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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9
votes
6answers
820 views
0
votes
2answers
127 views

Continuity of function-example

I'd like to examine the continuity of the following function: f[x_] := Limit[(n^x - n^(-x) ) / (n^x + n^(-x) ), n -> Infinity] I know that this function isn't ...
8
votes
1answer
224 views

Curious solutions of x' = Sqrt(x), x(0)=4

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
5
votes
1answer
95 views

Integrate gives Simplify::infd “simplified to Indeterminate” message

Using version 10.1 on windows 7 Integrate gives this Simplify::infd Kernel message. What causes it, is this a bug? ...
1
vote
2answers
103 views

Plotting a function based of a complicated integral

I would like to have help in making a plot of a complicated function based a definite integral. - desired graph My calculation: ...
4
votes
0answers
117 views

DiracDelta and version 10.0.0 [duplicate]

Note: This issue seems to affect version 10.0.0 only and is fixed in 10.0.1, 10.0.2, 10.1 and 10.2 When evaluating the following two inputs: ...
0
votes
0answers
68 views

Is there a way for me to get Mathematica show its steps? [duplicate]

I have seen similar questions but they were quite dated (3+ years). When performing, say an Integration, it would be beneficial to see the major steps such as variable substitution, change the order ...
0
votes
1answer
74 views

Using Assumptions in Expressions that Evaluate to be Elliptic Integrals

I have the following integral that I am trying to evaluate in Mathematica: $\int \sqrt{\alpha + m g l \cos(q)} dq$. If $\alpha > m g l$, then the result is a complete elliptic integral of the ...
0
votes
3answers
176 views

Revolution of two curves around the y-axis

I've looked through the other posts on rotating a function around the x or y axis and haven't had any luck. my question is this how do i rotate the area between the functions $f(x)=x^2+1$, and ...
13
votes
3answers
623 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 ...
0
votes
1answer
121 views

How to compute DSolve or NDSolve for kind of piece wise function?

I need to Compute the expression for two functions. q[t] and q1[t] over certain range of time. The code is given below. ...
5
votes
1answer
101 views

Second derivative of SmoothKernelDistribution PDF?

Does anyone know why I can't seem to get a second derivative of this interpolating function f? In this example, h[x] is zero ...
2
votes
1answer
121 views

Computing a Gamma function-Gaussian integral

I would like to compute the following function: Integrate[Gamma[k,0,Exp[-2 e x^2]],x] k is an integer and ...
2
votes
3answers
293 views

How do I find the area between two polar curves?

More specifically above r=6 and below r=4+4cos(θ) graph of the two curves PolarPlot[{6, 4 + 4 Cos[t]}, {t, 0, 2 Pi}]
5
votes
2answers
236 views

Double improper integral

I am trying to compute the following double integral: Integrate[(r BesselJ[0, r])/( 2 (r^2 + z^2)^(1/2)), {z, -Infinity, Infinity}, {r, 0, Infinity}] Which ...
10
votes
1answer
430 views

Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
1
vote
0answers
64 views

Multiplying two sets of data (x,y values, but different x density) followed by integration of the product

I've been trying to do this by myself today, but no luck yet. Please, see attached image. Basically, I do have two data sets A (x1,y1) and ...
0
votes
0answers
80 views

Multiple Integral of equation including dx prime? [closed]

I'm hoping someone can verify I've written this function properly since I'm a little new to Mathematica. What I'm attempting to do is code a function that describes a gravitational field of an ...
7
votes
2answers
331 views

Integrate fails for generic parameters but works for any specific values (v. 10.0.x bug)

Bug introduced in 9.0 and fixed in 10.1 I was trying to get the following integral ...
0
votes
1answer
127 views

Limit of a sum as number of terms approaches ∞

Is it possible to find the limiting value of function at large N? ...
7
votes
2answers
523 views

Integrating a function over a surface integral

From a first principles bandstructure calculation I get an energy scalar field in three dimensions $E(x,y,z)$. It's now easy to plot a constant energy (contour)-surface for dedicated values ...
3
votes
2answers
158 views

Strange results from evaluating a simple integral

I am trying to do a seemingly simple integral in Mathematica 10 and am getting strange results: ...
10
votes
1answer
279 views

Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
4
votes
2answers
133 views

Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
2
votes
0answers
99 views

How do I numerically integrate over a data set that has uncertainties? [closed]

I have a 1D data set {xi, yi} with no uncertainties in xi and with uncertainties dyi in yi. The resulting discrete function is monotonic and relatively smooth and I would like to integrate the ...
0
votes
2answers
61 views

Integrating expressions with several terms and delta functions

So I want to integrate an expression that looks something like this: Integrate[f[x]+DiracDelta[x-y]g[x],{x,-Infinity,Infinity}] With some more terms added with ...
2
votes
1answer
94 views

