You now have all of the math tools that you will need to understand the lessons on kinematics and dynamics. For some of you, the concept of partial derivatives is new, but you see how easy it is to apply. We have reviewed vectors and a little vector calculus that you will need in the next few lessons. Dot products and cross products will appear frequently in the next few lessons, so make sure that you are comfortable with them and their applications. We introduced a new operator, the “del” or “gradient” operator, which is essential for describing weather observations and how atmospheric properties vary in space. There are two major coordinate systems that are used to describe atmospheric motion: Cartesian and spherical. And there are three different coordinates that are used to define the vertical distance starting at Earth’s surface and rising radially: height z (m); pressure or logarithm of pressure p (hPa); and potential temperature $\theta $ (K). You will become skilled in converting between the meteorological wind directions shown on weather maps and in station weather plots and the wind direction needed to do calculations of wind motion and its effects. We introduced the concepts of the Eulerian and Lagrangian frameworks and showed that they are related by advection of a scalar, which is simply the dot product of the wind velocity and the gradient of the scalar.

Once you successfully complete the activities in this lesson, you will be ready to learn about atmospheric kinematics (the description of air movement) and atmospheric dynamics (the study of why air moves the way that it does).

#### Reminder - Complete all of the Lesson 8 tasks!

You have reached the end of Lesson 8! Double-check that you have completed all of the activities before you begin Lesson 9.