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
1answer
39 views

Efficient calculation of leading order behavior of rational function under a limit?

Considering a rational function, as for example myExpr=(x+3)(2+5x+6x^2)/(x(x-5)(x+20)) I would like to have a function that tells me the leading order behavior ...
4
votes
2answers
164 views

Derivative of piecewise function

I tried to find $f'(0)$ of this function: $$f(x) = \begin{cases} x\cdot\sin(\frac{1}{x}) & \text{if $x\ne0$} \\ 0 & \text{if $x=0$} \end{cases}$$ This is what I tried in Mathematica: ...
3
votes
1answer
94 views

Evaluate Limit only if both directions(sides) are equal?Ex: $\lim _{x\to 0}\left(\frac{1}{x}\right)=DNE$

I want the limit of a function to only evaluate if both the left and right hand side are equal. For example $\lim _{x\to 0}\left(\frac{1}{x}\right)$ doesn't exist(two sided limit). However, the right ...
1
vote
1answer
172 views

Plotting singular integral

I need to plot the following singular double integration $u(x,t)$ for $t=0, t=0.2, t=0.4, t=1$ and $t=2$ in one figure as a line. That is, I need $u$-coordinate vertically and $x$-coordinate ...
2
votes
1answer
101 views

How to evaluate the limit of a function consists of Range

I would like to evaluate the limit: $$ \sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\cdots}}}}} $$ Therefore, I write the following function of n: ...
4
votes
2answers
91 views

Defining arbitary Derivatives of functions

If I have two functions like these f[a_,b_] and g[a_,b_]. Lets say ...
1
vote
1answer
48 views

Apply Grad and Mod to Matrix

Let f:=x^3+y*x*z+z^3; Let mat = {{2, 2, 2}, {3, 1, 7}, {1, 6, 3},{4, 5, 1},{0,4,9}}; be a list of points . I want to compute ...
2
votes
2answers
83 views

How to fix internal error “too much recursion” when trying to compute a definite integral

I'm completely new to Mathematica. I got a 14 day free trial and I'm using the online version. I'm trying to use it to check the results of an integration I performed by hand. But I'm not getting any ...
0
votes
2answers
104 views

How can I calculate the following integral?

I tried to calculate Integrate[(9.07 - 5.60 Cos[.87 t] - 2.71 I Sin[.87 t] + 2.14 Cos[1.74 t] + 2.70 I Sin[1.74 t] )^0.5, {t, 0, T}] but the output is the ...
1
vote
1answer
91 views

Evaluation of this definite integral

I want to obtain the symbollic expression for this integral: $\int^\infty_{-\infty} \, dx \, \left(\frac{y - x}{R^2 + (y-x)^2}\right)\, e^{-\frac{(x - \mu)^2}{4 s^2} - \frac{i k (y - x)^2}{2 R}}$, ...
5
votes
2answers
91 views

Infinite sum not evaluated unless split into even and odd terms

This sum s = Sum[Gamma[k/2]/(2 k!), {k, 1, ∞}] $\sum _{k=1}^{\infty } \frac{\Gamma \left(\frac{k}{2}\right)}{2 k!}$ is returned unevaluated (version 10.1.0). ...
0
votes
1answer
158 views

Calculate overlap coefficient between two functions

I have two functions and I want to calculate the overlap coefficients between those two functions. A similar question has been answered for Python and R, however, I couldn't find an answer for ...
2
votes
3answers
119 views

Adding more specific assumptions to Integrate

Let's say I would like to find a symbolic form for the integral $$\int_0^{2\pi}\sin^nx\,\mathrm{d}x$$with the added condition that $n$ is not only an integer, but an even one at that. Can this be done?...
2
votes
0answers
95 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
2
votes
0answers
65 views

Good coding for integral substituions

This question is aimed at improving both my coding and my understanding of MMa's capabilities. A lot of my code is still hacks and workarounds for things I don't know how to do properly. I want to ...
4
votes
1answer
107 views

