Widely known as the little Spivak, this very comprehensive book serves as a natural continuation of the acclaimed Differential and Integral Calculus by the same author.
Written with similar vividness and clarity, it addresses those topics in Calculus - the analogs of curves and surfaces in higher dimensions, the generalized Green and Stokes theorems, differential forms, etc. - that require greater abstract thinking and finesse than what may be needed at the introductory level.
Following the remarkably successful presentation style of his Calculus, M. Spivak succeeds in this book in highlighting the inherent simplicity of the fundamental concepts and methods of his subject, without sacrificing mathematical rigor while also not avoiding the invocation of geometric intuition where necessary as a component of genuine understanding.
A valuable book for anyone wishing to go beyond the surface of basic mathematical concepts.
