This chapter introduced differential equations (DE), which are equations that describe the derivatives of an unknown function. In an ordinary differential equation (ODE), all derivatives are taken with respect to the same variable, as opposed to a partial differential equation (PDE), which includes derivatives with respect to more than one variable.
A first-order DE includes only first derivatives, and a linear DE includes no products or powers of the function and its derivatives. A differential equation is time dependent if the rate function depends on time.
When we solve a differential equation numerically, the time step is the interval in time between successive elements of the solution. A parameter is a value that appears in a model to quantify some physical aspect of the scenario being modeled.
Until now we have only put one function in each M-file, but in this chapter we wrote a top-level function, which is the first function in an M-file, and a helper function, which is any function in an M-file that is not the top-level function.
In the next chapter, we’ll solve systems of ODEs, which are used to describe physical systems with multiple parts that interact. But first, here’s an exercise where you can apply what you’ve learned so far.