# 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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### Numerical integration with parameter and plot

I'm working on this function: (0.0027 Sin[phi])/(1.05*Exp[-241w]+ Exp[239w]-Cos[phi]) I'd want NIntegrate this function on <...
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### Integrating the product of two imaginary error functions

I am trying to evaluate the following integral: Integrate[Erfi[y] Erfi[z + y] , {y, -L, L}] which simply returns the input. How could I force ...
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### Getting numerical values from integrated interpolating function [duplicate]

I have a list of data. I integrate them with interpolation. Lets say is the following: InterpolatingFunction[{{0.01, 4.82}}, <>][x] However, is that ...
76 views

### Define a function that is an integral that takes a function as argument [closed]

How can I define a function $F$ in Mathematica that does the following: $$F(a,b,P) = \int_a^b P(1-t) \, dt,$$ where $P(t)$ is some function, say, a polynomial? More specifically, I would like to be ...
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### Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
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### How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
58 views

### Evaluate list of determinant of Hessian at list of points

If f:= x^2y + z^3 + xz; and if {{1,2,9},{2,4,6},{9,5,9},{3,3,1},{6,5,3}} is a list of points. I need to evaluate the hessian at ...
150 views

### How to predict the degree of the first series coefficient?

Given an expression f that is a function of x and a number x0, what is the least integer <...
51 views

### Combining Manipulate and NDEigenvalues [closed]

I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following ...
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### if-conditional tracing a half-sphere [closed]

I have a 2D discrete plane (x,y) and I would like to assign an amplitude to each point in the plane. Each dimension runs from -1 to 1. Say I want to assign an <...
119 views

### Puzzled by Assumptions [duplicate]

I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ...
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### Unexpected Behavior from Integrate with PrincipalValue -> True

Bug introduced in 9.0 or earlier and persisting through 10.3 or later The following code, taken from my answer to 97024, ...
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### Find Values of a and b for a Limit

I am having trouble finding the values of a and b for which $\lim \limits_{x \to 0}$ $(\frac{\sin (ax) + bx)} {(x^3)}) = -32/3$. In Mathematica I have entered: ...
163 views

### How to do matrix calculus in Mathematica?

I would like to differentiate Ax with respect to A where A is a matrix. Now, obviously, I know the derivative is x but for more nasty expressions, is there a way to differentiate expressions with ...
173 views

### Bad performance of Integrate (and WolframAlpha) for an Integral of Bessel function of the first kind

The following returns unevaluated in WolframAlpha. Also in my machine Mathematica needs quite a lot of time to compute it. ...
156 views

### Derivatives of vectors

I have an issue with derivatives of vectors ...
126 views

### Why does Integrate[] return an expression with 'True' in it?

I am running Mathematica 10 on Windows 10. I'm trying to analytically evaluate a definite, principal value integral: ...
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### How can evaluate this function [duplicate]

Suppose this function F[c_, n_, s_] := Module[{}, Abs[s - 1 + (-1 + c)^n]] I calculate its second derivative on c ...
172 views

### Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
93 views

### Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
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### About taking limit of an integral on Wolfram Alpha/Mathematica [closed]

I tried computing this quantity on Wolfram Alpha, but I couldn't get any answer: ...
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### How can I solve this limit? [closed]

How can I solve this limit? thanks you!!!
102 views

### Hessian of function at many points

If f:= x^3 + 2yz + 5 x^2z is a function and if {2,0,1},{3,9,2},{8,5,6},{1,1,7} are points. I would like a Hessian of ...
206 views

### How would you calculate a contour integral? [duplicate]

How would you be able to calculate a contour integral of 1/(((z-1)^2)*(z-i)) over the contour |z-1| = 1? Not sure how to type ...
112 views

### Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta[0] at one of ...
130 views

### A 1D numerical integral Mathematica cannot compute, from physics

A well know result in theoretical physics is that a sum over Matsubara fermionic frequencies, i.e.: $$S = \sum_{n=-\infty}^{\infty} h(\omega_n) \hspace{32pt} \omega_n=(2n+1)\frac{\pi}{\beta}$$ can ...
135 views

### Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...
I've never used Mathematica before, so I'm really struggling to use it right now. I have a complicated function $\qquad \chi_{N}=\frac{[(2\cosh(J))^{N+1}(\lambda_{0}+\lambda_{1})^{N}((\mu_{0}+\mu_{1}... 2answers 92 views ### Please, help to find the area enclosed by the curves: ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}] Please, Help to find the area between two curves. ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}] 1answer 73 views ### Color three dimensional plot and contour plot the same Consider: ... 4answers 288 views ### Computing the first derivative in x, y ,and z I have the following function: f:=x^3+yz+z^2x; I need to compute the first derivative in x, ... 0answers 90 views ### Determining the order of continuity (smoothness) of a function Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ... 2answers 50 views ### Computation (or estimation) of an trigonometric Integral with a parameter I am trying to calculate the following integral which contains a parameter. I have used the Integrate and FullSimplify using assumptions but Mathematica fails to produce an analytical solution. <... 2answers 87 views ### Integration result with incomplete beta function I'm doing some calculations (double integration) which results in the incomplete beta function occurring as an end result. My input is: ... 1answer 121 views ### Plotting the exponential of 1/(y-x) What is the best way to handle this situation? ... 1answer 80 views ### is this a possible integration bug? [closed] I am find a discrepancy in evaluating an integral which has given me trouble all day. I have finally isolated where the problem is which I now frame: I define the integral in terms of a delayed ... 1answer 92 views ### How to calculate the volume of a solid enclosed by surfaces? [closed] I am asked to calculate the volume of the solid enclosed by the following equations: (in polar coordinates) r = Cos(θ) z = 2 + x² + y² z = 0 I know the second equation can be changed to its polar ... 1answer 103 views ### Derivative of$e^{-1/x^2}\$ [closed]
I'm trying to get derivative of $$e^{-1/x^2}$$ (also in other points than 0, e.g. 1) with D[E[-1/x^2], x] or ...