# 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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### How can I avoid a scoping problem when differentiating?

I simplify my real problem as follows: I define a rule function as Clear[rule]; rule[i_] := tt -> i; the real rule function is not this simple. I define a ...
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 ...
743 views

### How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" <...
179 views

### Calculate and plot the tangent hyperplane to a function of three variables

If f:= x^3 + y*x*z - z^2 + x*z and if {{1,2,1},{2,7,8},{6,0,2},{9,1,1}} are points, how can I find the tangent plane to <...
2k views

### Bug in mathematica analytic integration?

I found Mathematica provides me a wrong answer for a relatively simple analytically solvable integral: ...
751 views

### Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
450 views

### many indefinite integrals do not evaluate in 10.1, looking for the cause

Bug introduced in 10.1 and fixed in 10.2 Many integrals no longer evaluate in V 10.1 when they did in 10.0.2 Here are some 23 integrals as an example, that all produced results in V 10.0.2, but ...
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 <...
363 views

### How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
554 views

### Why is this infinite series wrongly computed by Mathematica?

Bug introduced in 7.0 and fixed in 10.0 Could you let me know if Mathematica (newer versions) is able to correctly compute this one? ...
119 views

### Strange behavior of FourierSinCoefficient

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
835 views

### Can Mathematica tell me if a polynomial has all real roots?

I am trying on this polynomial, ...
155 views

### Function to calculate finite difference

I wrote a function to calculate multivariate finite difference of different orders ...
143 views

### How to collect terms with z-derivative?

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

### 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, ...
165 views

### Multivariable Calculus Chain Rule

I am getting ready to write a notebook for the chain rule in Multivariable Calculus for my students. I do know: ...
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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 <...
278 views

### Convergence and value of a complex power series

I've done a little math and I got the following power series expansion of $\log z$ about $z_0=-2+i$. $$\log z=\log(-2+i)+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n(-2+i)^n}[z-(-2+i)]^n$$ I've shown that ...
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. ...
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] ...
3k views

### Usage of Assuming for Integration

For some reason, when I enter the following integration in Mathematica Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] the result turns out to be 0....
486 views

### Correct way to integrate a certain function

I want to integrate $$\int_{0}^{2\pi} dt_1 \frac{a + b\cos(t_1 - t_2)}{c + d\cos(t_1 - t_2)}$$ where $a, b, c, d, t_2$ are real numbers and $c + d > 0$ & $0 \leq t_2 \leq 2\pi$. I used a ...
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: ...