This is less a textbook than a workbook. It gives a few definitions, theorems, and a lot of worked examples — but no proofs. It seems to be intended as a companion to an advanced calculus course. In treatment and coverage it is similar to volumes in the *Schaum’s Outlines* series. It is a recent translation of the 2002 French-language work Analyse avancée pour ingénieurs.

The book covers vector calculus, complex variables, and Fourier analysis (including Laplace transforms). The first half of the book has brief statements of the theorems, worked examples, and many exercises. One selling point of the book is that, although no proofs are given, everything is stated carefully and rigorously. The second half of the book gives complete solutions to all the exercises. Applications are skimpy, and of a pure-math type: evaluating definite integrals, and solving differential equations without knowing where they came from. The translation is smooth, except that it consistently calls Green’s theorem “the Green theorem”. Somewhat mysteriously, the book uses the words div, grad, and curl in formulas instead of the del (nabla) symbol ∇.

A comparable book is Murray R. Spiegel’s *Schaum’s Outline of Advanced Mathematics for Engineers and Scientists* (McGraw-Hill, 1971). Spiegel’s book covers the same topics to the same depth, but has a much more thorough exposition on differential equations, including a lot about the special functions of mathematical physics.

Bottom line: a reasonable cookbook or reference for review and drill, but nothing special, and not competitive with the much-cheaper *Schaum’s Outlines* series.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.