For both the bivariate and multiple regression cases, this handout will show how this is done – hopefully shedding light on the conceptual underpinnings of regression itself.

In most cases, one can start from basic physical principles and from these derive partial differential equations (PDEs) that govern the waves. In Section 4.2 we will do this for transverse waves on a …

In these notes we apply Newton’s law to an elastic string, concluding that small amplitude transverse vibrations of the string obey the wave equation. Consider a tiny element of the string. various …

Deriving the Formula for the Sum of a Geometric Series In Chapter 2, in the section entitled "Making 'cents' out of the plan, by chopping it into chunks", I promise to supply the formula for the sum of a …

Changes in properties of a moving fluid can be measured in two different ways. One can measure a given property by either carrying out the measurement on a fixed point in space as particles of the …

In this section we derive the Maxwell equations based of the differentiation form of a number of physical principles. First, we discuss the Ampere’s law. Ampere’s law describes the fact of that an electric …

Formal Methods for Deriving Element Equations And the importance of “Shape Functions”