Forcing Exact Outputs for Integrate [closed]

I'm trying to compute the following triple integral: ...
1
vote
1answer
115 views

Partial derivative of defined function with vector input

Background: Have written a formula for the refractive index for a glass slab (n) that depends on the variables t,a and d. Now I want to calculate for example some sort of error and I'll be needing to ...
0
votes
1answer
64 views

Boundary condition not correctly imposed for NDSolve

I notice that when plotting the below NDSolveValue ...
2
votes
1answer
89 views

an Integral that should be doable:

Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta] - \[Alpha]]], {\[Beta], 0, 2 \[Pi]},Assumptions -> z \[Element] Reals] correct answer is [ I think ]: ...
9
votes
1answer
260 views

Why don't products of Dirac deltas integrate correctly?

Bug introduced in 10.0.0 and fixed in 10.0.1 The integral $\int \int \ \delta(x) \delta(y) \ dx dy=1$ evaluates to 0 in Mathematica ...
3
votes
1answer
106 views

Strange Integrate messages / $RecursionLimit being ignored

Bug introduced in 10.1.0 and fixed in 10.2.0 The following behavior was observed in Mathematica 10.1 (Windows 64 bit) When attempting to evaluate the following integral, Mathematica outputs ...
0
votes
2answers
95 views

Fix my code to return a table of values

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
-1
votes
1answer
57 views

It is possible to calculate a two vector integral

I have this problem: calculate the integral of: -1+Sqrt[2*d+1] with d being a distance of two points in a 60$\times$60 box ...
28
votes
1answer
446 views

many indefinite integrals do not evaluate in 10.1, looking for the cause

Bug introduced in 10.1 and fixed in 10.2 Many integrals no longer evaluate in V 10.1 when they did in 10.0.2 Here are some 23 integrals as an example, that all produced results in V 10.0.2, but ...
0
votes
0answers
46 views

Calculus with Mathematica, books, interesting examples [duplicate]

I'm looking for a book where I could find informations and interesting examples regarding examine functions of one variable like continuity of functions, limits, differentiability in Mathematica. I'd ...
4
votes
1answer
145 views

Mathematica does not help in this integral

I am trying to solve this integral with assumptions: ...
1
vote
0answers
51 views

Computing integral involving derivatives

I want to evaluate an expression $\int_C g(\nabla f)ds$. This is an integration along a curve $C$ in a plane given as a function of some parameter $s$: ...
0
votes
1answer
71 views

Can't obtain a closed form expression for an integral

I am trying to find the result of quite a complicated double integral. While the first part (being a Principal value integral) gave no particular problems, the second one is not providing any closed ...
8
votes
0answers
73 views

Finding simplifying substitutions for an integral involving limits and integrand

[The following is based on a William Lowell Putnam Mathematical Competition problem.] Consider the definite integral: $I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\sqrt{\log ...
2
votes
3answers
179 views

How can I get the exact value minimum of this function?

I want to find min of the function $$\frac{1}{\sqrt{2 x^2+\left(3+\sqrt{3}\right) x+3}}+\frac{1}{\sqrt{2 x^2+\left(3-\sqrt{3}\right) x+3}}+\sqrt{\frac{1}{3} \left(2 x^2+2 ...
0
votes
1answer
82 views

Four integrals, how can I expedite the calculations?

I have to calculate the following multiple integrals (4 integrals) ...
5
votes
2answers
388 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
1
vote
1answer
210 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
0
votes
0answers
109 views

How can I verify double integral solution?

I have a double integral as follows \begin{equation} 1-(\int_0^\infty (\frac{Cje\cdot Cte \cdot e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)^2} + \frac{e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)}) ...
1
vote
1answer
140 views

How can I simplify a triple integral with exponentials?

I want to simplify the following triple integral with exponential terms. \begin{equation} \int_0^\infty\int_0^\infty \int_0^\infty \frac{1}{R\,G} e^{-p(1+R\,a)-q\, b \frac{1+R\, a}{1+G\, x}}\, ...
6
votes
1answer
483 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. ...
4
votes
2answers
141 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
3
votes
3answers
75 views

Multiple integrals where the number of integrals is aribtrary

I know that I can do, say, a triple integral such as $$\int_{a_x}^{b_x}\int_{a_y}^{b_y}\int_{a_z}^{b_z}f(x,y,z)\,dz\,dy\,dx$$ with the input ...
-5
votes
1answer
76 views

Show steps to compute limit [closed]

I'm trying to use Mathematica to compute a limit, because I have no idea how to compute it by myself. The limit should be: $$\lim _{n\rightarrow \infty }\dfrac {2^{n+1}-n-2}{2^{n}}$$ Any ideas?