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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4
votes
4answers
405 views

$L = \lim\limits_{z \to 1} \frac{1-z}{1-z^\ast}$ evaluates incorrectly

I'm about 90% certain this is a Mathematica issue, not me making a silly mistake. I'm trying to evaluate $$L = \lim_{z \to 1} \frac{1-z}{1-z^\ast}.$$ Naively entering ...
0
votes
1answer
118 views

Writing a Code to plot a function that includes a double integral [closed]

I am trying to write a code in Mathematica. Here are my steps: F[u_] = Some nontrivial and long expression in terms of u; Umax[x_, y_] = Some expression in terms of x and y; W[x_, y_] := integral ...
6
votes
1answer
224 views

Incorrect evaluation of integral involving a DiracDelta, whose argument has infinitely many zeros

Let's say $X>0$ is a random variable with probability density $p_X(x)={\rm e}^{-x}$. Define the random variable $Y=\sin(X)$. From the transformation theorem for probabilities we know that its ...
1
vote
1answer
96 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
1
vote
2answers
87 views

Integrating a compound expression

I have an integral of the form I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])BesselJ[0,kr]dr where Besse1J[0,kr] is the modified ...
2
votes
1answer
524 views

Inverse gradient operator

I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
1
vote
1answer
125 views

Mathematica is able to compute an indefinite integral but not the corresponding definite one

I'm trying to compute the following definite integral (μ is a parameter): ...
7
votes
2answers
546 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
3answers
394 views

Bug in complicated Limit

The code Limit[Log[2 - Sin[x]*Cos[x]], x -> Infinity] outputs Interval[{0, Log[3]}] in Mathematica 10.0.2.0 . It should ...
3
votes
2answers
552 views

Color a Function by its Derivative

Mathematica's ColorFunction seems to struggle with coloring a function "y" by its derivative D[y,x]. This is a seemingly simple task, but Mathematica can't handle it. While I can certainly evaluate ...
0
votes
1answer
66 views

Integration of an expression yields wrong result

I'm trying to find a general expression for the definite integral of ...
2
votes
2answers
261 views

After definite integration the result is still integration variable dependent!

This integral $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\frac{\exp \left(\frac{2}{x^2+y^2+z^2+1}-2\right)}{\left(x^2+y^2+z^2+1\right)^4}dzdydx$ or ...
-4
votes
1answer
67 views

NDSolve a differential equation depending on some parameter

I have to solve the differential equation, to get a plot of T and R, ...
2
votes
1answer
419 views

Calculating the area under a curve

How can I calculate the area under a curve after plotting discrete data as per below? ...
1
vote
3answers
149 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
0
votes
1answer
63 views

Derivatives of overscript variables

If we have an expression with terms of some variable and terms of the same variable with some overscript, the differentiation of this expression does not entirely function. The problem is that ...
-1
votes
1answer
149 views
4
votes
2answers
193 views

Integration of a Rational Function returns RootSum[]

I am trying to solve an integral given below: Integrate[r^2/(-α r^3 + r^2 - 2 m r + Q^2), r] but since coefficients of this cubic polynomial are as parameters, ...
8
votes
4answers
372 views

Definite integral incorrectly giving a nonreal value

fixed in 10.1 (windows and Mac OS X) In Mathematica 10.0, when I enter N[Integrate[Sqrt[1+x^3],{x,-1,3}]] I get a nonreal value (i.e., the imaginary part is ...
0
votes
2answers
83 views

A simple integral operation

Evaluating the following expression results in a non-zero output FullSimplify[Integrate[2 f[x], {x,0,1}] - 2 Integrate[f[x], {x,0,1}]] I think the output should ...
1
vote
1answer
130 views

Partial differentiation mixes up variables

Consider $$ U \equiv \dot{\theta} - \theta \ ,$$ where as per usual $\dot{\theta} = \frac {d \theta}{dt}$. We then have $$ \frac {\partial U}{\partial \theta} = -1 \quad , \quad \frac {\partial ...
0
votes
0answers
99 views

Fourier Transformation of a List

As we know the FourierTransform goes a function of t ,for example, f[t] to ...
2
votes
1answer
164 views

Complex Integration

There are some sequential functions: ...
7
votes
1answer
212 views

Suspected bug in Integrate

Bug introduced in 9.0.1 or earlier and fixed in 10.1.0 In version 10.0: ...
0
votes
1answer
120 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 ...
2
votes
1answer
102 views

How to check if Integrate solved the integral?

