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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-2
votes
0answers
12 views

Proof left-continuous of fucntion [on hold]

Hello everybody I have really no idea how to solve this question:
2
votes
0answers
29 views

How do I numerically integrate over a data set that has uncertainties? [on hold]

I have a 1D data set {xi, yi} with no uncertainties in xi and with uncertainties dyi in yi. The resulting discrete function is monotonic and relatively smooth and I would like to integrate the ...
0
votes
0answers
22 views

How to define more “natural” partial derivative symbols? [duplicate]

I am struggling to use the notation package to display my input in a more natural notation.Of course,the following code fail to meet the need.How could I develop it? ...
0
votes
2answers
22 views

Integrating expressions with several terms and delta functions

So I want to integrate an expression that looks something like this: Integrate[f[x]+DiracDelta[x-y]g[x],{x,-Infinity,Infinity}] With some more terms added with ...
2
votes
1answer
63 views

Forcing Exact Outputs for Integrate [on hold]

I'm trying to compute the following triple integral: ...
1
vote
1answer
34 views

Partial derivative of defined function with vector input

Background: Have written a formula for the refractive index for a glass slab (n) that depends on the variables t,a and d. Now I want to calculate for example some sort of error and I'll be needing to ...
0
votes
0answers
38 views

Nest-Recursion leads to overflow - Numerical calculation of Lyapunov exponents [on hold]

I calculate the Lyapunov exponents of several dynamical systems and want to compare the results with other algorithms. One of the most famous puplications is the work of Marco Sandri, see this paper. ...
0
votes
1answer
25 views

Boundary condition not correctly imposed for NDSolve

I notice that when plotting the below NDSolveValue ...
2
votes
1answer
68 views

an Integral that should be doable:

Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta] - \[Alpha]]], {\[Beta], 0, 2 \[Pi]},Assumptions -> z \[Element] Reals] correct answer is [ I think ]: ...
0
votes
0answers
31 views

How do I input an integral that needs to use Cauchy's formula? [closed]

How do I tell it that it needs to use Cauchy?
2
votes
0answers
57 views

Strange Integrate messages / $RecursionLimit being ignored

Introduced in 10.1.0 The following behavior was observed in Mathematica 10.1 (Windows 64 bit) When attempting to evaluate the following integral, Mathematica outputs several messages which appear ...
0
votes
0answers
43 views

NIntegrate returning exactly what I inputted [closed]

I just want to get an approximate number for this definite integral. Help would be appreciated :)
0
votes
1answer
46 views

Adapt the code to produce a three column table containing the values of n, etc. (Numerical integration)

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
26
votes
1answer
328 views

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

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 now all returns unevaluated! I am hoping ...
0
votes
0answers
43 views

Calculus with Mathematica, books, interesting examples [duplicate]

I'm looking for a book where I could find informations and interesting examples regarding examine functions of one variable like continuity of functions, limits, differentiability in Mathematica. I'd ...
4
votes
1answer
124 views

Mathematica does not help in this integral

I am trying to solve this integral with assumptions: ...
0
votes
0answers
33 views

Computing integral involving derivatives

I want to evaluate an expression $\int_C g(\nabla f)ds$. This is an integration along a curve $C$ in a plane given as a function of some parameter $s$: ...
0
votes
1answer
63 views

Can't obtain a closed form expression for an integral

I am trying to find the result of quite a complicated double integral. While the first part (being a Principal value integral) gave no particular problems, the second one is not providing any closed ...
-1
votes
0answers
26 views

Adapt the code to produce a three column table (rectangle rule of numerical integration) [duplicate]

I was given the following program implementing the rectangle rule of numerical integration: ...
7
votes
0answers
46 views

Finding simplifying substitutions for an integral involving limits and integrand

[The following is based on a William Lowell Putnam Mathematical Competition problem.] Consider the definite integral: $I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\sqrt{\log ...
2
votes
3answers
137 views

How can I get the exact value minimum of this function?

I want to find min of the function $$\frac{1}{\sqrt{2 x^2+\left(3+\sqrt{3}\right) x+3}}+\frac{1}{\sqrt{2 x^2+\left(3-\sqrt{3}\right) x+3}}+\sqrt{\frac{1}{3} \left(2 x^2+2 ...
0
votes
1answer
72 views

Four integrals, how can I expedite the calculations?

I have to calculate the following multiple integrals (4 integrals) ...
0
votes
0answers
29 views

numerical integration with parameter

Now I'm trying to integrate a function numerically. But it shows always an error message. x=y is not a valid limit of integration I know that this function ...
5
votes
2answers
351 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
0
votes
0answers
28 views

How to solve this linear equation? [migrated]

$(\frac{dy}{dx})^2+6\frac{dy}{dx}+4y=x^{2}e^{2x}$ how to solve this. this is linear equation. what type of equation is it? first order?
0
votes
1answer
49 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
0
votes
0answers
77 views

How can I verify double integral solution?

