# Tagged Questions

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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### Curve fitting with this modified integrated log-normal function and extracting fitted?

The data to be fitted is for y vs x. We have y and x points. We do not have data for w. In fact, w variable is being varied during integration from 1e-9 to 100e-9. The fitting parameters are Ms,sigma,...
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### Does Mathematica interprets representations of Dirac's Delta? [duplicate]

Hello I'm trying to take the limit of this expression in Mathematica I know this is a representation of Dirac's Delta (more precisely pi times Delta), but when I do this, the answer is 0. So my ...
I have a complicated function $f(x)$ whose analytical form does not exist for the following integral $$g(x)=\int_0^x\mathrm{d}x'\,f(x').$$ I finally need to evaluate the following integral $$\int_0^... 1answer 80 views ### Integration of harmonic function I am trying to calculate the average distance of electron above the surface. However when I did the Integral, for the first couple of state(n from 1 to around 15) the results are pretty good. However, ... 2answers 84 views ### Defining the Hirota operator The Hirota D-operator (derivative) is mathematically defined as follows:$$D_x^n f\cdot g=\left.\frac{\partial^n}{\partial s ^n} f(x+s)g(x-s)\right|_{s=0} $$An example of this operator acting on ... 4answers 193 views ### Why does Mathematica return Indeterminate for this converging infinite sum? Limit[Sum[k/(n^2 - k + 1), {k, 1, n}], n -> Infinity] This should converge to 1/2, but ... 1answer 44 views ### Modified Derivative Definition Does Not Thread Over Sum I'm redefining how a derivative of a polynomial is taken. I have polynomials or posynomials where x is to a fractional power, and derivatives are of integer order. But if the order of the derivative ... 1answer 69 views ### Strange behavior of derivative when using Abs[] [duplicate] This code where I try to visualize Newton's Method on the function f(x)=\sqrt{|x|} works fine when I define f(x) piecewise. Then why doesn't it work when I define ... 0answers 155 views ### integrate giving wrong result Bug introduced in 7.0 or earlier and persisting through 10.4.1 or later A question with the same title has been asked many times, but I can't find the solution of my problem in their answers. The ... 1answer 83 views ### How do I integrate with respect to f, where {f,10,1000} using mathematica? [closed] ... 1answer 64 views ### Dealing with numerical integration singularities I'm trying to perform the following integral (numerically) (1) And their behaviour is where PV denotes principal Value. In principle I don't know the functions \rm{Im}(\alpha) and \rm{Re}(... 1answer 313 views +50 ### How do I numerically evaluate and plot the Fabius function? The Fabius function is a well-known example in analysis of a non-analytic function that is infinitely differentiable. I want to be able to numerically evaluate the function for any real argument, as ... 2answers 97 views ### Integral of rational function is indeterminate I need to integrate the rational function$$\frac{t^n}{bt+t^2+1}$$where n is a integer. Of course, it's no problem for Mathematica to do this. ... 0answers 38 views ### Setting derivative of function equal to 0 at x=0 using UpValues I'm trying to set the derivative of a function to zero at a specified point. This will act as an initial condition for an algorithm I'm writing: so I'm specifying the value of the function at x=0, and ... 1answer 51 views ### Constructing a root solution diagram (not to tell bifurcation) Suppose I have a third order equation depending of one parameter say .5 4 x (1 - x) (x - .5) - .5 m x^2 where m the parameter. Obviously there are 3 roots for ... 1answer 76 views ### Cauchy integration [closed] I am evaluating Integrate[1/(1 + 3*cosin(x)*cosin(x)), {x, -Pi, Pi}] in Mathematica, which should give me Pi, but instead I ... 2answers 77 views ### Integrate over a piecewise function [closed] I want to calculate the indefinite Integral of$$f(x)=\begin{cases} 2x\cos(\frac{1}{x})& \text{ if } x\ne 0 \\ 0& \text{ if } x=0 \end{cases}.$$I use the following code: ... 1answer 42 views ### How can I solve this integration numerically? [closed] how can I integrate this function numerically w.r.t r from 1 to 8, the function is as, ... 