Calculus through Data & Modeling: Precalculus Review

In this module, we will review some of the key concepts from Precalculus. Exponential and logarithmic functions arise often when modeling natural phenomena, and are important to Calculus. In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (i.e., percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences, as in a self-reproducing population, a fund accruing compound interest, or a growing body of manufacturing expertise. Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics.

Equally important are the trigonometric functions, some of the most well-known examples of periodic or cyclic functions. Common phenomena have an oscillatory, or periodic, behavior. This is observed through ocean waves, sound waves, or even the regular beating of your heart. All these phenomena can be modeled using equations based on the familiar sine and cosine functions. In this module, we will see how to apply and construct functions that permit us to model cyclic behavior.

In classical Euclidean geometry, vectors are an equivalence class of directed segments with the same magnitude (e.g., the length of the line segment (A, B)) and same direction (e.g., the direction from A to B). Vectors are used both in abstract sense as well as for applications, particularly in physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are not located at a specific place, in contrast to scalars, which have no direction. For example, velocity, forces and acceleration are represented by vectors. In this module, we will study vectors specifically in the xy-plane and in "3D" space.