All Questions
Tagged with calculus-and-analysis function-construction
113 questions
1
vote
2
answers
131
views
Issue with variable within Sum[] bounds
I have the following sum that starts from a variable lower bound index $n$:
$$\sum _{y=n}^x \frac{n^2! \left(n^2\right)^{-x} \mathcal{S}_x^{(y)}}{\left(n^2-y\right)!}$$
I tried to compute a closed ...
- 197
0
votes
0
answers
44
views
2
votes
1
answer
140
views
Symbolic multiple Integrals not delivering expected zero result
Consider the following function defined as a double-integral:
$ int_{2D}(h)=\int_0^h \int_0^{t_1}f(t_1,t_2) dt_2 dt_1 $.
Clearly,
$int_{2D}(0)=0$
as long as $f(t_1,t_2)$ is well-behaved.
The previous ...
- 71
5
votes
0
answers
134
views
Create custom definition for chain rule of partial derivative of a vector-valued function
I'm trying to calculate derivatives of expressions involving an unknown function $F: \mathbb{R}\times\mathbb{R}^n\times\mathbb{R}^n \rightarrow \mathbb{R}^n$, with respect to a parameter $h \in \...
- 191
3
votes
1
answer
175
views
Is it possible to ask Mathematica to obtain the function describing the upper and lower boundaries of a combinations of functions?
Assume that I have three one-variable non-periodic functions $f(x),g(x),h(x)$ for $x>0$. The question is: is it possible to ask Mathematica to obtain the function describing the upper and lower ...
- 749
2
votes
2
answers
180
views
How to make delayed function evaluate to zero
I have a function
y[r_] := D[otherfunction[r],t] + D[r,t];
where $r$ can pick up a time dependence depending on the problem. When it does not I am having issues ...
- 23
1
vote
1
answer
86
views
Find minimum of integral with two variable terms
I wanted to see an approach to solving this problem with Mathematica: https://math.stackexchange.com/questions/4723531/how-would-you-attack-this-problem
Determine real numbers a and b so that the ...
- 3,464
2
votes
3
answers
181
views
How to write a function in the following form f[a_, b_, c_,...] so that it is flexible with respect to the number of arguments?
@lericr have written under several of my questions that the way I try to modernize the code could be made much simpler. Below is the original part of the code. The remaining parts have similar designs,...
- 1,893
2
votes
1
answer
89
views
How to correctly reassign variables {c11 -> p11, c12 -> p12} using a Table or some other similar structure?
Why is the value of the function Pxx[1,2] is a number but the function Pxxx[1,2] is an expression? Isn't this construction ...
- 1,893
2
votes
2
answers
112
views
How to use sequence of variables (Sequence) correctly?
Why does the function EER[1,2] have a different value than the function EERR[1,2]? Isn't the entry ...
- 1,893
1
vote
2
answers
71
views
Why does Mathematica not see some of the function PxB1[a10_, b10_, qa0_, qb0_, c11_, c12_] variables?
Why does Mathematica not see the c11 and c12 variables in the function PxB1[a10_, b10_, qa0_, qb0_, c11_, c12_]? How to fix it?
...
- 1,893
2
votes
2
answers
77
views
The correct notation of a function that contains an expression with NIntegrate
I tried to set the function Px[a1_, b1_, qa_, qb_]. Why does Px[1.22, 0.44, 1.40, 1.81] not give out a specific number?
...
- 1,893
3
votes
2
answers
167
views
Optimizing execution time and exploring closed form solutions in Mathematica's DSolve
I am encountering two issues while running the following code in Mathematica:
Slow execution: I have been running the code for approximately 30 minutes, but it is still executing. I am using Windows ...
- 873
3
votes
1
answer
162
views
A workaround needed to overcome the Derivative function anomaly in Mathematica 13
Edits:
Additional illustrations are provided for comparison with D[] in Mathematica 12, as clarifying examples, supplemented at the end.
An erroneous Derivative ...
- 345
1
vote
2
answers
150
views
I want Mathematica to evaluate $\int(1 + \delta (x - \text {x0})) p[x] dx$ as $p[x0]+\int p[x] dx$, where $p[x]$ remains unspecified
I define the simple function:
Simp[h_] := Integrate[h[x] p[x], {x, -∞, ∞}]
where the function p[x] is continuous, but I want ...
- 11
0
votes
0
answers
58
views
How to double sum or triple sum up over the list of functions?
I'm dealing with a summation problem by now using a list of function $F(x; \theta_i)$. The function is defined as
\begin{align*}
F(x; \theta) = 1 - \Phi[\Phi^{-1}(1 - \frac{x}{2}) - \theta] + \Phi[-\...
