Functions of Several Variables

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This book systematically develops differential and integral calculus for functions of several variables, incorporating traditional topics like maxima and minima, multiple integrals, and Stokes's theorems. It uniquely employs vector notation and emphasizes the distinction between n-dimensional Euclidean space and its dual, integrating elements of Lebesgue theory. The text introduces exterior algebra and differential forms, positioning vector analysis as special cases within this framework. Suitable for advanced undergraduates, it can be adapted for a one-semester course, with a new chapter on elementary topology added based on classroom feedback.