# 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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### 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: ...
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 '...
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 ...
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 ...
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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### 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: ...
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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### 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 ...
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/...
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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### 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 ...
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: ...
73 views

### How to find this limit in Mathematica? [closed]

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

### Symbolic derivative over summations

How to take the symbolic derivative of an expression over two summations? Below is the expression: ...
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 ...
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 ...
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) ...
123 views

### Is it a bug of Integrate?

Integrate[1/(1 - x^2), x] // FullSimplify ArcTanh[x] But as we see in follow graphcs: ...
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 ...
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 ...
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 ...