This textbook provides a readable, though rigorous, introduction to the differentiation and integration of functions of several complex variables. In addition to presenting the classical theory of the subject, the author includes informal explanations of many proofs along with numerous exercises and problems that will help readers gain an in-depth understanding of the subject. Students are not assumed to have more background than a standard first course in calculus of one variable. Key concepts that are introduced include ...
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This textbook provides a readable, though rigorous, introduction to the differentiation and integration of functions of several complex variables. In addition to presenting the classical theory of the subject, the author includes informal explanations of many proofs along with numerous exercises and problems that will help readers gain an in-depth understanding of the subject. Students are not assumed to have more background than a standard first course in calculus of one variable. Key concepts that are introduced include the composition of functions of several variables, compactness, uniform continuity, and connectivity. The author goes on to develop the theories of differentiation and integration, including Taylor's theorem, Lagrange's multipliers, the implicit function theory, inverse function theorem, iterated integration, improper integrals, and the change of variable theorem for integrals. As a special feature, the author offers a logically sound treatment of partial differentiation in Euler's notation. The book concludes with an indication of how the subject may be further developed. With its clear style and fresh approach, this text provides a useful bridge between the elementary calculus of one variable and the theory of functions in abstract spaces.
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