Advanced Calculus for Applications, Francis B. Hildebrand, Prentice-Hall, Englewood Cliffs, NJ, 1962

In an earlier review, I promised that I would include a review of this book in a few days.  So many months later here it is.  The present book is a revision of Advanced Calculus for Engineers, first published by the same publishing house in 1948.  This earlier edition is now available as a photographic reprint from Martin Fine Books at a modest price.  A second edition was published in 1976, the paperback of which is still readily available - but used hardbacks are available at better prices, especially for the earlier editions.

This is one of the few books that lives up to its name - it really is advanced calculus for applications.  It covers ordinary differential equations and their numerical solution, Laplace Transforms, series solutions, boundary value problems and characteristic-function representations, vector analysis, higher dimensional calculus, partial differential equations, with particular emphasis on those met in physics, and complex variable theory including contour integration and conformal mapping.

This is a very useful book. Don't hesitate to get a copy of any edition!