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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1
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1answer
43 views

How to apply Simplify only to elements of list that cause specific Warning

I have a set of replacement rules I use to analytically compute nested integrals of very long symbolic expressions since Integrate literally takes forever. To do ...
5
votes
1answer
69 views

Integrate yielding a ConditionalExpression but I don't think the condition is necessary

Suppose I take the PDF of the LogNormal distribution with parameters m and s evaluated at x. I obviously get an expression involving m. I now want to integrate that expression not with respect to x ...
1
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0answers
35 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
0
votes
1answer
50 views

Partial derivatives with respect to multiple variables

For any natural number $N$: $$_t k_{mn}^1 = \frac{1}{m!n!}\frac{\partial^{n+m} k_1 (0, 0)}{\partial x^m \partial t^n}, \qquad (m,n=0,1,\ldots, N)$$ where $k_1(x,t)$ is a known function, for example ...
9
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1answer
191 views

Why doesn't Mathematica evaluate this simple limit?

I want to evaluate $$\displaystyle\lim_{n\to\infty}\left(n-\sqrt{\sin(n)+10n+n^2}\right)^2$$ I used this code ...
3
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2answers
126 views

Finding the equation of a level curve

Is there a way in Mathematica to determine a parametric equation of a level curve in Mathematica. For example, consider: ...
0
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2answers
76 views

Easy way to add another parameter to Manipulate

Vector definitions: I'm sorry that I didn't include the Vector definitions. I forgot because I had them in initialization cells. Here they are: ...
-2
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0answers
49 views

order of convergence of iterative method [closed]

can anyone tell me whats the error in the code as it runs first time accurately and output the required result. but the second time the code started giving errors ...
0
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0answers
54 views

Formally invert a $C^\infty$ diffeomorphism

I'm having a problem with a calculation. Starting with $f: \mathbb R^2 \to \mathbb R^2$ having an invertible gradient, I want to compute $\nabla^2(g \circ f^{-1})$. While I know $f$ and $\nabla f$ ...
2
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1answer
41 views

Limit problem calculating directional derivative

Given $f(x,y)=1-x^2-y^2$, find the directional derivative at the point $(x_0,y_0)$ in the direction of the unit vector $\vec u$. I am experiencing some strange behavior with the Limit function. I ...
0
votes
1answer
63 views

Integrate with symmetric volume assumption [closed]

My problem is the following: I have the following matrix: S = {{0, -z, y}, {z, 0, -x}, {-y, 0, x}}} The integral of this matrix over any symmetric domain is 0. ...
0
votes
1answer
130 views

Taylor Series vs. Series Function [closed]

Could someone please explain why the these two functions give two different results ...
4
votes
2answers
138 views

A Chain rule proof using Mathematica

If $z=f(x,y)$, where $x=r \cos\theta$ and $y=r\sin\theta$, how can I use Mathematica to prove that: $$\frac{\partial^2z}{\partial x^2}+\frac{\partial^2z}{\partial y^2}=\frac{\partial^2z}{\partial ...
14
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2answers
366 views

Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
2
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0answers
69 views

How can I get constant of integration? [closed]

When using Integrate, Mathematica sets a constant of integration automatically. But sometimes we are given that constant already and it should be used in order to ...
2
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0answers
104 views

Function for the Second Derivative Test

I wrote the following function. It is based on Mathematica for Rogawski's Calculus, 2nd Ed, 2007, Based on Mathematica 7. See: http://users.rowan.edu/~hassen/Math_Rogawski_Calc.htm, Chapter 14. I made ...
-1
votes
1answer
64 views

How can I prove the following equality [closed]

I have the following equality : $$\int_0^\pi \frac{\cos(2t)}{a^2\sin^2(t)+b^2\cos^2(t)}dt=\frac{a}{a+b}-\frac{1}{2}$$ where $0 <b \leq a$. I used the residues but I could not prove this equality
1
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1answer
73 views

Multivariable Calculus Chain Rule

I am getting ready to write a notebook for the chain rule in Multivariable Calculus for my students. I do know: ...
0
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1answer
45 views

Setting trigonometric polynomial terms to zero

Consider an expansion $$\eta = a\cos (kx-\omega t) +\frac{1}{2} a^2 k \cos 2 (kx-\omega t).$$ I would like to compute expansions like $$ V = \frac{1}{2\pi} \int _0^{2\pi} \eta^2 \ d\theta ,$$ ...
1
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0answers
43 views

Numerical Derivative after numerical integration [closed]

I am trying to find the numerical derivative of a function whose argument defines the bounds of a numerical integral. ...
1
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1answer
71 views

