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.
3,913
questions
0
votes
0answers
22 views
Output problem to define a Table with the valued assumed by an interpolating function
I have a little Input/Output problem defining a Table with the values of an interpolating function.
I create the points to interpolate:
...
0
votes
1answer
22 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 '...
0
votes
2answers
40 views
Converting an indefinite integral to definite integral
For example, I have the following integral expression:
g[x, y] = Integrate[f[x, y],x]
How can I modify the above expression to achieve the following definite ...
3
votes
3answers
120 views
Problems with Integrate in Mathematica
I would like to analytically integrate a function in Mathematica. However, I have found a problem with the final result when I compare it with the numerically integration of the same function. Here it ...
-1
votes
0answers
30 views
Calculating an unsimplified expression containing derivative of an expression which is substituted instead of a function
I have the following expression:
Derivative[0, 1][Integrate[E^(-(n*\[Tau]) - I*k*y*Cosh[\[Tau]])*B[\[Tau]], \[Tau]]][x, y]
which is created by substitution of a ...
-1
votes
1answer
28 views
Simplifying an equation in which all the terms are integrals with respect to the same variable
I have an equation in the following form:
Integrate[A[x], x] + Integrate[B[x], x] == Integrate[C[x],x]
How can I simplify this equation to get:
...
0
votes
1answer
53 views
Evolution of different species of universe
Very poor knowledge of coding and Numerical solutions. please any body help me.
I want to solve the following equations
(a'[t])^2=(-κ/3)*(-(φ'[t])^2+V(φ))
a''[t]/a[t]=(-2κ/3)(1+3ω)((-Φ'[t])^2+V(φ))
φ''...
-1
votes
1answer
36 views
Calculating the derivatives of an integral expression
I have the following function:
ee[x, y] = Integrate[x^2 + y^2, x]
I want to calculate the derivatives of this function w.r.t x ...
-2
votes
0answers
75 views
Code for calculating the number of real roots of the polynomial [closed]
I'm trying to create a code that estimates the number of real roots of a polynomial. General algorithm is outlined in this document:
http://stellar.mit.edu/S/course/6/sp10/6.256/courseMaterial/topics/...
3
votes
4answers
104 views
Line integral over a rectangular path
I have a little problem. I need to calculate an line integral of a function on a rectangular oriented closed path.
For example I define
f[x_,y_]:= x-2y
and the ...
1
vote
1answer
99 views
Mathematica stuck on partial derivative calculation
I was experimenting polynomial gradient descent on Mathematica, but it got stuck on partial derivative calculation. Formula below:
Traditional Form:
$$
mse = \frac{\sum_{i=1}^{n}\left(y[[i]] - \left(a\...
0
votes
1answer
81 views
Volumes of solids via rotation of regions between two 2D functions [closed]
I'm trying to see if Mathematica can simplify/automate finding the volume when the area between two 2D functions is rotated about an axis.
For example: What is the volume of the solid when we rotate ...
4
votes
1answer
76 views
Posible variable naming bug?
First integral and second integral are the same just replacing $\text{pb}$ <--> $x$. While Mathematica is not able to evaluate the first integral, it can evaluate the second one
...
0
votes
1answer
81 views
Can this previously solved three-dimensional constrained integration also be solved with certain added products in the integrand?
In Solved3DConstrainedIntegration
the constrained three-dimensional (Hilbert-Schmidt-metric-based HSmetric) integration problem for the absolute separability probability of the two-qubit (quantum bit)...
1
vote
3answers
97 views
Find the area enclosed by the x = t^2 − 2t, y = √ t and the y axis [closed]
How do I find the area for these parametric equations :
x=t^2-2t
y=sqrt(t)
and y axis
Please help
1
vote
2answers
63 views
Why the animation of a function gives different results from the integral?
My function is:
A1[B_, x_, t_] := (AiryAi[B*(x - (B^3*t^2)/4)])^2
(B is a constant) and if I use "Manipulate" :
...
