I have waited for some professional mathematician to review this book, since I think it is such a good book. This has not happened, so here is my un-professional review:

I am a retired electrical engineer, and the last three years I have worked on refreshing my old and forgotten school math, and also to going a bit further than during school. When I bought this book I had the following wishes, all of whom it fulfilled brilliantly:

1. It should be usable for self study.

2. It should refresh my fourier series and transforms.

3. It should put these things in context, by presenting physics problems and also by widening the scope to wet the appetite for functional analysis and partial diff eqs.

4. It should do something for my sorely lacking "mathematical maturity".

All of these things it did and I just want to add that Mr. Vretblad is an outstanding pedagogue and that the book contains very few typos. (I found two or three in the whole book, none of them important).