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I have a piecewise function that has as one piece the result of a numerical approximation, like in the example below: Y = 1; a = 1; b = 0.9; alphalowx = a*Log[a + b]; alphahighx = Y + a*Log[a + b] – (a + b – 1); f1[x_?NumericQ] := Piecewise[{{0, x <= alphalowx}, {xRead more

I have stumbled upon a problem for which I need some help. I am trying to solve an equation which is basically a function of (theta1 and theta2). The function has the following functional form: f[theta1_,theta2_] := -(Cos[phi – theta1]) – (Cos[phi – theta2]) + (((Sin[theta1]^2) + (Sin[theta2]^2))) + Cos[theta1 – theta2]; I have toRead more

Consider a class $ \mathcal{F}$ of continous and differentiable functions whose derivative is upper bounded by $ L$ . Let $ f \in \mathcal{F}$ , where $ f: \mathcal{X} \mapsto \mathbb{R}$ and $ \mathcal{X} = [0,T]$ for some $ T>0$ . Assume that $ f$ has a bounded energy, namely $ \int_{\mathcal{X}}|f(x)|^2 \, \mathrm{d}x$ isRead more

What is the derivative for the following series $ $ \frac{\mathbf d}{\mathbf d n} \sum\limits_{k=1}^n f(n)g(k), \qquad n\text{ is integer}$ $Read more

I have been reading up on Open Source licensing, but there is this one term that I think needs clarification. When is work derivative? If I have an image viewer that accepts a zip file and I use an open source library under creative commons licensing, then I see two possible interpretations of the terms:Read more

I’m writing my own FEM Poisson equation solver in C++ and I’m using Mathematica as a benchmark – currently it seems that my program outputs a correct solution, however I want to check whether the laplacian of the result is equal to the right-hand side. Unfortunately, the interpolation itself raises a warning “Interpolation on unstructuredRead more

I am a physics student and would apologize if in advance if you find my way of asking the question inapproperiate. I have the following function $ F(x)=2f(x) – f(2x).$ Given that $ \frac{d}{dx}f(x) > 1$ , what can one say about $ \frac{d}{dx}F(x)$ ? Since $ \frac{d}{dx}F(x) = 2\frac{d}{dx}f(x) – \frac{d}{dx}f(2x)$ . The firstRead more

i have the following equation : R = y \[Function] Evaluate[ Simplify@ Piecewise[{{1.31446 Tan[1.58986 y] + 0.91209 y, Abs[y] < 0.84136}, {1./(sign[y] – y), 0.841360 <= Abs[y] < 1.}}]]; how can i override the derivative of the function to be (R'[y_]:=) : 1./(1./R[y]^2 – 1./Sinh[R[y]]^2)Read more

I’ve got a problem with finding this derivative, our math teacher at college gave us this for homework, but i don’t really know how to start. If the f was an actual concrete function, i wouldn’t have a problem but it isnt. Ihope you guys can help me or at least give me some adviceRead more

I have a question, I would be grateful if you helped me. imagine I have these function in Mathematica. te[x_] := x^2 te1[x_] := te[x] x Now how would be possible to obtain numerical differentiate of te1 with respect to to something like D[te1[x], te[x]] and ND[te1[x], te[x]] I know there are much easier wayRead more