Multivariate Calculus and Geometry (Springer Undergraduate Mathematics Series)

Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with a deep understanding of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems. In this revised edition, which includes additional exercises and expanded solutions, Seán Dineen gives a solid description of the basic concepts, via simple familiar examples which are then tested in technically demanding situations. The author recognises the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a comprehensive and unified understanding of the Differential, Integral and Geometric Calculus of Several Variables.