I have a double integral as follows \begin{equation} 1-(\int_0^\infty (\frac{Cje\cdot Cte \cdot e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)^2} + \frac{e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)}) ...
1
vote
1answer
82 views

How can I simplify a triple integral with exponentials?

I want to simplify the following triple integral with exponential terms. \begin{equation} \int_0^\infty\int_0^\infty \int_0^\infty \frac{1}{R\,G} e^{-p(1+R\,a)-q\, b \frac{1+R\, a}{1+G\, x}}\, ...
4
votes
1answer
204 views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
4
votes
2answers
118 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
3
votes
3answers
56 views

Multiple integrals where the number of integrals is aribtrary

I know that I can do, say, a triple integral such as $$\int_{a_x}^{b_x}\int_{a_y}^{b_y}\int_{a_z}^{b_z}f(x,y,z)\,dz\,dy\,dx$$ with the input ...
-4
votes
1answer
41 views

Show steps to compute limit [closed]

I'm trying to use Mathematica to compute a limit, because I have no idea how to compute it by myself. The limit should be: $$\lim _{n\rightarrow \infty }\dfrac {2^{n+1}-n-2}{2^{n}}$$ Any ideas?
0
votes
1answer
49 views

Cauchy Principal Value integral- no result is obtained [closed]

I have a particular Cauchy Principal Value integral that I need to numerically solve for my thesis research. It is the following $$ ...
4
votes
2answers
240 views

Using Mathematica to confirm Bernoulli's inequality

I have several challenges that I want to confirm is true. I have chosen this one because it is rather simple (proof by induction). There are times when I do not want to spend ages trying find proofs. ...
0
votes
0answers
26 views

Use implicit differentiation to find the slope of the tangent line to the curve 4 xy^3+ 5 xy= 45 at the point ( 5 , 1 ) [duplicate]

Use implicit differentiation to find the slope of the tangent line to the curve 4 xy^3+ 5 xy= 45 at the point ( 5 , 1 )
3
votes
3answers
88 views

How to Integrate trivial products of DiracDelta

A long while ago I was able to integrate with Mathematica: $$\int_0^1 \delta(1-x)\delta(x) f(x) \,dx = 0$$ using ...
0
votes
1answer
60 views

How to do this triple integral?

I have a triple integral which is kind of complex, and I want to use Mathematics to help me do the integral. However, when I press "Enter" and "Shift" the software get stuck. I wonder whether this ...
0
votes
2answers
78 views

Finding the equation of tangent lines where a function has a specified slope [closed]

A function is defined as f[x_] := 3x^4 + 8x^3 - 24x^2 - 48x + 19 I need to find the equation of the tangent lines at the points where the tangent line has a ...
1
vote
1answer
54 views

Integrating with assumptions and limits of integration [duplicate]

I have an integration with assumptions and limits of integration. I tried to use Mathematica to solve this problem, but I cannot get any results. ...
4
votes
2answers
363 views

Real integral giving imaginary answer

Hello I am trying to evaluate the following integral Integrate[4279/Sqrt[0.6817 + 0.3183*(1 + x)^3], {x, 0, 20}] my mathematica 9 gives me ...
-1
votes
1answer
77 views

how can use $\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$ [closed]

How can calcul $$\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$$
0
votes
0answers
70 views

Mathematica can't, or won't evaluate an integral (again)

I'm relatively new to Mathematica and really need some help here to spot what's going wrong with my integration issues; Mathematica doesn't evaluate my integral, after a fair amount of time running, ...
0
votes
1answer
70 views

How to make Mathematica show intermediate steps in integral [duplicate]

I want to know how Mathematica evaluates this integral: $PV \int _ {0} ^ {i \infty} d \tau \, \frac{e^{-\frac{\tau^2}{2 M^2}}(b^2 - 3 τ^2)^2 (|b^2+\tau^2|-(b^2-\tau^2))}{\tau (\tau^2 - b^2)}$, where ...
0
votes
1answer
101 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
0
votes
1answer
36 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $K_{i,n}\left(x\right)=\intop_{x}^{\infty}K_{i,n-1}\left(y\right)dy$ where ...
0
votes
2answers
86 views

Why does FindMinimum return 'The function value Null is not a real number'?

I am working with the following function ...
3
votes
1answer
143 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
1
vote
0answers
61 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
2
votes
0answers
45 views

Getting error messages from a Plot expression containing an integral [closed]

This should be a really simple question, but I just got confused. Plot[Integrate[x, x], {x, -5, 5}] Integrate::ilim: Invalid integration variable or limit(s) ...
-2
votes
1answer
75 views

Help me with sum [closed]

good morning $$ \begin{array}{l} \left\{ \begin{array}{l} u_0 = 1 \\ u_n = 3 - \frac{4}{{1 - v_n }} \\ \end{array} \right.\quad \\ \;v_n = \left( { - 3} \right)^{n + 1} \\ s = v_{1436} ...