Chapter 1 was on Vectors and Functions. I don't want to say it's a review of fundamental concepts because I think there is some material in here that would be new even if someone had Linear Algebra and such. Since I've been running at this topic so many years, it wasn't entirely unfamiliar to me.
1. Vector Basics
I know vector addition and basic dot products. I've seen the terms orthogonal and orthonormal. I've seen the concept of "inner product."
2. Dirac Notation
Susskind had already introduced me to Dirac notation, as well as "bras" and "kets." Fleisch does so much better.
3. Abstract Vectors and Functions
This section was much more helpful than Susskind. I don't have a complete sense of what an abstract vector is but I'm trying to treat it as a game. You can follow the rules of a game without knowing why those rules are helpful. I don't fully understand the use of a Hilbert space, but one can still use the rules to identify one, in particular whether functions have a finite norm.
4. Complex Vectors
I've known complex numbers since high school. The only real addition here is how to find the norm of a complex function.
5. Orthogonal Functions
Very easy with three dimensional space. Doing it abstractly isn't too hard. Sometimes remembering some of the more complicated trig identities really helps. The website for this book is a phenomenal help.
6. Finding Components Using the Inner Product
This is probably the hardest section in the chapter but I made it. I knew the Kronecker delta from an incredibly helpful book on relativity called, A Most Incomprehensible Thing. I'd love to write a book like this on quantum mechanics, but it's obviously out of my reach at this time.
Onward!
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