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
42 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
35 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
166 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 : ...
12
votes
3answers
345 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 ...
-2
votes
1answer
46 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
0
votes
1answer
97 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
1
vote
1answer
90 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
5
votes
1answer
242 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. ...
2
votes
1answer
97 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
0
votes
0answers
33 views

Series Expansion of Differential Operators [duplicate]

We know about the possibility of series expansion of a function in Mathematica. Same as below, where a function f[a x] is expanded around zero up to 5th order. ...
3
votes
3answers
93 views

Factoring a separable integral with a product of independent integrands

I would like to input someFunction[Integrate[p[x] p[y], {x, -1, 1}, {y, -1, 1}]] and to get the following output ...
0
votes
0answers
45 views
0
votes
2answers
60 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 ...
3
votes
0answers
40 views

Indeterminate expression 0(I*Infinity]) on indefinite integrals on first use only

I do not know if this is new or not, I googled before. Windows 7, 10.1 64 bit: Integrals generate this error message The strange thing also is that the message shows up the first time the command ...
4
votes
2answers
65 views

Inconsistent Integration involving DiracDelta at boundaries

I'm working on integrals involving DiracDelta functions at the boundary of the integrals. I'm confused by the output Mathematica v10.1.0 gives me in this case: ...
5
votes
1answer
56 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? ...
7
votes
1answer
142 views

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

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
2
votes
1answer
90 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
1
vote
2answers
82 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: ...
3
votes
0answers
79 views

DiracDelta and version 10.0.0

Note: This issue seems to affect version 10.0.0 only and is fixed in 10.0.1, 10.0.2, and 10.1 When evaluating the following two inputs: ...
3
votes
1answer
184 views
0
votes
2answers
83 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: ...
0
votes
1answer
54 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
0answers
44 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
3answers
82 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 ...
0
votes
1answer
81 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. ...
23
votes
1answer
724 views

Undocumented use of Integrate: Integrating over regions

I have come across a few questions asking about integrating over regions. And while the answers are impressive there should be a better more consistent way. So my question is, are there ways, ...
2
votes
1answer
64 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: ...
3
votes
6answers
863 views

Compute Triple Integral on spherical coords

I need to compute: $\int \int \int z dxdydz$ over the domain: $\{x^2+y^2+z^2\leqslant 16,z\geqslant 0\}$ Im trying to use spherical coords as: $$\int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} ...
1
vote
1answer
298 views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
0
votes
1answer
92 views

Limit of a sum as number of terms approaches ∞

Is it possible to find the limiting value of function at large N? ...
2
votes
1answer
66 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 ...
8
votes
2answers
309 views

About an infinite product

I have a curiosity as regards the infinite product below. I wonder why Mathematica v.8.0. says the limit is $1$. This is not true. ...
3
votes
2answers
137 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: ...
1
vote
3answers
141 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}]
0
votes
1answer
188 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
5
votes
2answers
143 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 ...
5
votes
0answers
83 views

Integral formula for the inverse Laplace transform doesn't work?

The direct implementation of the definition of the inverse Laplace transform using Integrate fails in the following case: ...
1
vote
0answers
38 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 ...
1
vote
0answers
47 views

Calculating perturbative expansion in qft

Is there an easy way to use mathematica to take functional derivatives to do perturbation theory in qft? I know there is a package for functional derivatives, but can I get an example of how to use it ...
5
votes
2answers
417 views

Probability: Calculating a multiple integral

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=2,5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Cauchy Distribution having location parameter $\mu_{10\times 1} = ...
5
votes
0answers
113 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 ...
9
votes
1answer
300 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
2
votes
0answers
35 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
27 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 ...
1
vote
1answer
42 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
34 views