The main ingredient of learning mathematics is problem solving. This is the strength, and undoubtedly the reason for the longevity of the book "Advanced Mathematics" by Prof. Spiegel. 

Its collection of solved and unsolved problems remains part of this second edition. Advanced mathematics is not a simple theory. The various hypotheses, however, including vector analysis, series with infinite terms, and special functions, have the common characteristic of dependence on the fundamental concepts of mathematical calculus. An important purpose of this second edition was the modernization of terminology and concepts, in order to make the relationships between them clearer. 

For example, according to modern usage, real variable functions are automatically monotonic. Differentials are defined as linear functions, and the global nature of vector notation and vector theory is emphasized.