 views

Create polygon using edge lengths and area

Four-sided convex land plots are usually denoted with edge lengths and area. How do I create a Polygon Object with these parameters in Mathematica ?
0
votes
0answers
87 views

Interpretation of output derivative expression [duplicate]

I am trying to write Mathematica file to find Div, Grad, Laplacian, etc. in coordinates ...
2
votes
1answer
715 views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
1
vote
2answers
219 views

Finding normals to a curve through a given point

I want to find x on curve $y(x)$, where curve $y(x)$ is perpendicular to point $(x_0,y_0)$. for this I minimize the distance between points $(x,y(x))$ and $(x_0,y_0)$, here's an example for point ...
2
votes
1answer
776 views

Laurent series expansion

Can someone share how to find a Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at zero on the annular disk $1<|z|<2$?
7
votes
1answer
253 views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
2
votes
0answers
116 views

Real integral evaluating as indeterminate

Mathematica evaluates the following integral as: ...
3
votes
1answer
255 views

n-fold symbolic integral in Mathematica

I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this ...
0
votes
1answer
200 views

Can I take derivative of a function that represents a piece of music?

Can I take the derivative of a function that represents a piece of music? The music is given in .mp3, .midi or whatever comes in handy.
10
votes
2answers
518 views

Numerical partial derivative

For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before: ...
0
votes
1answer
389 views

No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]

Is my input below correct? I've received no response from Mathematica. N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]] Thank ...
2
votes
0answers
47 views

Verifying integration by parts of an arbitrary function [duplicate]

Suppose that I have an arbitrary differentiable function $G$ which depends on $s$: $G(s)$. Now suppose that I want to do the following integral: $$\int ds \;\; s \frac{\partial G(s)}{\partial s}.$$ ...
10
votes
5answers
3k views

Finding the centroid of the area between two curves

When I have an area bounded by curves, is there a built-in way to find the center of the area? Or do I have to plot it first and then use ComponentMeasurements on ...
1
vote
1answer
136 views

Derivative inside a function

I am trying a problem that should be simple: to create a function that contains a derivative. I need to do a more complex example, but even with the simplest I'm having trouble: Let's consider ...
1
vote
0answers
221 views

Cauchy principal value integral of a list of numbers. How?

I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
9
votes
1answer
282 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
5
votes
3answers
642 views

recursive integration

I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer $n$: $\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') ...
13
votes
2answers
305 views

What kind of hypergeometric function is it?

I found a formula for an integral of a product of three Bessel functions at The Wolfram Functions Site: I cannot understand what kind of hypergeometric function it is. The Mathematica code given ...
2
votes
3answers
149 views

Manipulate fails with f[x]=x^k/(1+x^k)

I have: Clear[f] f = Function[x, x^k/(1 + x^k)]; Manipulate[ Plot[f[x], {x, 0, 5}], {k, 1, 10}] But nothing draws as I move the slider. Am I missing something? ...
3
votes
1answer
393 views

Evaluating double Integral

While trying to evaluate the integral $\int_{y=0}^{x_2}\int_{x=0}^{min(x_1,y)} n (n - 1) (1 - y)^{(n - 2)}dxdy $ , Mathematica does not seem to yield any results. ...
6
votes
4answers
521 views

How do I obtain the correct double limit?

The command Limit[(Sin[x^2] + Sin[y^2])/ (x - y) /. x -> 0, y -> 0] (* 0 *) I think that Mathematica finds the iterated limit instead of the double ...
15
votes
4answers
3k views

Finding Limits in several variables

Is there a way to find a limit of a multivariable function, like $$\lim_{(x,y)\to (0,0)} f(x,y)$$ with Mathematica? When $f$ is continuous, we can use $$\lim_{(x,y)\to (0,0)} ...
6
votes
1answer
652 views

How to expand a function into a power series with negative powers?

Is there any way to expand this expression a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)]) (where a, ...
2
votes
2answers
280 views

Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
3
votes
1answer
538 views

Definite and Indefinite integral give different results for piecewise function

I have the following function: $$ f(q,y)= \begin{cases} \tfrac{11720+p}{37791360} & -11720<p<-7720 \\ 0 & \text{True} \end{cases} $$ where $p = 443\ y-777600\ \sin^{-1}\left(\frac{q ...
1
vote
1answer
113 views

Integration of a rational function

I am trying to solve the following rational integral (I got assistance here): $$\int_{-\infty}^{\infty}{\frac{a+x}{b^2 + (a+x)^2}\frac{1}{1+c(a-x)^2}}dx$$ where $\{a, b, c\}\in \mathbb{R}$. I would ...
2
votes
0answers
118 views

Is this result wrong because of calculation time? (and more questions about Assumptions)

I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case: ...
0
votes
1answer
179 views

Integrate of Heaviside Function returns an error answer

I try to evaluate an Integral of a Heaviside function, but it turns out with an erroneous output(zero). Here is my integral: ...
0
votes
1answer
105 views

Taking derivative of Euler relation [closed]

I have defined the following function, which is the Euler relation for $\cos\,x$. f[x_] := 1/2*(Exp[I*k*x] + Exp[-I*k*x ] ) I want to take the derivative with ...
1
vote
3answers
426 views

How do I evaluate several n-th derivatives of a function at one point?

I have a question where I have to compute a Table containing $f^{(n)}(0)$ for n = 1, ..., 5, where $f^{(n)}$ denotes the $n$th ...
9
votes
2answers
445 views

Find closed form expression for series expansion coefficients [duplicate]

Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function? Series will only give the explicit ...
9
votes
1answer
181 views
13
votes
1answer
228 views
4
votes
2answers
126 views

Strange behavior of Integrate

I'm trying to calculate the following integral using Mathematica 9.0.1.0 a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}] This should be a simple problem; however, it ...
1
vote
1answer
200 views

how to reduce the time to calculate triple integral

i want to evaluate the following integral, but it takes 15 min to do it. i must reduce the time to calculate it, i have to do a table and create a graph, but takes too long. anyone have an idea ? ...
1
vote
1answer
123 views

Assumptions are not being applied to integral

I am trying to use assumptions to simplify an integral, but I can't seem to get the assumptions to apply themselves. Here is the code I am using: Note the expressions in the assumption can be found ...
0
votes
1answer
56 views

Is there a more idiomatic way to solve this implicit differentiation problem?

Here's an exercise from a calculus text by Larson and Edwards: Find the rate of change of the distance between the origin and a moving point on the graph of $y = x^2 + 1$ if $dx/dt = 2$ ...
2
votes
0answers
171 views

Derivatives of list elements

Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
0
votes
0answers
33 views

Plot derivative of integral with changing limits [duplicate]

My code is: Plot[D[Integrate[E^(t*(-x^2)),{x,t+2,t^2}],t],{t,-2,3}]. The errors/warnings are: ...
9
votes
0answers
241 views

Why does Mathematica give an incorrect answer to this multiple integral?

This is not a new problem but I would like to understand why Mathematica gives the result that it does. (Volume of a hypersphere) ...
3
votes
3answers
910 views

Definite integral takes a very long time

I'm trying to integrate the following function: $$ r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}} $$ where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
3
votes
2answers
1k views

How do I evaluate a double or triple integral over a region?

Say I need to evaluate the integral $\iiint_W f(x,y,z) dx dy dz$ and $W$ is a region given to me like $W = \{ (x,y,z) : 1 \leq x^2 + y^2 \leq 4, 1 \leq z \leq 5\}$. I don't how to do this with a ...