- 121
0
votes
0
answers
48
views
How to find the sequence function $f(n,x)$ of the three given functions?
I have the three functions $f(2,x)$, $f(3,x)$ and $f(4,x)$ where $x>0$
...
- 749
3
votes
3
answers
137
views
How to test a recursive formula using Mathematica?
Through taking the derivative of $\binom{n}{k}$ w.r.t $n$ repeatedly, I found the recursive formula:
$$\frac{\partial^a}{\partial n^a}\binom{n}{k}=\sum_{j=0}^{a-1}\binom{a-1}{i}\frac{\partial^j}{\...
- 645
2
votes
2
answers
374
views
Integration by parts for deriving gamma function
Well, there is an integral that has quite a lot to do with $n!$, and that is the following :
$f(n)$ = Integrate[x^(n - 1)/E^x, {x, 0, Infinity}] =$\int_0^{\infty } \...
- 669
0
votes
1
answer
107
views
Errors appear after integration of an interpolating function
I have a little question about integration of an interpolating function.
There is an error in assumptions of the integral.
I have a function that was obtained with an interpolation method:
...
5
votes
2
answers
344
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Using Piecewise to create a periodic waveform
I want to create a piecewise function that repeats after t=T.
...
- 59.6k
1
vote
1
answer
92
views
Interpolation of a set of points that include a non-numeric real constants
I have a set of data like:
matrix=Table[{x,y,x+y*c1},{x,0,1,0.1},{y,0,1,0.1}]
where 'c1' is a real constant.
I'm trying to create an interpolation function called '...
1
vote
2
answers
57
views
How to assume some variables to "not" be a function of other variables at the time of defining a function [closed]
I have a function with the following definition:
F[x]=Exp[q*w*x];
I want to take total derivatives of F.
How can I define that q and w are not dependent on x at the ...
- 420
0
votes
2
answers
82
views
Integrate of simple equation but is not solving!
I have this simple integral but I don't know why Mathematica can't solve it?!
FullSimplify[Integrate[x/(-x^2 + a x + b)^(1/2), {x, Sqrt[b], Sqrt[R^2 + b]},Assumptions -> {a > 0, b > 0}]]
- 153
0
votes
1
answer
39
views
How to write a function taking limit of multivariables in sequence?
I'm trying to write a function to calculate the limit of a function on a number of variables in sequence.
Here I take a function with four variables x, ...
- 2,111
4
votes
3
answers
103
views
A function created by Integrate which can be plotted only with certain argument names; NIntegrate works better, but
Here's the function:
...
- 2,166
1
vote
3
answers
351
views
Slope of a line
Just a quick question. Is there a fast inbuilt function to calculate the slope of a line segment passing through two points {p11,p12} and ...
- 4,963
1
vote
1
answer
53
views
How to continually simplify derivatives of function defined in a system? [closed]
For example, if I input something like
b'[t_] = a[t];
a'[t_] = -Sin[b[t]];
a''[t]
it outputs just a''[t].
Is there a way to ...
1
vote
0
answers
62
views
Differential operator in Mathematica
I am fairly new to Mathematica and I wanted to know if I can define the following operator
$E:=(x^2\sqrt{1-K(x^2+y^2+z^2}+y^2+z^2)\gamma^{1}\partial_{1}+(y^2\sqrt{1-K(x^2+y^2+z^2}+x^2+z^2)\gamma^{2}\...
- 113
5
votes
1
answer
323
views
2
votes
1
answer
156
views
How to make this moving surface a continuous and derivable function?
I'm having troubles in defining a function of three variables: $t$, $x$, $y$, from a moving bumpy surface that should be derivable relative to its three variables. Here's the animated surface code, ...
- 4,133
2
votes
1
answer
83
views
Function that accepts functions and returns an expression containing their partial derivatives
I would like create a function that takes functions as input and includes different partial derivatives of the input functions, for simplicity's sake say:
$\qquad m(f(x,y),g(x,y))=f_{xxx}(x,y)+g_{xyy}(...
4
votes
1
answer
434
views
How to convert a Piecewise function in a HeavisideTheta function?
I want to convert a Piecewise function in a HeavisideTheta function in order to correctly evaluate its derivatives at the point of abrupt change and then integrate the result along the axis. How can I ...
- 75
1
vote
3
answers
344
views
NIntegrate with a function defined with conditions
Good afternoon,
I am trying to integrate a function that is defined with a conditional. The simplified code is the following:
...
