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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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: ...
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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 '...
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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 ...
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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 ...
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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 ...
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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: ...
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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''...
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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 ...
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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/...
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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 ...
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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\...
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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
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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 ...
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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)...
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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
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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" : ...
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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: ...
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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
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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: ...
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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}}]; ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ( ...
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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 ...
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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] ...
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1answer
129 views

One more incorrect result of Integrate

Let us consider int = Integrate[ArcSin[Sin[n*x]], {x, 0, 1}, Assumptions -> n > 10] ...
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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: ...
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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 ...
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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_{...
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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 ...
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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: ...
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2answers
73 views

How to find this limit in Mathematica? [closed]

I have the following four expressions evaluated in Mathematica. ...
1
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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, ...
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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, ...
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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} ] ...
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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 ...
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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
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1answer
70 views

Symbolic derivative over summations

How to take the symbolic derivative of an expression over two summations? Below is the expression: ...
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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 ...
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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 ...
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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) ...
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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: ...
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3answers
433 views
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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 ...
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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 ...
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0answers
52 views

Choose branch cut of sqrt so that function is continuous?

I am willing to plot the following function ...
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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 ...

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