# 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.

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### Product and limit of many (>2) matrices

So I have a matrix like this $$\begin{bmatrix} 1+iA & iAe^{-2ian/N} \\ -iAe^{2ian/N} & 1-iA \end{bmatrix}$$ in mathematica form is like this ...
0answers
24 views

### Trapezoidal Rule Apprx. step size n=10 Issue [closed]

I am attempting to use the trapezoidal rule to find an integral approximation. Can someone see where I am going wrong, please? ...
0answers
40 views

### Mathematica with multi-threaded processors [closed]

Recently I became the owner of a PC based on AMD Ryzen 7 2700 Pro processor. This is a multi-threaded processor (8 cores / 16 threads), other specifications are shown below. In addition, 16 GB of RAM ...
2answers
87 views

### Fitting data to equation with one fitting parameter

If I have the following data (x value is composition and y value is temperature): ...
1answer
53 views

### Extract real part of a complex function

I have a problem for extracting the real part of a complex number. The problem is the following: Suppose $f(z)=\frac{1}{z+\frac{\Delta_{1}}{z+\frac{\Delta_{2}}{z+\frac{\Delta_{3}}{z+...}}}}$, in which ...
1answer
138 views

### Integrate real function returns complex function [closed]

I want to compute the integral $$\int_0^c \exp(-cx+x^2) \mathrm{d}x,$$ where $c>0$ is an unknown constant. In Mathematica Version 12.2.0 ...
1answer
89 views

0answers
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### How to set PDE coefficient as a list of discrete data

How to set a pde time-dependent coefficient, not as an analytic function in time, but as a discrete data vector or list, each element of that list represents the coefficient value on a specific time ...
1answer
60 views

### How to calculate fractional differences of a timeseries?

I have a timeseries I am looking to transform with fractional differences per the following description: The idea being to retain the essence of stationarity of, say, a log transformed integer series ...
0answers
58 views

### One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
0answers
44 views

### How to compute an indefinite integral for a general parameter choice?

I am trying to compute the integral: Integrate[E^(a*InverseCDF[NormalDistribution[0, 1], (1 - x)]), x] for a >= 0. The ...
1answer
57 views

### Solving a complicated time-dependent function

I want to solve the following time-dependent system of equations: ...
3answers
77 views

### A function created by Integrate which can be plotted only with certain argument names; NIntegrate works better, but

Here's the function: ...
2answers
123 views

### Why can't Mathematica express a minus operation between two decimal numbers with several places? [closed]

A example of the problem. This is a print from mathematica with the demonstration of the issue.
1answer
87 views

### Asymptotic value of an integral [closed]

When I evaluate the integral $$n \int_0^1 t^{r-1}(2t-t^2)^{n-1}(2-2t) dt$$ I get the following : $$2^{(-1 + 2 n)}\,n\,t^{(-1 + r)}(\mathsf{Beta}(1/2, n+r-1, n) - 4 (\mathsf{Beta}(1/2, r + n, n))$$ ...