0answers 39 views ### NIntegrate and Integrate seem to over-estimate an integral involving a sharp Lorentzian (Cauchy) distribution I am trying to do a numerical integral with NIntegrate, but it seems that I get a bigger number than I should. The integral is fairly simple: ... 0answers 34 views ### NSolve on a function with NIntegrate I have a function defined with an NIntegrate. The function is of x,y,z, integrated across t: ... 2answers 123 views ### Using Limit with the Option Assumptions I want to calculate the following limit$$L=\lim_{r \to 0} \left( 1 + r \frac{El^{'}(r)}{El(r)} \right)$$by letting Mathematica to know$$\lim_{r \to 0} \frac{El^{'}(r)}{El(r)} = A $$where A ... 1answer 64 views ### Collect partial derivatives and rewrite them with delta/nabla Ultimately, I wish to get the higher generalized product rule for Laplacian. That is, we have \Delta(fg)=f\Delta g+2\nabla f\cdot\nabla g+g\Delta f but what is \Delta^n(fg)? I am tying to guess ... 1answer 87 views ### How is Integrate Implemented? [duplicate] At the end of this 90 minute lecture by Stephen Wolfram on the history of the development of Mathematica, Wolfram takes questions from the audience. One of those questions asked how the ... 1answer 76 views ### Drawing a tangent plane to the torus I'm trying to draw a torus and a plane tangent to it. Here is my code so far: ... 0answers 42 views ### Numerical derivative step size I am trying to perform a numerical derivative of some function using ND. I want to know if there is a way to set the step size of differentiation to the specific ... 2answers 85 views ### Multivariate integration of a compicated expression I have an expression in multiple variables that is something like ... 2answers 134 views ### Inflection point and curvature Through a coordinates list and then interpolating them I got a f[x]. ... 1answer 46 views ### Do double vertical bars in ConditionalExpression mean 'or'? [closed] I have a very simple interpretation question. I think that double vertical bars in a ConditionalExpression given by Mathematica as the result of an integration must mean 'or', but I am hoping to ... 0answers 110 views ### Bug in the “PrincipalValue” method of NIntegrate? Update 2 The technical support suggests setting AccuracyGoal. As I quote here It does appear that the program is returning an incorrect result along with a ... 3answers 83 views ### Evaluating \int_0^\infty dx /{(x^2-a^2)^2+b^4}  returns a negative number I am trying to evaluate \int_0^\infty dx /((x^2-a^2)^2+b^4). And I seem to have an error that I cannot detect. Using ... 3answers 72 views ### Derivative of a 2D Interpolating function I cannot find a way to obtain the partial derivatives of a 2D Interpolating Function obtained with ListInterpolation. I didn't find anything useful on the web. Any ... 1answer 67 views ### Einstein summation and traditional form of partial derivative of implicit function I am quite new in Mathematica (1 week new) and after many trials I did not manage to make my partial derivatives to look traditional way. There are few topics such as How to make traditional output ... 1answer 211 views ### Mathematica implementation of Zeilberger's algorithm (previously done in Maple) I have this Mathematica code: ... 1answer 55 views ### Differentiation and series expansion of dot product - inconsistent results If I differentiate a dot product, I get the result I expect D[a.b[x], x] (* a.b'[x] *) However, a series expansion of the same expression gives a very different ... 0answers 37 views ### Coordinate transformation for gradients expressions [duplicate] Let's suppose I have an expression in cartesian coordinates, involving gradients, such as: F[x,y]:=D[f[x,y],x]/D[f[x,y],y]+D[f[x,y],y,y] f[x,y] Now, I would like ... 1answer 102 views ### Computing integrals in Mathematica I am trying to actually compute \int \sqrt{\cosh{y}-\cos{x}}e^{inx} dx in mathematica. As an example i tried computing \int \sqrt{1-\cos{x}}e^{inx} dx and got a result. But when i try \int \... 1answer 67 views ### Can this expression be calculated symbolically? I want to do definite integration of the following expression ... 1answer 82 views ### integrating with multiple indicator functions depending on each other I need to compute the following integral with three indicator functions, I(x), I_1(x_1) and I_2(x_2),$$ \int_0^1\int_0^1I(x)\left( \ I_1(x_1)\,x_{1} + I_2(x_2)\,x_{2}-1 \right) dx_1 dx_2  ...
I am attempting to evaluate the integral $$\int_{\infty-i\pi}^{\infty+i\pi} dt \frac{e^{-\frac{l}{n}t}}{[(X'-X)^2+r^2+s^2- 2rs \cosh(t)]},$$ the only variable being $t$, ...