This seems something that must have been asked before, but I am not able to find something. Integrate does not return status nor throw error when it can't find antiderivative. It just returns the ...
0
votes
3answers
76 views

Listing all cubic order derivatives of a function of 4 variables

What would be the best way to list/print all cubic order derivatives of a function of 4 variables? I was thinking about iterating Derivative[i,j,k,l][func][0,0,0,0] ...
25
votes
2answers
330 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
0
votes
1answer
112 views

Graphic solution lagrange multiplier (cant get one)

I need to find the maxima and minim of a function. I did analytically with no problem but now I need to show in a graphic the intersection of the functions. My function is: ...
7
votes
1answer
83 views

Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
3
votes
1answer
115 views

How to perform “implicit” integration? [duplicate]

(I wasn't sure what to put for the title, so feel free to improve it if you can think of a better one.) How do I evaluate an integral that contains an unknown function of the integration variable ...
0
votes
0answers
78 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
-3
votes
1answer
121 views

Integration with mathematica? [closed]

I am very new to Mathematica. I am trying to evaluate ∫ (1+lnx)Sqrt(1+(xlnx)^2) using Mathematica. I know a substitution must be done so I have set ...
-1
votes
1answer
68 views

Taking the third derivative of: $f = (ln (x) + e^{4 (x - 1)})^{15}$? [closed]

I am VERY new to Mathematica and struggle to solve this question: Let $f = (ln (x) + e^{4 (x - 1)})^{15}$ and calculate what value $f^{(3)}(1)$ have. How would you go about to solve this in ...
0
votes
1answer
68 views

Finding the limit of powers to infinity [closed]

Limit x -> Infinity (1 - e^-x)^e^x I keep getting that the answer is 1 but according to wolfram alpha it is 1/e. Could someone show me how. Thanks.
2
votes
0answers
72 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
0
votes
2answers
743 views

How to find volume of an egg [closed]

I am a first time user of mathematica. I've been trying to figure out how to find the volume of a) f(x)=(ax^3 + bx^2 + cx + d)sqrt(1-x^2). I have been scouring the internet for a solution on how to ...
0
votes
1answer
93 views

How should i correct this error?

Sn = Sum[1/((k + 1)^2), {k, 1, n}] SSn = Sum[Sn*Fibonacci[n], {n, 0, m}] Limit[(1/(Fibonacci[m + 2] - 1))*SSn, m -> Infinity] Limit::ztest1: Unable to ...
7
votes
1answer
337 views

How to code around known MMa special-case failures?

Fourier Analysis and Signal Processing often require these integrals on functions f[x] that won't be known in advance. ...
1
vote
1answer
116 views

How to rotate vectors in vector plot?

I'm writing an exam for my calculus students and am seeking help with using Mathematica on a particular problem. Here's my idea: I want to give a multiple choice problem that has four choices of ...
0
votes
0answers
131 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. The equation below presents the final form ...
4
votes
1answer
278 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
-4
votes
1answer
49 views

How to Integrate [duplicate]

I have the following Table ...
-2
votes
1answer
137 views

How to integrate a table? [closed]

I have the following Table (dy/dx)={24,24.5,25,25.4} How do I proceed to interpolate the table and compute Integrate[Sqrt[1+(dy/dx)^2],{x,65,68}] ?
1
vote
2answers
89 views

Integrate full derivative

I want mathematica to do Integrate[D[f[x],x], {x,0,t}] and achieve the answer f[t]-f[0]. But Mathematica doesn't intergrate ...
5
votes
2answers
181 views

Multidimensional integral to compute the end-to-end distribution of a FENE ideal chain

How do I evaluate the mean end-to-end squared distance of a FENE ideal chain at fixed inverse temperature $\beta$ in the canonical ensemble? This quantity is defined as the mean value ...
2
votes
1answer
79 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
1
vote
0answers
85 views

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
3
votes
2answers
156 views

Calculating a Volume Integral limited by two z planes and a given conical surface [closed]

I have been given this question to integrate a function over a region, and I have been at it for 6 days now and I can not for the life of me come up with a solution because the integral is way too ...
1
vote
0answers
118 views

Where can I learn to use mathematica comprehensively? [duplicate]

I've heard great things about all the wonders and capabilities of mathematica. I've had the software for sometime now, but all I know how to do are simple calculations and stuff shown in the hands on ...