Mathematica shuts down when calculating this limit

Bug introduced in 9.0.0 and fixed in 9.0.1 I'm trying to compute this limit: Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity] But, when I run the code above, ...
19
votes
2answers
320 views

Derivative of a pure function with SlotSequence

I can live with this but I can't figure out why the following is 0: Derivative[1][f[##] &][x] 0 From documentation ...
16
votes
1answer
271 views

Integrate returns imaginary answer for smooth, real function

Bug introduced in 7 or earlier and persisting through 10.4 I'm trying to evaluate the integral: $$\int_0^{\infty} \frac{1}{4 b \sqrt{\pi} r} e^{-(b-r)^2}(e^{4 b r} - 1) \mathrm{d}r$$ with $b>0$...
2
votes
1answer
102 views

Problem with imaginary/real parts of a complex function

I have a problem with this code: ...
0
votes
1answer
120 views

Reflective and Constant Flux Boundary Conditions

Can anyone tell me how I can use NDSolveValue to model reflective and constant heat flux boundary conditions. I am solving the heat equation. Essentially I have a ...
0
votes
0answers
38 views

Possibility of an output for this integral

Any clues as to whether an output exists for this expression where t and f are positive real numbers that can be treated as constants ...
3
votes
1answer
70 views

Numerical integration with parameter and plot

I'm working on this function: (0.0027 Sin[phi])/(1.05*Exp[-241w]+ Exp[239w]-Cos[phi]) I'd want NIntegrate this function on <...
1
vote
1answer
54 views

Integrating the product of two imaginary error functions

I am trying to evaluate the following integral: Integrate[Erfi[y] Erfi[z + y] , {y, -L, L}] which simply returns the input. How could I force ...
0
votes
1answer
68 views

Getting numerical values from integrated interpolating function [duplicate]

I have a list of data. I integrate them with interpolation. Lets say is the following: InterpolatingFunction[{{0.01, 4.82}}, <>][x] However, is that ...
2
votes
1answer
74 views

Define a function that is an integral that takes a function as argument [closed]

How can I define a function $F$ in Mathematica that does the following: $$F(a,b,P) = \int_a^b P(1-t) \, dt,$$ where $P(t)$ is some function, say, a polynomial? More specifically, I would like to be ...
1
vote
0answers
55 views

Mathematica refuses to integrate a function it knows how to integrate [closed]

Let $a$, $b$, and $k$ be positive real numbers, and consider the integral $$ \iiint\limits_{\mathbf{x} \in \mathbb{R}^3} \delta(a \lVert \mathbf{x} \rVert^k -b) \ \mathrm{d}^3\mathbf{x} = \frac{4\pi}{...
4
votes
1answer
117 views

Integration of a piecewise function

Define f[x_, i_] := Piecewise[{{1/n, 0 < x < (i - 1)/n}, {(i/n - x), (i - 1)/n < x < i/n} , {0, i/n < x}} ]; I would like to compute ...
1
vote
1answer
180 views

Dealing with indicator functions

I am calculating the integral of two indicator functions with Mathematica. I'm having difficulty in imposing assumptions. What I have done so far: To define an indicator function: ...
7
votes
3answers
1k views

Region bounded by x^2+y^2=1, y=z, x=0, z=0, in first octant

I need to draw (pencil and paper) the region bounded by $x^2+y^2=1$, $y=z$, $x=0$, and $z=0$ in the first octant. So the first assistance I asked of Mathematica is: ...
2
votes
1answer
111 views

How to solve this definite integral in mathematica?

