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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3
votes
1answer
281 views

Sum and NSum gives different solutions

I'm working on a Mathematica lab for Calc. 2, and I ran into a problem last night. I was trying to calculate the midpoint approximation of the definite integral of ...
2
votes
3answers
166 views

Manipulate fails with f[x]=x^k/(1+x^k)

I have this code: Clear[f] f = Function[x, x^k/(1 + x^k)]; Manipulate[Plot[f[x], {x, 0, 5}], {k, 1, 10}] But nothing draws as I move the slider. Am I missing ...
1
vote
2answers
163 views

Solve f'[x]==0 for x

I tried the following: f[x_] := x^n/(k + x^(2 n)); Solve[f'[x] == 0, x] But I got the following response: Solve::nsmet: This system cannot be solved with the ...
0
votes
2answers
434 views

Using Mathematica to find poles of Gamma functions

I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper: $$\int\frac{d^d ...
9
votes
2answers
496 views

Find closed form expression for series expansion coefficients [duplicate]

Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function? Series will only give the explicit ...
0
votes
1answer
1k views
0
votes
1answer
214 views

Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
15
votes
4answers
4k views

Finding Limits in several variables

Is there a way to find a limit of a multivariable function, like $$\lim_{(x,y)\to (0,0)} f(x,y)$$ with Mathematica? When $f$ is continuous, we can use $$\lim_{(x,y)\to (0,0)} ...
2
votes
1answer
379 views

Volterra integral equation : 'literally match the independent variables' message

I want to solve an Volterra type Integral equation, and as a practice I entered the following code to my mathematica: ...
7
votes
2answers
672 views

How to change coordinates of integration?

Is there some built-in routine, some easier method to change variables of integration, without/before solving the integral? Say I have ...
2
votes
3answers
912 views

Multiple assumptions in integral

I want to add two assumptions, so I can get this probability density function to equal 1, though I can't get a solution. ...
0
votes
1answer
237 views

NumericQ prevents evaluation at a numerical value sometimes

I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers. The evaluation after assigning numbers to the symbols is still symbolic for some reason. The ...
2
votes
1answer
205 views

Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}]

I evaluated Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}] . thinking the answer should be approximately $\sqrt{\pi n/2}$. Mathematica gave me ...
5
votes
3answers
284 views

Integration gives ComplexInfinity when it shouldn't

A simple example of my problem is that Assuming[k ∈ Reals, Integrate[Exp[l]/((1 + Exp[l])*Exp[k*l]), l]] /. {k -> 2} gives ...
4
votes
0answers
137 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
15
votes
2answers
291 views

Inconsistent results from equivalent integrals

Why is Mathematica returning different values for these two integrals: I am just being introduced to complex integration, so it's possible that I have a misunderstanding of how this works, but in ...
9
votes
4answers
1k views

Plot a 2D vector path onto a surface

In my calculus 3 course, we're studying gradients and have a project that takes a combination of 3D Gaussian radial surfaces and a basic parametric path $r(t) = \{x(t),y(t)\}$ to see how the gradient ...
4
votes
4answers
293 views

Differentiating space curves

I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by ...
3
votes
1answer
138 views

Why is the output of my limit expression an interval?

Why is the output of the limit below an interval? It should be precisely $1$. ...
5
votes
1answer
189 views

Definite Integral over a path

What does Integrate[f[z], {z, a, b, c, d}] exactly calculate? Is it $$\int_a^b f(z)\, \mathrm{d}z +\int_b^c f(z)\, \mathrm{d}z +\int_{c}^d f(z)\, \mathrm{d}z ...
0
votes
1answer
208 views

Integrate function without specifying limits of integration

I've been having trouble to make mathematica evaluate an integral without specifying the values of the limits of integration. I mean, if I write ...
1
vote
1answer
220 views
0
votes
1answer
400 views

No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]

Is my input below correct? I've received no response from Mathematica. N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]] Thank ...
2
votes
2answers
513 views

3N-dimensional integral

I'm trying to compute a multidimensional integral with a variable number of dimensions. The integral is as follows: $$ \int d^{3N}\!p~e^{-\frac{\beta}{2m}\vec p^2}. $$ I have tried this ...
-5
votes
1answer
119 views

Help in coding of differential equations [closed]

I need some help with Mathematica. How can I do the following? Starting with f = y[0]^2 (y[0] is basically y with 0 subscript) ...
3
votes
1answer
4k views

Quick Hessian matrix and gradient calculation?

