# 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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### Plotting a dispersion curve with complex wavevectors [duplicate]

I want to reproduce a dispersion curve from P. Zou's thesis found here: http://www.ipd.anl.gov/anlpubs/2001/06/39620.pdf on Pg. 31, Eq. 2.13. The problem is, the code below only gives values for the ...
299 views

### Extrema of a function of three variables

To identify and classify the critical points of the function $f(x,y,z)=x^3+xz^2-3x^2+y^2+2z^2$, I used the Hessian matrix method. ...
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### Evaluating Real and Imaginary parts in a dispersion equation via ContourPlot [closed]

I want to reproduce a dispersion curve from P. Zou's thesis found here: http://www.ipd.anl.gov/anlpubs/2001/06/39620.pdf on Pg. 31, Eq. 2.13. The problem is, the code below only gives values for the ...
65 views

### Integrate complains about incompatible quantities in integration limits

When I run the following code, Integrate throws ...
77 views

### How to get a difference of two contour integrals depending on integer parameter?

I have two following functions: ...
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### 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 ...
182 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: ...
102 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: ...
94 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 ...
169 views

### Taylor Series vs. Series Function [closed]

Could someone please explain why the these two functions give two different results ...
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### 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 $f_x(0,0)=f_y(0,0)=0$. ...
329 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 ...
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### 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 ...
131 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 ...
151 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 ...
260 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 $x$ ...
95 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 ...
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### 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 ...
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### Existence of an analytical form for integral

Can the following integration be performed with an analytical output? ...
260 views

### ParametricPlot3D with tube and arrow

I have this: f[x_, y_] = x y/(x^2 + y^2); ParametricPlot3D[{t, 2 t, f[t, 2 t]}, {t, -1/2, Sqrt[0.002]}, PlotStyle -> Directive[Red, Thick]] /. Line -> Tube ...
168 views

Consider: ...
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### 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 ...
303 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 ...
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### 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: ...
68 views

### How can I get the value displayed by a labeled animator control to read in degrees?

I have thus far: ...
101 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: ...