Some people think Dover books, being cheap, ought to be bad. In fact, this Dover series specializes in "salvaging" great titles that went out of print and are of great intellectual/pedagogical value. Such is the case again for this title.
Very well written. Of course, C.H. Edwards is notorious for his book on the history of calculus.
Exceedingly clear. I started reading it while taking Calculus II, in search of some more elaborate perspectives. It is that clear.
Chapter 1 is a brief incursion in some topological aspects. Chapter 2 directional derivatives, differentials. Ch3. Chain rule. Ch.4 Critical points. Ch. 5 MANIFOLDS (patches ?! ) and Lagrange multipliers (and this is around a bit over page 100!). Ch 6 Taylor's in one and Ch. 7 several variables. Ch 8 Classification of critical points. Part III begins with Newton's method and contraction mappings. Then goes to Multivariable mean theorem, Inverse and Implicit Mapping Theorem. Ch 4 (III) is Manifolds in Rn and finishes with higher derivatives. Part IV is Multiple Integrals, n-dimensional integrals, Riemman sums, Fubini's theorem, Change of Variables, Improper Integrals, Path Lenght and Line Integrals, Green's theorem, some applied problems, Line and Surface Integrals. Book end with Differential Forms, Stoke;s theorem, Classical Theorems of Vector Analysis, Closed and Exact Forms, Normed Vectors Spaces, Variational Calculus the Isoperimetric problem.
Lots, lots of bangs for your bucks. Because of the breadth of the exposition, clarity and price, it's a must-have.
You can kind of draw a parallel between this and Hubbard's Vector Calculus, Linear Algebra and Differential Forms. Both kind of span the same space. Of course, being older, it doesn't have the same computational flavor as Hubbard's (but then again, it's not really about numerical methods, is it?).