- 11
1
vote
2
answers
266
views
Why can't Mathematica evaluate this integral?
I want to work with the rectangle function, which I define by
f[x_, m_] := Limit[1/((2*(x - m))^(2*k) + 1), k -> Infinity];
(I know that in theory I can use <...
- 2,335
2
votes
1
answer
391
views
How to find formula from a table?
I recently started using mathematica for simple tasks like simplifying etc.
First of all let me say if this breaks any rules I apologize since I'm a novice in using this and I'll remove the question.
...
- 123
1
vote
2
answers
191
views
How to take limits in Fourier series?
I have a Fourier series which produces an impulse train of period j+1. In principle, it is given by
...
- 2,335
0
votes
0
answers
88
views
Defining an mathematical operator
I'm trying to learn mathematica to use in my thesis. I have basic problems with definitions, calculations etc. Let me ask a question.
I want to define anti derivative operator and derivative operator, ...
- 3
7
votes
3
answers
529
views
Iterated differential operator
I would like to implement the following differential operator in Mathematica,
$$
\prod_{j=1}^n \left({\mathrm d \over \mathrm d x}-j\right)
$$
On a case by case basis, I can just expand it out and ...
- 81
1
vote
3
answers
236
views
How to write a custom function to judge whether a bivariate function is differentiable at a certain point?
We know that the necessary and sufficient conditions for a multivariate function to be differentiable at a certain point are complicated:
Suppose the function $z = f (x_ 1, x_ 2, ..., x_n) $ is ...
5
votes
2
answers
387
views
Building a function to calculate the series solution to this Solved Boundary value problem
I have the following code which solves for $(1)$ (i.e. solves for $C_1$ and $C_2$)
$$
T(x,y,z)=\sum_{n,m=0}^{\infty}(C_1 e^{\gamma z}+C_2 e^{-\gamma z})\sin\bigg(\frac{\alpha_n x}{L}+\beta_n\bigg)\sin\...
- 297
2
votes
1
answer
590
views
Define function of n variables and integrate [closed]
Im looking at n particles and functions of their coordinates which I want to integrate over:
...
- 123
4
votes
1
answer
333
views
A complicated boundary value problem leading to third order Eigen sytem [Help in continuing forward] [EDITED]
I have the following elliptic PDE (describing temperature in a plate, w in thermal contact with two fluids h and c):
$$\lambda_h \frac{\partial^2 \theta_w}{\partial x^2} + \lambda_c V \frac{\partial^2 ...
- 297
1
vote
1
answer
61
views
Create vector/matrix function from derivatives of scalar functions
I am attempting to plot the determinant of a Jacobian matrix that is defined by deriving scalar functions and combining these derivatives into a matrix function (the Jacobian) and then taking its ...
- 487
2
votes
0
answers
172
views
How to handle Units when Integrating?
I have some functions defined, which are to use units. Now another function is used to integrate over those, with the integration variable also quantified and the input to said function. I better just ...
- 83
5
votes
2
answers
296
views
Define an $n$-variable function with $n$ undefined?
I would like to define an $n$-variable function with $n$ undefined. For example, I want something like this:
$$
f(x_1, \, \dots, \, x_n) = x_1 + \dots + x_n
$$
And afterwards I want to take its ...
4
votes
1
answer
213
views
Why does D ignore conditions specified on a custom function?
I define a function with a condition like so.
ClearAll[foo];
foo[expr_] /; FreeQ[expr, bar] := expr
Such that foo[12] returns ...
- 185
0
votes
1
answer
68
views
How to define a function through so that it has an integral of a fixed value?
I have a quite complex function of two-variables, let's say $\alpha(a,b)$ that has a parameter $c$ and I want to set this $c$ so that $\int_{-\infty}^{\infty} \alpha(a,b) \: \mathrm{d}a \: \mathrm{d}b ...
user67469
1
vote
1
answer
81
views
define function as a result of gradient returns unexpected result
This is probably very simple problem, but what am i doing wrong?
c[x_, y_] := x*y;
Grad[c[x, y], {x, y}]
d[x_, y_] := Grad[c[x, y], {x, y}];
d[1, 1]
Returns:
<...
- 4,036
4
votes
2
answers
366
views
Find constant that allows an integral to be finite
I have a function which is a not-so complicated polynomial, depending on a parameter $c$:
$$f(r,c) = \frac{-2 r^4-4 r^3-6 r^2-6 r-3}{8 r^3}-\frac{c \left(-2 r^2-2 r-1\right)}{4 r^3}$$
What I am ...
user67469