Analysis for Applied Mathematics

Rating:
Summary: Solid resource for the applied mathematician
Review: Cheney's book is a good overview of the main topics in real and functional analysis, especially aimed at the applied mathematician. Don't be confused by the title - the book contains few examples of analytical methods applied to physical or engineering problems. Rather, the book covers the abstract analysis that provides the rigorous basis for such applied techniques as function approximation, calculus of variations, PDEs, and Fourier analysis. That's the stated goal of the book, and it achieves it relatively well. My main complaints are the following. First, the previously mentioned deficiency in applied examples. Second, the notation is occasionally not precise or is not clearly explained or is nonstandard. This occurs infrequently and rarely poses a serious problem. The discussion of important definitions and theorems can be terse. The strong points of the book are its excellent selection of topics, large number of well-chosen and challenging exercises, and the concise proofs given for most theorems. The verdict: if you are an applied mathematician or work in the physical sciences, you should consider this book if you want a solid basis in real and functional analysis.