I am absolutely new to Mathematica and I actually want to try implementing a little optimization method . Long story short assuming I have a predefined two-variable function f(x,y) I want to ...
8
votes
0answers
193 views

Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
0
votes
2answers
307 views

Integrating hat functions

I am trying to integrate a hat function for a project that I am doing and have found a method to do so but I find it sloppy. Currently I have the basis function ...
3
votes
3answers
371 views

Symbolic derivative of $n$-term product

I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that $$ \frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0, $$ where $$ ...
5
votes
1answer
442 views

Integration over region given by inequality [duplicate]

Sometimes we need to integrate over some bounded region given by inequality/inequalities. Consider the following simplest example of area of an ellipse (LaTeX code): $\int_S dx dy$, where $S = \{ ...
-1
votes
1answer
131 views

Solving an equation for asymptotic dependence of the solution on a coefficient

I have an equation I want to solve, so I entered the following into Mathematica. (x^(17/6))/(a^(17/6)) - (x^2)/a -1 == 0 where I assume $a>>1$ and $x$ is ...
2
votes
1answer
128 views

How can I calculate a limit with a free variable?

For example, when I evaluate Limit[(1 + x^n + (x^2/2)^n)^(1/n), n -> Infinity] Mathematica does not output any result. When I evaluate ...
3
votes
1answer
340 views

Integrating over Bessel Function erroreous? (Hankel Transform)

The Hankel Transform is given by Integrate[f[x] x BesselJ[0,x t],{x,0,Infinity}] It is self-inverse, so ...
2
votes
1answer
272 views

How can I handle curve singularity in this NIntegrate integration?

Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region. (Why ...
0
votes
1answer
997 views

Given x[u,v], y[u,v], and f[x,y] how do I find D[f,x] in terms of u,v?

I have two functions x = x(u,v) and y = y(u,v). The chain rule says that for a function f(x,y), df/dx = df/du du/dx + df/dv dv/dx, and similarly df/dy = df/du du/dy + df/dv dv/dy. How do I get ...
9
votes
3answers
5k views

Finding unit tangent, normal, and binormal vectors for a given r(t)

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
1
vote
1answer
248 views

Calculus 1 Related Rates -Total Derivative issues

I'm trying to do part a) of this calculus 1 problem in Mathematica V9: http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx#Deriv_Rates_Ex4 Warning noob code below! ...
3
votes
3answers
1k views

Definite integral takes a very long time

I'm trying to integrate the following function: $$ r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}} $$ where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
3
votes
2answers
267 views

integral, explicit form

I want to estimate the ratio of integrals: $$ \frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
4
votes
1answer
170 views

Why does Assuming for Integrate not work as expected?

I'm trying to perform the following integral with Mathematica 7: ...
2
votes
0answers
158 views

About calculating Integrals

I am trying to Integrate the following Integral (all of the variables are reals) $$\int Exp(-(\cos^{-1}\left[\frac{\text{n}_0 (\text{v}_0-\text{x}_0)+\text{n}_1 (\text{v}_1-\text{x}_1)+\text{n}_2 (u ...
20
votes
4answers
774 views

An apparently “simple” limit?

Let $c$ and $h$ be real values. I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression: $$ \frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
3
votes
0answers
132 views

A triple sum related question

I'm trying to compute the triple sum Sum[1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}] but Mathematica doesn't return any value. ...
1
vote
0answers
48 views

Interested in knowing what substitutions were made to perform an Integrate[]? [duplicate]

Possible Duplicate: How does Mathematica integrate? Mathematica can perform the following integral with apparent ease (returning very fast with the result) ...
2
votes
1answer
175 views

Computing derivatives of a moment generating function

Dear Mathematica users, I'm trying to compute higher order derivatives of a moment generating function and then evalutate them in 0 (in order to get some moment conditions for a GMM estimation). ...
0
votes
1answer
180 views
6
votes
1answer
725 views

How to expand a function into a power series with negative powers?

Is there any way to expand this expression a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)]) (where a, ...
0
votes
1answer
493 views

Evaluate multivariable function [closed]

I'm trying to use Mathematica to evaluate many values of $f(x,y) $, like $f(-\pi,\pi) $ for $$f(x,y) = \left( \frac{-1}{4}\sin \left( \frac{x-y}{2} \right)\sin y \right)\left( \frac{-5}{4}\sin ...
1
vote
1answer
298 views

How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...
4
votes
1answer
419 views

Order of integration changes output of indefinite multiple integral in Mathematica 7

I'm trying to integrate a form-factor used in the calculation of radiation between two rectangles in perpendicular planes. While the integral is usually done over fixed limits, I am trying to do the ...