Handbook of Differential Equations

This and its predecessor of the late 1980s are the best compendiums of differential equation solution and approximation methods that I have ever seen in terms of (a) comparison of different methods, (b) number of methods compared, (c) description of details of each method, (d) organization such as alphabetizing under each category and categorization of methods, (e) description of and comparison of where each method can be applied in the physical and other sciences, both deterministic and statistical/probabilistic ("stochastic"). This accomplishment cannot be overemphasized from the point of view of Creative Genius - in my opinion, comparing and contrasting and organizing and summarizing data and information are fundamental requirements for creative genius. The book may be intended as a reference book, but it should really be used also as a textbook provided that the teacher overviews the areas and gives some supplementary background and latest results. Both the student and reference user can easily be overwhelmed by the sheer number of methods, and I would recommend putting short descriptions of each (1-2 lines on front and 1-2 lines on back) on flash cards to keep them and their relationships fresh in your mind (shuffle the cards, learn them backwards and forwards, learn them alphabetically, in separate categories, then non-alphabetically and in mixed up categories, etc.). I would recommend that future editions list some of the unsolved equations and open research questions in the field.

For anyone that finds differential equations beautiful; for the theoretical scientist in whatever field; this is nearly as indispensable as Abromowitz and Stegun (The Big Ugly Blue Book).