Manipulate to determine $\delta$ given $\epsilon$ in continuity question

This is a continuation of a question I posed at: Examining the function $f(x,y)=xy(x^2-y^2)/(x^2+y^2)$. The quest is to analyze the partial derivative $$ f_x(x,y)=\begin{cases} ...
5
votes
1answer
75 views

Examining the function $f(x,y)=xy(x^2-y^2)/(x^2+y^2)$

Consider the function $$f(x,y)=\begin{cases} xy\dfrac{x^2-y^2}{x^2+y^2},&(x,y)\ne(0,0)\\ 0,&(x,y)=(0,0) \end{cases}$$ I can show that $f_x(0,0)=f_y(0,0)=0$. ...
2
votes
1answer
144 views

Evaluating a surface integral

I'm trying to compute the integral $$\int_S x^2+z^2\,{\rm d}S,$$where $S$ is the surface $$S\colon~ \frac{x^2}{2} + \frac{y^2}{3} + \frac{z^2}{2} = 1, \quad y \geq 0.$$ One possible parametrization ...
0
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0answers
62 views

Clairaut's Theorem

Clairaut's Theorem: Suppose $f$ is defined on a disk D that contains the point $(a,b)$. If the functions $f_{xy}$ and $f_{yx}$ are both continuous on D, then $$f_{xy}(a,b)=f_{yx}(a,b).$$ Now, check ...
1
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0answers
79 views

Meaning of D[f[x,y],x,y]

In calculus, we show our students: $$\frac{\partial^2 f}{\partial x\partial y} =\frac{\partial}{\partial x}\left(\frac{\partial f}{\partial y}\right) $$ Now, in Mathematica, which of the following ...
4
votes
1answer
101 views

Difficulty with total derivative

I am trying to introduce myself to the total derivative Dt in the documentation tutorial/TotalDerivatives. But I ran into what I think is a problem. There seems to be a serious problem in the ...
3
votes
3answers
169 views

Partial derivatives of an implicit equation

Looking for an easy way to find partial derivatives of an implicit equation. For example: Find $\partial z/\partial x$ and $\partial z/\partial y$ if $z$ is defined implicitly as a function of $x$ ...
0
votes
1answer
85 views

Why is the indefinite integral $e^\frac{x}{2}x^\frac{g}{2}dx$ the upper Gamma function in Mathematica? [closed]

I have an indefinite integral $e^\frac{x}{2}x^\frac{g}{2}dx$, I try to solve in Mathematica. Solve[Int[e^{x/2}x^{g/2-1}dx ,x]] (* Gamma[g/2,x/2] *) How does ...
0
votes
1answer
61 views

Divergent integral error

I'm integrating a product of two functions which is bounded on the interval from -Inf to 0, and diverges from 0 to +Inf. The error that I get says that the integral diverges on {0,+Inf}... How did ...
0
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1answer
102 views

Existence of an analytical form for integral

Can the following integration be performed with an analytical output? ...
5
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1answer
108 views

ParametricPlot3D with tube and arrow

I have this: ...
3
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1answer
55 views
6
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1answer
101 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
10
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1answer
161 views

Dirichlet coefficients as limits: wrong

Perhaps I should have included the word "bug" in my question. Here we go There is a bug in this Limit Limit[3^s (-1 - 2^-s + Zeta[s]), s -> ∞] (* 0 *) which ...
1
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0answers
47 views

Partial Derivative of f with respect to x1 [duplicate]

How can I calculate the partial derivative of a series like e.g. $$ a = \sum _{i=1}^n \left(2 x_i^2+z\right) $$ with respect to $x_{1}, x_{2},... x_{n}$ using Wolfram Mathematica? I tried it with: ...
2
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1answer
83 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: ...
2
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0answers
59 views

Minimax for conditioned UnitStep functions

I made a simplified version of my problem, and I have now: ...
3
votes
1answer
70 views

How do I color Riemann integral rectangles using conditionals?

I'm builind a function to visualize the Riemann Integration process to any function using rectangles. Everything is fine, except that I need the color of the rectangles to change if they're under the ...
2
votes
2answers
124 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: ...
6
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3answers
192 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 ...
5
votes
1answer
236 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 ...
1
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2answers
83 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 ...
6
votes
2answers
211 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 ...
1
vote
2answers
60 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: ...
4
votes
3answers
130 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: ...
6
votes
1answer
152 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 ...
2
votes
2answers
305 views

How I can integrate $\int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$?

How can I get a solution to the integral given below ? $\quad \quad \int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$ where $a,\,b,\,c$ and $n$ are constants and $J_0$ is a Bessel function of the ...
0
votes
1answer
80 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 ...