-1
votes
0answers
51 views
Calculating complex integral representation of the Hankel function of the first kind
I was wondering if any one can help me calculate this integral using Mathematica.
This is a form of integral representation of Hankel function of first kind:
...
1
vote
2answers
38 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 ...
3
votes
1answer
178 views
Why can I not numerically integrate a smooth, integrable function?
Consider the function $cosec(t)sin(3t)$ on the interval $[0,\pi]$. This is a perfectly well-behaved smooth function, as can be seen when plotting it:
...
0
votes
1answer
37 views
Difficult on integration the normalization of a piecewise function
I have a little problem; I have defined the following Piecewise-function in the variables {x,L,w}:
f[x_, L_, w_] := Piecewise[{{x w (L - x), 0 <= x <= L}}];
...
0
votes
0answers
51 views
Having trouble plotting sin functions [closed]
I'm trying to find the equation of a tangent line and plot the original function and the tangent line equation on the same graph. I can find the tangent line equation just fine but I'm having trouble ...
0
votes
2answers
44 views
Error complex function ERFI(X): looking for alternative function representations?
I have some analytical results from a physics problem, where the Mathematica gives the results in terms of complex error function. I would like to explore another function representation using ...
0
votes
0answers
51 views
How to evaluate simplify an expression containing derivatives
I have an expression that is a derivative of order 2. I want to assign value to derivatives of orders lower than 2(e.g. the expression itself) which should cause the derivatives of higher order become ...
0
votes
0answers
27 views
Mean error of finite differences derivative
I wrote a module that computes the 4-th order finite difference derivative of a function at $N$ equidistant points of an interval and the difference between the exact and numerical value at those ...
1
vote
0answers
93 views
I want MathLie setup for mathematica [duplicate]
I tried to find Math lie in Mathematica but I didn't find setup.
Can anyone share Math lie setup for Mathematica?
0
votes
0answers
47 views
Issue with the solution of a integral
it's been a while since the last time I used mathematica so i am quite rusty with the syntax
I was trying to calculate the integral of the following function of the cosmological scale factor a ( ...
-1
votes
1answer
94 views
A No-linear differential equation
I'm recently figuring out how to make this equation solved but Mathematica does not solve this??!!
DSolve[{ y'[t]== ((3 a)/2 (y[t] - b/(2 a))^2 + k ((3 a)/2 - 1) t^-2 - ((a f)/2 + (3 b^2)/(8 a)))/(t ...
0
votes
2answers
162 views
Why the difference in fundamental solutions?
Finding a fundamental solution of a linear differential operator
$f''-c^2f$, I try in 12.3.1 on Windows 10
DSolve[f''[x] - c^2*f[x] == DiracDelta[x - y], f[x], x]
...
3
votes
1answer
129 views
One more incorrect result of Integrate
Let us consider
int = Integrate[ArcSin[Sin[n*x]], {x, 0, 1}, Assumptions -> n > 10]
...
0
votes
0answers
50 views
Biot-Savart Integral on a curved path
I am calculating the following Biot-Savart integral according to the suggestion of @Ulrich Neumann in a previous post called Biot-Savart Integral:
...
0
votes
0answers
49 views
How can I change the derivative symbol ' in output
The derivative symbol in "output" is always like this f'(x) but I want something like D[f[x],x] or ...
1
vote
1answer
42 views
Series expansion of QPochhammer symbol
Mathematica has an internal function QPochhammer[a,q,n] which is given by
$$\text{QPochhammer}[a,q,n]=\frac{\text{QPochhammer}[a,q]}{\text{QPochhammer}[a q^n,q]}=\frac{\prod_{k\geq 1}(1-a q^k)}{\prod_{...
2
votes
1answer
109 views
Biot-Savart Integral
I want to calculate the magnetic field of a finite wire of current along the z axis. I assume a frame of reference like the one in Fig. below:
It is a classical problem with a well known solution for ...
