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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2
votes
1answer
76 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
58 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
120 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
185 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
114 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{...
2
votes
1answer
258 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
53 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
546 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
379 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
179 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
141 views

How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
1
vote
1answer
58 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
150 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
51 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
50 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
119 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
120 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
161 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
173 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
155 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: ...
0
votes
1answer
47 views

How can evaluate this function [duplicate]

Suppose this function F[c_, n_, s_] := Module[{}, Abs[s - 1 + (-1 + c)^n]] I calculate its second derivative on c ...
1
vote
2answers
172 views

Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
2
votes
2answers
93 views

Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
1
vote
1answer
76 views

About taking limit of an integral on Wolfram Alpha/Mathematica [closed]

I tried computing this quantity on Wolfram Alpha, but I couldn't get any answer: ...
0
votes
1answer
46 views

How can I solve this limit? [closed]

How can I solve this limit? thanks you!!!
0
votes
1answer
102 views

Hessian of function at many points

If f:= x^3 + 2yz + 5 x^2z is a function and if {2,0,1},{3,9,2},{8,5,6},{1,1,7} are points. I would like a Hessian of ...
1
vote
2answers
206 views

How would you calculate a contour integral? [duplicate]

How would you be able to calculate a contour integral of 1/(((z-1)^2)*(z-i)) over the contour |z-1| = 1? Not sure how to type ...
4
votes
0answers
112 views

Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta[0] at one of ...
4
votes
1answer
130 views

A 1D numerical integral Mathematica cannot compute, from physics

A well know result in theoretical physics is that a sum over Matsubara fermionic frequencies, i.e.: $$ S = \sum_{n=-\infty}^{\infty} h(\omega_n) \hspace{32pt} \omega_n=(2n+1)\frac{\pi}{\beta} $$ can ...
1
vote
0answers
135 views

Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...
0
votes
1answer
79 views

Finding the limit of a complicated expression [closed]

I've never used Mathematica before, so I'm really struggling to use it right now. I have a complicated function $\qquad \chi_{N}=\frac{[(2\cosh(J))^{N+1}(\lambda_{0}+\lambda_{1})^{N}((\mu_{0}+\mu_{1}...
0
votes
2answers
92 views

Please, help to find the area enclosed by the curves: ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}]

Please, Help to find the area between two curves. ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}]
2
votes
1answer
73 views
0
votes
4answers
288 views

Computing the first derivative in x, y ,and z

I have the following function: f:=x^3+yz+z^2x; I need to compute the first derivative in x, ...
1
vote
0answers
90 views

Determining the order of continuity (smoothness) of a function

Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ...
1
vote
2answers
50 views

Computation (or estimation) of an trigonometric Integral with a parameter

I am trying to calculate the following integral which contains a parameter. I have used the Integrate and FullSimplify using assumptions but Mathematica fails to produce an analytical solution. <...
2
votes
2answers
87 views

Integration result with incomplete beta function

I'm doing some calculations (double integration) which results in the incomplete beta function occurring as an end result. My input is: ...
1
vote
1answer
121 views

Plotting the exponential of 1/(y-x)

What is the best way to handle this situation? ...
0
votes
1answer
80 views

is this a possible integration bug? [closed]

I am find a discrepancy in evaluating an integral which has given me trouble all day. I have finally isolated where the problem is which I now frame: I define the integral in terms of a delayed ...
-1
votes
1answer
92 views

How to calculate the volume of a solid enclosed by surfaces? [closed]

I am asked to calculate the volume of the solid enclosed by the following equations: (in polar coordinates) r = Cos(θ) z = 2 + x² + y² z = 0 I know the second equation can be changed to its polar ...
0
votes
1answer
103 views

Derivative of $e^{-1/x^2}$ [closed]

I'm trying to get derivative of $$ e^{-1/x^2} $$ (also in other points than 0, e.g. 1) with D[E[-1/x^2], x] or ...
1
vote
1answer
55 views

How could I check if a differential equation crosses a specific value? [closed]

I'm designing a magnetic field to simulate relativistic speeds in a small cyclotron. I need to see if the ratio -R/B * dB/dR crosses 0.2 in a certain range, and right now I'm trying to do that by ...
0
votes
1answer
75 views

Only real numbers (Fullsimplify) [duplicate]

I've to do some complex calculation with Mathematica and if I put in my code it gives me something big back, so is it possible to say that my variables are strictly real numbers, by sing the ...
12
votes
1answer
172 views

Why do singularities disappear when performing convolutions with the Dirac Delta function?

I am attempting to perform a convolution involving the Dirac Delta function: $\int_{-\infty}^{\infty} \frac{1}{t+1} \cdot \delta(t+1)\ dt$ I would expect that the result of this integral is ...
2
votes
0answers
59 views

How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...