Tagged Questions

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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1answer
662 views

How does Mathematica integrate?

Basically, this question can be considered to be an extenstion to my other question. What I wanted to do was this integral as homework (it is indefinite BTW so no approximations using Simpson's Rule ...
4answers
923 views

Generating evenly spaced points on a curve

In the KnotData package a simple command such as points = Table[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi, 0.1}]; will ...
1answer
326 views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
3answers
844 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 ...
1answer
257 views

Plot showing discontinuity where it shouldn't

I was trying to integrate a continuous function with a kink and I did it two ways and both ways the plot of the result shows a discontinuity. I also later want to differentiate the Integrated ...
2answers
658 views

Bug in Integrate for Mathematica

Consider the following: ...
2answers
223 views

How to simplify the integration result of the following program?

In the following program, the fec[x] is a function depending on $x$ while q3[t] and q5[t] ...
2answers
199 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 ...
2answers
896 views

How to find (numerical) value of a derivative at point?

I have the following function: f[0, 0] = 0 f[x_, y_] := Exp[-(x^2 + y^2)^(-1)] How do I find its partial derivatives at any given point, including $(0,0)$? This ...
3answers
243 views

How do I evaluate several n-th derivatives of a function at one point?

I have a question where I have to compute a Table containing $f^{(n)}(0)$ for n = 1, ..., 5, where $f^{(n)}$ denotes the $n$th ...
2answers
1k views

How to specify assumptions before evaluation?

If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example : ...
3answers
458 views

Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
4answers
411 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 ...
5answers
993 views

How can you compute Itō Integrals with Mathematica?

How can you compute Itō Integrals with Mathematica? I tried searching through the documentations but I didn't find anything. P.S. I was not at all sure how to tag this question. I had to put in at ...
5answers
926 views

Using implicit differentiation to find a line that is tangent to a curve at a point

A few days ago I asked about using differentiation to find a line that is tangent to a curve at a given point. J.M. provided a very elegant way to solve these kinds of problems in Mathematica. Now ...
3answers
997 views

Derivative of real functions including Re and Im

When deriving functions using Re, Im or Arg (and probably some other functions as well), ...
3answers
580 views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
5answers
626 views

Does $x>0$ imply that $x\in\mathbb{R}$?

Let’s assume I input Assuming[x > 0, expression] Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
2answers
1k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
1answer
253 views

Finding residues of multi-dimensional complex functions

Say I have a function $f$ of $n$ complex variables, $\{ z_i \}_{i=1}^{i=Nc}$. And then I want to contour integrate the expression such that for each $z_i$ its an integration on an unit circle about ...
1answer
233 views

ReplaceAll[] and Limit[] don't give correct results for this expression under extreme variables [duplicate]

Possible Duplicate: Funny behaviour when plotting a polynomial of high degree and large coefficients 1/x^2 + (3 + x)/(6 (1 - Exp[x] + x)) ——This is a ...
2answers
381 views

Why aren't these additions of integrals and summations equal?

I have the following code: Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]] To test: \int{\left(f(x) + ...
1answer
333 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, ...
5answers
559 views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

Consider the function f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to ...
1answer
409 views

Hankel Transform integrals won't work in Mathematica

I'm trying to do this integral, which is shown on the Wikipedia page on the Hankel transformation: $$\int_0^{2\pi}\mathrm d\varphi\;e^{\mathrm im\varphi}e^{\mathrm ikr\cos(\varphi)}$$ The answer is ...
1answer
429 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 ...
2answers
888 views

Equation of a line that is tangent to a curve at point

A common problem in the derivative section of calculus texts is "find the equation of the line that is tangent to the curve $y = \ldots$ at the point $P$." To find the line that is tangent to \$y = 2 ...
2answers
446 views

Suppressing negative roots in Mathematica

Problem Using Mathematica's Solve operator can sometimes lead to an output involving a positive and negative root (say when solving for a variable such as ...
4answers
354 views

How to make a Line[] with no end?

I'm trying to do this: In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
5answers
377 views

simplifying $\frac{\log x^a}{a} = \log x$

If one makes the assumptions $x>0,a>0$, then $\frac{1}{a}\log x^a = \log x$. Thus, in Mathematica, Simplify[1/a*Log[x^a], {a > 0, x > 0}] returns ...
1answer
233 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 ...
3answers
519 views

how to simplify symbolic integration

The following is the code: ...
4answers
538 views

Mathematica gives wrong answer for integral

When I execute the following, Integrate[Exp[-w^2 + I w^3], {w, -\[Infinity], \[Infinity]}] I get ...
3answers
399 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 ...
2answers
247 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 ...
2answers
192 views

Using Mathematica to find poles of Gamma functions [closed]

I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper: \int\frac{d^d ...
2answers
361 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 ...
2answers
144 views

Why does Integrate declare a convergent integral divergent?

When I try this command Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10] Mathematica declares that the ...
3answers
150 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 ...
3answers
480 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 ...
1answer
217 views

Check homework integration in Mathematica

Given in my homework I have to compute (by hand) $$\iint\limits_{x^2+y^2\leq 1}(x^2+y^2)\,\mathrm dx\,\,\mathrm dy.$$ My solution so far: Let $f(x,y)=x^2+y^2$ and \$K=\{(x,y)\in\mathbb{R}^2:x^2+y^2\leq ...
1answer
92 views

Why does Assuming for Integrate not work as expected?

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

Simple ways to evaluate a derivative at a point?

The contrast in behavior between, say, f[x_] = Sin[x^2]; f'[2] vs. u[x_, y_] = Cos[x + y^2]; has always bothered my ...
2answers
215 views

Strange result when integrating BesselJ functions

Consider the following integral: ...
1answer
97 views

how to reduce the time to calculate triple integral

i want to evaluate the following integral, but it takes 15 min to do it. i must reduce the time to calculate it, i have to do a table and create a graph, but takes too long. anyone have an idea ? ...
0answers
196 views

About doing an integral

For a given integer $N$ and some function $f(x,y)$ I want to be able to do an integration of the kind, \$\int_{0} ^{\infty} \prod_ {i=1}^N da_i e^{[\sum_{n=1}^{\infty} \frac{1}{n} \left[ N + ...
1answer
138 views

How to collect q[t] from the following integration

As shown in the following program, the q[t] in a can be collected from the integration by defining the integration of ...
2answers
392 views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
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