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Here is an introduction to the differential and integral calculus of functions of several variables for students wanting a thorough account of the subject. The authors provide clear though rigorous proofs to the classical theorems of vector calculus, including the Inverse Function Theorem, the Implicit Function Theorem, and the integration theorems of Green, Stokes, and Gauss. Exercises are carefully chosen and graded, and there are ample examples to illustrate theories. The book requires a knowledge of elementary linear algebra and one-variable calculus.