I am a beginner in mathematica. I tried to solve this integration but not able to solve it. Can any body help me how to solve this integral in mathematica? Here is my integral, $$\int_{a}^{b} \frac{...
0
votes
0answers
64 views

To calculate the differential of a function

I need to calculate the differential of a function WaveNumber. However, when I compile the code, it generates followig error: Infinite expression 1/0. ...
2
votes
1answer
226 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
1
vote
1answer
51 views

Convergence of numerical integration with parameter in the region of integration

I would like to solve the integral: $ f(a)=\iiint\limits_{\mathcal{R}(a)}\frac{\sqrt{12\left(\left(\frac{x-y}{x+y}\right)^2+\left(\frac{y-z}{y+z}\right)^2+\left(\frac{x-z}{x+z}\right)^2\right)}}{\exp(...
1
vote
1answer
481 views

Why is my expression not a quantified system of equations? [closed]

Who can help me to understand why my code is wrong? It is giving me a message saying "is not a quantified system of equations and inequalities"?
6
votes
3answers
368 views

Using Grad, Div, etc in polar coordinates

I'm trying to use the newish functions Grad and Div to work with a PDE with circular or spherical symmetry and getting what looks to me like a wrong result. However, I'm not sure of this--perhaps I ...
2
votes
3answers
174 views

Calculate and plot the tangent hyperplane to a function of three variables

If f:= x^3 + y*x*z - z^2 + x*z and if {{1,2,1},{2,7,8},{6,0,2},{9,1,1}} are points, how can I find the tangent plane to <...
1
vote
0answers
147 views

A triple integral involving Abs over an ellipsoidal region

I'm a newbie and I'm trying to calculate a triple integral. But Mathematica doesn't output for half an hour and the CPU occupancy rate of my Wolfram doesn't changed when it's calculating. Here is the ...
1
vote
1answer
95 views

Help with singular integral

I'm new in Mathematica. I need solve a singular integral like $$\int_a^b \frac{A_0 + A_1 s + A_2 s^2 + A_3 s^3}{(B_0 + B_2 s^2 + B_4 s^4)(t-s)}ds$$ where $A's$ and $B's$ are reals and $0<a<t&...
4
votes
1answer
124 views

How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
1
vote
1answer
55 views

Evaluate list of determinant of Hessian at list of points

If f:= x^2y + z^3 + xz; and if {{1,2,9},{2,4,6},{9,5,9},{3,3,1},{6,5,3}} is a list of points. I need to evaluate the hessian at ...
10
votes
1answer
149 views

How to predict the degree of the first series coefficient?

Given an expression f that is a function of x and a number x0, what is the least integer <...
1
vote
0answers
46 views

Combining Manipulate and NDEigenvalues [closed]

I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following ...
0
votes
1answer
49 views

if-conditional tracing a half-sphere [closed]

I have a 2D discrete plane (x,y) and I would like to assign an amplitude to each point in the plane. Each dimension runs from -1 to 1. Say I want to assign an <...
4
votes
0answers
117 views

Puzzled by Assumptions [duplicate]

I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ...
6
votes
1answer
119 views

Unexpected Behavior from Integrate with PrincipalValue -> True

Bug introduced in 9.0 or earlier and persisting through 10.3 or later The following code, taken from my answer to 97024, ...
1
vote
1answer
90 views

Find Values of a and b for a Limit

I am having trouble finding the values of a and b for which $\lim \limits_{x \to 0}$ $(\frac{\sin (ax) + bx)} {(x^3)}) = -32/3 $. In Mathematica I have entered: ...
5
votes
1answer
147 views

How to do matrix calculus in Mathematica?

I would like to differentiate Ax with respect to A where A is a matrix. Now, obviously, I know the derivative is x but for more nasty expressions, is there a way to differentiate expressions with ...
4
votes
1answer
170 views

Bad performance of Integrate (and WolframAlpha) for an Integral of Bessel function of the first kind

The following returns unevaluated in WolframAlpha. Also in my machine Mathematica needs quite a lot of time to compute it. ...
2
votes
1answer
153 views

Derivatives of vectors

I have an issue with derivatives of vectors ...
0
votes
2answers
126 views

Why does Integrate[] return an expression with 'True' in it?

I am running Mathematica 10 on Windows 10. I'm trying to analytically evaluate a definite, principal value integral: ...