Calculus for Engineers II

This unit, we look at two major methods of integration. Like all of the methods other than IBP, these are actually just subclasses of substitutions, but they are far from obvious and deserve separate treatment. There are a lot of things happening here and plenty of example videos in which to see these details in action. Go through the material carefully and remember that you want to be able to understand when to use each method.

We begin in earnest our study of differential equations. These tremendously useful tools for science and engineering end up being rather pesky in terms of the ways we go about solving them. In this unit, we will be introduced to two types of DEs, as well as a numerical method for approximating solutions.

Through the three sections in this unit and the two sections in the next, we look at a few definitions and then study when series converge and diverge. We discover a number of tests that will help us figure out this information, including some very unusual-looking ones. The goal of this chapter is to allow us to use the information here when we try to express functions using certain infinite polynomials (we will call them power series). Knowing when a series converges or diverges will let us find out when our power series exist.

We begin our study of Taylor Series by looking at each half of the phrase individually - first we study (finite) Taylor polynomials. Then, before we extend them forever, we look at how series with a variable behave.

In this chapter, we start examining the effect of having an independent variable determine two (and, in the next chapter, three) dependent coordinates. The most common applications are those in which we use the parameter of time to describe physical motion through the plane and through space.