“Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.”— Bertrand Russell (1872–1970)
Before we begin our study of mathematical methods in physics, perhaps we should review some things from your past classes. You definitely need to know something before taking this class. It is assumed that you have taken Calculus and are comfortable with differentiation and integration. You should also have taken some introductory physics class, preferably the calculus-based course. Of course, you are not expected to know every detail from these courses. However, there are some topics and methods that will come up, and it would be useful to have a handy reference to what it is you should know.
Most importantly, you should still have your introductory physics and calculus texts to which you can refer throughout the course. Looking back on that old material, you will find that it appears easier than when you first encountered the material. That is the nature of learning mathematics and physics. Your understanding is continually evolving as you explore topics more in depth. It does not always sink in the first time you see it.
In this chapter we will give a quick review of these topics. We will also mention a few new things that might be interesting. This review is meant to make sure that everyone is at the same level before moving on to new topics.