10.3: Chapter Review

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In this chapter, we used ode45 to solve a system of first-order differential equations. As an exercise, you’ll have a chance to solve the famous Lorenz equations, one of the first examples of a chaotic system.

Here are the terms from this chapter you might want to remember.

A row vector is a matrix that has only one row, and a column vector is a matrix that has only one column. The transpose operation transforms the rows of a matrix into columns (or the other way around, if you prefer).

A system of equations is a collection of equations written in terms of the same set of variables.

In a rate function, we often have to unpack the input variable, copying the elements of a vector into a set of variables. Then we have to pack the results into a vector as an output variable.

The state of a system is a set of variables that quantify the condition of the system as it changes over time.

When we solve a system of differential equations, we can visualize the results with a phase plot, which shows the state of a system as a point in the space of possible states. A trajectory is a path in a phase plot that shows how the state of a system changes over time.

In the next chapter, we’ll move on to second-order systems, which we use to describe systems with objects moving in space, governed by Newton’s laws of motion.