# Questions tagged [calculus-and-analysis]

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

3,649 questions
Filter by
Sorted by
Tagged with
3answers
213 views

### How to express the function $a(t)$ knowing a parametrization $a(\eta)$ and $t(\eta)$?

I have this function : \begin{equation}\tag{1} a(\eta) = \sqrt{\sin{2 \eta}}, \end{equation} and this time variable : \begin{equation}\tag{2} t(\eta) = \int_0^\eta a(\eta') \, d\eta'. \end{...
1answer
106 views

### How can I find the domain of $x$ for which the function $g(x)\geq0\;$?

I have this function ($x>0$) $$f (x)=\frac{\sqrt{g (x)}+4 x \left(x^2+1\right) \sin (\pi x) \cos ((3+\pi ) x)}{x^4+2 x^2+1+\left(4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)\right)}$$ ...
2answers
1k views

### How to determine if a function is continuous?

I wish to write code for Riemann-Stieltjes integrals in Mathematica. A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed real ...
0answers
63 views

### How to do a fast numerical computation of an oscillatory integral including HeunC function using Mathematica?

I am trying to numerically compute the following integral in Mathematica ...
2answers
51 views

### How to make derivative as a function

g[z_] := z^2 l[z_] := D[g[z], z] How to make the derivative of a function as a new function. Here I am showing the simple case.
3answers
102 views

### Get curve values at a given altitude

If I have the following data: ...
0answers
76 views

### Numerical integration of a function with singularity

I am trying to find the following integral numerically, ...
3answers
80 views

### Superimposed data on top of each other in a Do Loop

If I have 4 different types of data such (that I get from an Excel file) as: https://pastebin.com/j3Bgfxqm I am trying to implement a ...
1answer
258 views

### Bug: Wrong limit in Mathematica 11.1.1 and current WolframAlpha

Bug introduced around 11.1.1 and fixed in 11.2 ...
1answer
335 views

### Getting wrong limit with Bessel

Bug introduced in 7.0 or earlier and fixed in 11.3 I computed a following limit (related to the asymptotic expansion of the sequence A000009 - number of partitions ...
0answers
62 views

### Calculating the integral

The question is asked in the mathstackexchange. There is no answer. I can't solve it by hand, also. Maybe we can solve it with Mathematica. Appreciate all your help, effort. Best regards. ...
1answer
148 views

### Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
1answer
74 views

### I'm getting 0 when I evalute an integral I know is non-zero [closed]

Here is my code: ClearAll[n, y]; Integrate[(1 - y^n)/(1 - y^2), {y, 0, 1}, Assumptions -> Re[n] > -1] When I evaluate it, Mathematica 12.0 is giving me $0$, ...
1answer
104 views

### Solving an equation with Reduce

In the equation shown in the code that follows, I must find or eliminate rb, but Mathematica is reluctant to work with my Reduce ...
4answers
347 views

### Solving Integral Equation -numerical solution

I am trying to find a (numerical) solution to the following integral equation: where $\epsilon$ is a real valued function and $\beta$ and $c_0$ are constants. MMA code: ...
1answer
166 views

### How do I draw a conformal mapping from the z-plane to the w-plane

I am total beginner in Mathematica. Don't know a thing. I need to draw some diagrams for showing the conformal nature of map $w=e^z$. I need to draw some contours in $z$-plane; e.g., horizontal line, ...
1answer
66 views

### Laplace Transform - Differentiation in Time property demonstration

I have a signal x[t_]=t/3 Exp[-3t] UnitStep[t] and the laplace transform as ...
0answers
53 views

### Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
1answer
161 views

2answers
378 views

### Calculating a double integral

I want to calculate the following integral: \int^{10}_{0}\int^{\pi}_{0}\sqrt{(37-\frac{45\cdot37\cdot x^2}{74\cdot 150})^2\cdot \sin(t)^2-(40-\frac{27\cdot37\cdot x^2}{16\cdot 150})^2\cdot \cos(t)^2}...
0answers
80 views

### How reliable is AsymptoticIntegrate?

In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
0answers
22 views

### Can't plot derivative of Hankel function [duplicate]

I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...
3answers
519 views

### Computing the surface area and volume of molecules

Here is a somewhat difficult problem I've had for a long while. Space-filling models of molecules can be easily generated by ChemicalData[], ...
1answer
64 views

...