Providing a thorough introduction to the differentiation and integration of functions of several real variables, this book is aimed at second year undergraduates and above who have completed a first elementary course of analysis. It covers many of the topics of advanced calculus including extremum problems and vector calculus. Topological notions such as compactness and connectedness are studied in the concrete setting of Euclidean space to ease the students' encounter with these important concepts. There is a detailed study of continuity and diffentiability of functions plus a comprehensive treatment of the important inverse and implicit function theorems. Very little background knowledge is taken for granted, many basic notions are reviewed, and proofs are carefully explained. Worked examples are included throughout the book, complemented with a wide selection of problems. These are provided with hints for solutions while complete solutions for all problems are given at the end of the text.
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