Week 3: Vector functions, Modeling projectile motion, Arc length and the unit tangent vector T.

Thomas Calculus (11th edition), (pages: 906 - 935)

Chapter 13 Vector Valued Functions and Motion in Space

In this chapter, we use calculus to study the paths, velocities, and accelerations of moving bodies. As we go along, we will see how our work answers the standard questions about the paths and motions of projectiles, planets, and satellites.

Sec 13.1 Vector Functions

In this section we introduce the concept of vector functions concentrating primarily on curves in three dimensional space. We will illustrate how to find the domain of a vector function and how to graph a vector function. We will also show a simple relationship between vector functions and parametric equations that will be very useful at times. We also have defined the limit, continuity and derivatives of a vector valued function in a similar way as we have defined for the real valued functions.

Sec 13.2  Modeling Projectile Motion

When we shoot a projectile into the air we usually want to know beforehand how far it will go (will it reach the target?), how high it will rise (will it clear the hill?), and when it will land (when do we get results?). We get this information from the direction and magnitude of the projectile’s initial velocity vector, using Newton’s second law of motion, that we will be discussed in this section.

Sec 13.3  Arc Length and the Unit Tangent Vector T

In this section, we study the features of a curve’s shape that describe mathematically the sharpness of its turning and its twisting perpendicular to the forward motion.