# Recent content by Pietair

1. ### Expectation operator - linearity

Thank you for your reply. I know that the probability distribution of the sum of two or more random variables is the convolution of their individual pdf's, but as far as I know this is only valid for independent random variables. While $E(aX+bY)=aE(X)+bE(Y)$ is true in general, right?.
2. ### Expectation operator - linearity

1. Homework Statement Show that the expectation operator E() is a linear operator, or, implying: E(a\bar{x}+b\bar{y})=aE(\bar{x})+bE(\bar{y}) 2. Homework Equations E(\bar{x})=\int_{-\infty}^{+\infty}xf_{\bar{x}}(x)dx With f_{\bar{x}} the probability density function of random variable...
3. ### Plate floating on oil - linear momentum equation

1. Homework Statement 1: Determine the wall shear stress that acts at the lower side of the plate. 2: Determine the force Fx that is needed to give the plate a speed of u = 1m/s. 3: Determine the speed V, that is leaves an air jet that blows against the plate and which creates the same force...
4. ### Definition: flow velocity

Thank you for your reply. But now I wonder, how is the mean flow of the element defined? If we look at a flowing liquid (for example water), now we can theoretically draw a fluid element and give it a velocity U, but how can we determine what U should be? Is it wrong to say that the velocity...
5. ### Definition: flow velocity

Good day, In my book, the following definition for flow velocity is given: So summarized, the flow velocity at a point in space is the velocity of an infinitesimally small fluid element as it sweeps through that point. But now my question; how is the velocity of an infinitesimally small...
6. ### Linearizing an explicit differentiation scheme

1. Homework Statement Consider the following implicit scheme: y_{n+1}=y_{n}+\frac{\Delta t}{2}\left [f(y_{n+1})+f(y_{n})] By linearization one can obtain an explicit scheme which is an approximation to this - with approximation error O(\Delta t^{3}) 2. Homework Equations The solution...
7. ### Second derivative of an integral

Good day, I don't understand the following: \frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\phi''(t) All I know is: \frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\frac{d^{2}}{dt^{2}}\int_{0}^{t}t \cdot \phi...
8. ### Inverse Laplace Transform

Awesome, thanks a lot!
9. ### Inverse Laplace Transform

1. Homework Statement Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s} 2. The attempt at a solution I know: L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}} and: L^{-1}({\frac{1}{s}})=1 But how to continue?
10. ### How do I solve (a+b)^(-c)?

Re: (a+b)^(-c) Exactly.
11. ### How do I solve (a+b)^(-c)?

Re: (a+b)^(-c) (1/x). I have got the equation: r = 1/(a + bcos(c)) This should be equal to: r = (1/a) * (1/(1+bcos(c))) I just can't figure out why.
12. ### How do I solve (a+b)^(-c)?

Re: (a+b)^(-c) In my case, c = 1, so I have got: (a+b)^-1
13. ### How do I solve (a+b)^(-c)?

Good day, How do I work out (a+b)^(-c)? Thanks.
14. ### Unique solution of 1st order autonomous, homogeneous DE

How can I calculate the integral of x(t) when I don't know the corresponding function? x(t) can equal (t^2) or (t-3) and so on, right?
15. ### Unique solution of 1st order autonomous, homogeneous DE

Thank you for your answer. I can work it out when x(t) = x, but this is not the case, is it?