2
votes
2answers
79 views
Calculation of composite integrals
I am facing trouble calulating the following integrals. Could you give me any advice?
My code is the following:
...
0
votes
2answers
73 views
How to find this limit in Mathematica? [closed]
I have the following four expressions evaluated in Mathematica.
...
1
vote
1answer
57 views
plot and volume of y^2+z^2=1 cut by the plane y=x and x=1 in the first quadrant
I need to plot and find the volume of y^2+z^2=1 cut by the plane y=x and x=1 in the first quadrant
So far,
...
1
vote
1answer
33 views
Density plot f(x,y,z)=1+x+y+z bounded by x^2+y^2=1 and y = z, x= 0, z=0
Density plot roh(x,y,z)=1+x+y+z bounded by x^2+y^2=1 and y=z, x=0, z=0. In the first octant
So far,
...
0
votes
1answer
30 views
Integration of product of two quantile functions gives a conditional expression in the integrand
Integration of product of two quantile functions
Integrate[
Quantile[NormalDistribution[0, 1], p] *
Quantile[StudentTDistribution[0, 1, 5], p]
, {p, 0, 1} ]
...
29
votes
3answers
818 views
Is it possible to write a MMA version of LineInt like Maple?
I know there's no direct method to do line integrals in Mathematica as of 2021. But we now have more mature Region schemes, and that makes it very easy to compute ...
1
vote
0answers
54 views
Why does Mathematica only solve this indefinite integral for two values of n?
I'm trying to estimate this integrate:
where "a" and "b" are real constants and n> 0.
I use the code
...
2
votes
1answer
70 views
Symbolic derivative over summations
How to take the symbolic derivative of an expression over two summations? Below is the expression:
...
0
votes
0answers
22 views
Adaptation of existing code to multivariable system
I am trying to adapt the existing code from "Mathematica package for analysis and control of chaos in nonlinear system" by Gutierrez. This existing code calculates the Lyapunov Exponent by ...
1
vote
0answers
47 views
How to use only real values in a notebook?
I am wondering how to make Mathematica only evaluate real numbers by creating an initialization line in the beginning of a notebook.
I would like to prevent the following:
complex trigonometric ...
1
vote
1answer
56 views
Converting system of ODE from polar to rectangular coordinates
I am trying to convert the following system of equations from polar coordinates to rectangular coordinates. (A,phi)->(u,v)
...
1
vote
1answer
123 views
Is it a bug of Integrate?
Integrate[1/(1 - x^2), x] // FullSimplify
ArcTanh[x]
But as we see in follow graphcs:
...
4
votes
3answers
433 views
Why can't Mathematica evaluate the limit of this hypergeometric function? Is there any way to find the answer?
I have the following function
...
0
votes
1answer
66 views
How to get the numerical answer to NIntegrate[t^(1/3)-t^(2/3),{t,-1,0}] in Reals only
I need to integrate the expression (t^(1/3)-t^(2/3)) from t=-1 to t=0, using Mathematica version 7, and I want the real answer only. How do I do this? I am not sure whether I use NIntegrate or if it ...
-3
votes
1answer
65 views
Confused on Numerical Integration: Making a plot [closed]
I want to make a plot for the following integral:
$$\frac{4B^{\frac{3}{2}}}{\sqrt{\pi}}\displaystyle\int_{\sqrt{2gz}}^{\infty}dv\frac{v^2 e^{-Bv^2}}{\sqrt{v^2-2gz}}$$
I would like to plot this for ...
0
votes
0answers
52 views
Choose branch cut of sqrt so that function is continuous?
I am willing to plot the following function
...
0
votes
0answers
20 views
Treating a pre-defined function as a variable for differentiation
I just started using Mathematica for my thesis, so I'm still a bit clueless about what's going on.
I have an expression for the Hamiltonian of a system wrt 4 dynamic variables (r, u, v and lambda) and ...
