Intermediate Mathematical Analysis

This textbook provides an introduction to the theory of the differentiation and integration of functions of several variables, covering informal explanations of many of the proofs of results as well as the classical theory of the subject. There are exercises and problems which aim to enable the reader to gain both an understanding of and confidence in the subject as well as an intuitive feel for the main themes. The text also aims to provide a useful bridge between the elementary calculus of one variable and the theory of functions in abstract space. The reader is introduced to key concepts such as the composition of functions of several variables, compactness, uniform continuity and connectivity. The author develops the theory of differentiation (including Taylor's theorem, Lagrange's multipliers, the implicit function theorem and inverse function theorem) and integration (including iterated integration, improper integrals and the change of variable theorem for integrals). The book concludes with an indication of how the subject may be further developed.