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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2
votes
1answer
96 views

Implicit derivatives in one line. How do I do it?

I have this little script to derive implicitly $PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; Example: ...
10
votes
6answers
789 views

Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
4
votes
2answers
126 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: ...
26
votes
1answer
461 views

Are greek symbols causing different evaluation?

I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me. Let us define a piecewise function: ...
6
votes
2answers
231 views

Curvature Application

I found these amazing animations at https://courses.engr.illinois.edu/tam212/avt.xhtml#avt which I think will be wonderfully useful when teaching multivariable calculus next semester. I've started to ...
3
votes
2answers
485 views

How to numerically integrate this integral

I am unable to do this definite integral in Mathematica 9. Is there any command so that I can get the numerical value of the above integration? Code: ...
5
votes
3answers
242 views

Limit of Nested Radical $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+…}}}$

I want to find limit of infinite nested radical $\quad \quad \sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$ but I don't know how to define this expression in Mathematica. How can I define it and ...
7
votes
1answer
373 views

Need help with the Lagrange multiplier method

Well I am new to Mathematica and got really stuck solving this problem. In class, I was ask to use the Lagrange multiplier method to find the maximum and minimum value of $f(x,y) = x^2+y^2$ which ...
15
votes
5answers
888 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 ...
11
votes
2answers
5k 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 ...
1
vote
2answers
88 views

Ask about the variable and constants in partial derivative in a loop

EDITED I have a function in a list like : func={2(x^2)+x*y+3(y^2)}; I want to have a UI that ask me which parameter (x or y) is a variable in a ...
2
votes
2answers
153 views

MaxValue of a periodic function

I want to find the maximum of a periodic function on the interval [-Pi,Pi]. What I tried is the following: ...
10
votes
2answers
288 views

Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$

I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$ I tried ...
4
votes
3answers
146 views

How to get multiplication of the elements of a specific list/Matrix

Assume there is a list: List1={a,b,c,d}; Then I want to get these calculation: ...
1
vote
2answers
64 views

How to tell Mathematica that a limit converges to a product of two variables

I have looked through the manual and Im simply just stuck trying to make Mathematica solve this: ...
2
votes
0answers
127 views

Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
6
votes
1answer
181 views

Defining a function implicitly and calculating its derivatives

I'm interested in using Mathematica's symbolic manipulation to obtain, for a particular function $f$, derivatives of arbitrary order evaluated at zero. Normally I'd use the ...
0
votes
1answer
94 views

FullSimplify not giving me a physically useful answer for Mott scattering

I am using Mathematica to find the cross-section for Mott scattering over an extended target. I evaluated ...
3
votes
3answers
167 views

Calculating $\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$

How can we force Mathematica to compute this limit? $$\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$$ It seems it ...
5
votes
1answer
243 views

How to plot the result of this singular integral?

Please I open a new post here after this one : http://mathematica.stackexchange.com/a/59203/10158 Now I want to plot the function $f(a,b)$ as a function of $b$ for different values of $a$ : $a=0.5$ , ...
2
votes
1answer
209 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
3
votes
1answer
130 views

Why does Mathematica list the variables in a double integral backwards?

I am an advanced novice Mathematica user and have done a fair amount of single-variable calculus things with it. This semester I am using Mathematica for multi-variate calculus and when I tried to ...
0
votes
0answers
50 views

Bounds of a closed curve

how to find the rectangular bounds of a curve which is of the form f(x,y) and forms a closed loop. The sides of the rectangle are parallel to the axes and are tangents to the curve. The time taken for ...
1
vote
2answers
94 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 ...
11
votes
3answers
389 views

Find asymptotics of $\sum\limits_{i=0}^{n/3} 2^i \binom{n-i-1}{\frac{2n}{3}-1}$

I have an expression 2^n / Sum[ 2^i Binomial[ n - i - 1, 2n/3 - 1], { i, 0, n/3}] ...
4
votes
1answer
93 views

Formal Differentiation

I'm trying to formally differentiate an expression. (I am aware of how to differentiate formally?, but am unable to generalize the idea) For example: ...
2
votes
1answer
121 views

Integration doesn't work

I'm trying to obtain the following integral: ...
0
votes
0answers
87 views

PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
18
votes
5answers
1k views

Mathematica gives wrong result while Wolfram|Alpha is correct

Why does Mathematica and Wolfram|Alpha give different results based upon the same code? I know Wolfram|Alpha's 7.85 is correct.
2
votes
1answer
121 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
1
vote
1answer
125 views

Absolute uncertainty and error propagation with lists [closed]

I am trying to do some error propagation using mathematica. This is my second day using the program. I am trying to take the derivative of a numerical function that is made up of the following lists. ...
6
votes
1answer
243 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I ...
0
votes
0answers
52 views

Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
2
votes
2answers
179 views

Two ways to speed up slow Integrate[]s? (Can't do either)

I run into problems like this all the time on the complicated integrands I pass to Integrate. The following code works but takes a veeery looong time: ...
15
votes
6answers
526 views

No response to an infinite limit

Trying to compute this limit, things seem to get frozen, even for hours. What would you recommend to fastly compute it? ...
0
votes
2answers
141 views

How to help MMA to simplify integrands?

MMA sometimes has to grind for LONG time on easy integrals: ...
8
votes
2answers
618 views

Weird plot with SphericalPlot3D

Taking the equation $x^2-y^2-z^2=1$ and using ContourPlot3D: ContourPlot3D[ x^2 - y^2 - z^2 == 1, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}] Yields the proper image. ...
5
votes
3answers
277 views

Derivative of contour in ContourPlot

Sorry to bring this question up again, since there are many similar questions on the site. I use to think this is a easy job to do, because for the worst case I can follow the answers on this site. ...
1
vote
1answer
56 views

How to find all gaps of a domain of a function with Mathematica 9?

I tried it liek this: My test-function: fuu[x_] := Expand[FullSimplify[1/x]] how i find the domain: ...
0
votes
0answers
18 views

Not Simplify automatic some expression(values)

I try to calculate $$\text{res}\left(h(z) (\psi ^{(0)}(z)+\gamma )^2,\{z,-4\}\right)$$ the result is $$\frac{1}{6} \left(6 h'(-4)-25 h(-4)\right)$$ the result it is possible to write as $$2 \left(6 ...
6
votes
2answers
155 views

Different results of the integrate $\int \frac{\sin (\pi s)}{(s-0.5)^2+90} \,ds$?

Following results are given of big different values. I think NIntegrate's one is right but others are not explained. ...
8
votes
3answers
562 views

Biot-Savart Law/Magnetostatics Solution

I am working on solving the Biot-Savart Law equation for the magnetic field around a charged ring of uniform current density. The expression that Mathematica gives is rather nasty, as expected. Notice ...
2
votes
1answer
132 views

Numerically integrate and plot $f(x;p)$ for a range of the parameter $p$

Suppose we have an integral of the form $$I = \int_a^b dx \, \sin(px), \tag{1}$$ where I've take $f(x;p) = \sin (px)$ to be specific. I want to plot this integral for a range of values of the ...
2
votes
0answers
52 views

Better to have infinities in limits or integrands (`NIntegrate`)? [closed]

I'm using ListPlot to plot the integral of a function with respect of the function's second variable: ...
8
votes
4answers
395 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 ...
1
vote
0answers
41 views

Which type of integrals are better for Mathematica [closed]

Is it in general better to type in a integral with its limits, or is it better to type an indefinite integral into Mathematica? With better I mean: Likelihood that Mathematica can solve it, ...