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
306 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 ...
1
vote
2answers
169 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 ...
2
votes
2answers
578 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 ...
2
votes
3answers
1k 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. ...
5
votes
3answers
297 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 ...
2
votes
1answer
210 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 ...
0
votes
1answer
264 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I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers.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 ...
15
votes
2answers
300 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 ...
4
votes
0answers
140 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: ...
7
votes
2answers
561 views

Simplifying the derivative of $|x|$

Context In[855]:= D[Abs[x], x] /. x -> 1 Out[855]= Derivative[1][Abs][1] In[856]:= D[x, x] /. x -> 1 Out[856]= 1 Question Why is ...
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
314 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
141 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
195 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
224 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 ...
-5
votes
1answer
124 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) ...
0
votes
2answers
331 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 ...
8
votes
0answers
205 views

Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
3
votes
3answers
390 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
483 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
135 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
134 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
379 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
294 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 ...
1
vote
1answer
264 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! ...
20
votes
4answers
799 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
2answers
282 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 ...
2
votes
0answers
165 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 ...
4
votes
1answer
178 views

Why does Assuming for Integrate not work as expected?

I'm trying to perform the following integral with Mathematica 7: ...
3
votes
0answers
138 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
49 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
186 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). ...
1
vote
1answer
317 views

How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...
3
votes
1answer
295 views

Turn list of edges into a polygon function

I have a list of coordinates that define the edges of a polygon and I would like to get a function defining the area Inside out if it (The polygon is convex and the points are in order) So that for ...
1
vote
1answer
492 views

How to solve this integral

I'm trying to deal with this article, but I don't understand how equations 5.9 and 5.10 were obtained. I tried to use Mathematica 8 to solve it, but the answer was different. I have a problem with ...
8
votes
1answer
333 views

Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
2
votes
4answers
196 views

How to evaluate this indefinite integrate $\csc(4x)\sin(x)$

I tried to integrate the following integral using Integrate[Sin[x]Csc[4x],x] and I am getting a strange result. $$\frac{1}{8 \sqrt{2}}\left(-2 i ...
6
votes
3answers
253 views

How to calculate this sum?

I want to find the sum $$S=f\left(\dfrac{1}{2012} \right) +f\left(\dfrac{2}{2012} \right) +\cdots + f\left(\dfrac{2011}{2012} \right), $$ where $$f(x) = \dfrac{4^x}{4^x + 2}.$$ I tried ...
8
votes
2answers
833 views
6
votes
2answers
246 views

Force integration to be linear over sum?

Is there an obvious way to force Mathematica to separately integrate the terms in a sum? According to the docs, When part of a sum cannot be integrated explicitly, the whole sum will stay ...
1
vote
1answer
117 views

Simplifying an Integral over Two DiracDeltas

Integrate[DiracDelta[a + k] DiracDelta[-b + k], {k, -\[Infinity], \[Infinity]}] (*DiracDelta[a + b]*) This works fine. But ...
4
votes
1answer
614 views

Computation of parametric integral

I am trying to compute the integral Integrate[(g^(u^(g - 1)))/(1 + u^g), {u, 0, t}] but as an answer I get my input expression. There must be something wrong ...
2
votes
1answer
867 views

Lie-Bracket of two vector fields

I'm new to Mathematica (installed couple of hours ago) and I need to compute a few Lie brackets between two vector fields $f$ and $g$. $$ f\left(\mathbf{x}\right) = \left( \begin{array}{c} ...
12
votes
3answers
3k views

Multivariable Taylor expansion does not work as expected

The basic multivariable Taylor expansion formula around a point is as follows: $$ f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot ...
0
votes
2answers
466 views

Why Can't Mathematica Integrate this?

I have the following problem from a textbook I am trying to integrate: So, following the directions in text, I am required to integrate each function. However, I cannot get Mathematica to integrate ...
10
votes
3answers
317 views

Typeset unbalanced brackets

In LaTeX, you can typeset expressions containing unbalanced brackets, by balancing them with an invisible delimiter \left. or ...
2
votes
1answer
643 views

How to find all roots and maxima and minima and graph them

I need to find all the roots of this function. I know it is simple to find by hand, however, I wish to learn how to do it so I can apply it later. The problem is that it only gives me one root. ...