Brief on Calculus and Appreciation to Leonard Susskind for his Lectures

Hello everyone!

I have been working on the book project with Leonard Susskind. I just completed an 11-page overview of calculus with detailed material on limits, derivatives (including a short table of derivatives), integrals (with another short table of integrals), differential equations (covering mostly separation of variables), and Taylor series.

I am thinking of adding sections on partial derivatives, maxima and minima, and maybe curvature.

Of course, Leonard has not committed to anything yet; I certainly have not produced enough material to do more than whet his appetite for more. It is possible that something could happen to prevent me from finishing, and he probably does not want to stick his neck, or his reputation, out for someone who is not too well known.

I am having great fun writing this material. It is extremely challenging to develop short and clear explanations for these topics. My olf Mind of a Theorist column is good for this, the philosophy that Iadopted for the column is the same the Leonard has in the lectures.

To quote from the introduction, "What is this course about? Who am I teaching to? While undergraduate or graduate students will be able to read this, it is mostly designed for people who are interested in getting into the meat of physics right away. This is not a standard physics course. This is the real deal, theoretical physics at full scale! We use equations, and sometimes hard equations, but we try to use the simplest equations that will do the job. Basically, we try to keep it minimal. The goal here is to get to the basic ideas fast. So we will be telling you what you really, really, need to know to get to the next level. Sometimes the basics can be hard; we will do them anyway, but will only spend the minimum time required to get them right. And here we mean getting them really right, not by metaphors or analogies, but equations when necessary."

I am dazzled by the structure of the video lectures. In lecture one he introduces the ideas of dynamical systems, phase space, and conservation laws with no mathematics; just some diagrams and very clear explanations. Wonderful!