Kreysig starts off with vectors and linear algebra, IIRC, then moves into differential and integral vector calculus, covering multiple integrals and the basic vector calculus theorems like Green and Stokes. Complex variables and their calculus are also covered, with topics like the residue theorem and conformal mapping getting some attention. Kreysig covers a few elementary topics for things like harmonic functions, but to no great depth as I recall. There is some refresher treatment for ODEs and a start at PDEs. I think some of the later editions might cover an introduction to topics like finite elements, but I can't say for certain. I believe I have the 6th (red cover) and seventh (tan cover) editions from the 1970s and a later (perhaps ninth or tenth edition) from the 1990s. The two earlier editions are very similar, while the more recent edition was overhauled quite a bit in terms of content and organization.