In Visualizing vector fields I showed how to plot vector fields using Python and Matplotlib. Streamlines are a concept that is closely related to vector fields. Mathematically speaking streamlines are continuous lines whose tangent at each point is given by a vector field. Each line, and therefore also streamlines, can be parametrized by some parameter $t$.… Continue reading Visualizing streamlines

A vector field assigns to every point in space some vector. Vector fields are used in many branches of physics, e.g., to describe force fields, electromagnetic fields or velocity fields. Two-dimensional vector fields can be easily visualized using Python and the popular matplotlib package. As an example let us visualize the vector field \begin{equation} \vec… Continue reading Visualizing vector fields

Let us consider a random sample $x_1,x_2,\dots,x_N$ drawn from a normal distribution with unknown mean $\mu$ and unknown variance $\sigma^2$. The best point estimates for the mean and the variance are given by the sample mean\begin{equation} \hat\mu = \frac{1}{N}\sum_{i=1}^{N} x_i \end{equation} and the sample variance \begin{equation} \hat\sigma^2 = \frac{1}{N-1}\sum_{i=1}^{N} (x_i-\hat\mu)^2\,, \end{equation} respectively. The sample mean… Continue reading Point and interval estimation in Python