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59 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...
88 views

Real and imaginary parts of complex logarithm

I need to obtain the real and imaginary parts of the below expression with Mathematica: $(- i a - m^2) \ln(\frac{i m^2}{2 a})$, where $a$ and $m$ are real. So we have: ...
34 views

167 views

To plot branch cut of logarithm

I like to see the branch cut of the function: $$1 - z \ln[(1+z)/z].$$ If I plot it in the complex plane: ...
56 views

Unexpected difference between integral and summation?

I am trying to integrating something like: Integrate[Exp[-i*(k*x+k*z)]*Exp[-(x^2+z^2)],{x,-largenumber,largenumber},{z,-largenumber,largenumber}] My issue is that ...
36 views

Interesting output in Integrate [closed]

I found interesting behaviour, best illustrated in the following example. When trying to evaluate Integrate[1/(d^2 - 1), d] Mathematica 11.3 gives the following ...
632 views

Weird result in complex limit

I am trying to evaluate a limit: gamma[w_] = Sqrt[-(u*e)w^2 + I*(u*s)w]; Limit[Re[gamma[x]], {x -> DirectedInfinity}] I calculated the limit by hand, and ...
823 views

Why does Arg'[1. + I] return -0.5?

From the document we know that Arg[z] gives the gives the argument of the complex number z. Then how about ...
85 views

How to take a derivative of a function with a real part taken

Consider f[x_]=Re[x^3] I now take the derivative of this D[f[x],x] and the result is ...
722 views

How to use Mathematica to do a complex integrate with poles in real axis?

I want to use Mathematica to compute the following complex integral: Integrate[Exp[I z ] 1/z, {z, -Infinity, Infinity}] Mathematica reports that it does not ...
196 views

Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?

Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
169 views

Conjugate & Derivative

I have some problem with the derivative of the 'conjugate' expression: Here I define the functions: ...
71 views

Solution… 2nd Transcendental Equation with Graphical method [closed]

If $2x^3 + \ln x = 5$, then what is $x$? For beginning we started to find a solution for equation \begin{align}\label{eq:eq} \ln x + cx = b \tag{1} \end{align} We know from W function ...
178 views

What does “ Im' ” mean? [closed]

I am trying to take the curl/derivative of the function A. What does " Im' " mean here? Why does Mathematica attempt to take the derivative of the Im function here? ...
112 views

268 views

Having problems integrating a function of a complex variable [closed]

I've tried to calculate the integral And I got the result $16i \pi ^3$. I wanted to check my calculation, so I ran this code in Mathematica: ...
36 views

Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
90 views

How to maximize the modulus of a multivariate complex-valued function?

My problem is the following. I have a messy, complex-valued function ...
183 views

How to force a real function to appear with real components [closed]

The command Integrate oftentimes produces output that seems to be a mix of real and complex components even though the result is a real function. The question is ...
91 views

Calculus of residues

I try to calculate the following residue ...
262 views

Contour integral calculation [closed]

There is an integral of a complex function to calculate: $$\oint_{|z|=2015}\frac{3i(z^3+z-2)}{\pi(z-3)}e^{-\frac{1}{z}}dz,$$ where the contour is a circle of radius 2015. Calculating it manually I ...