Includes bibliographical references and index.

Front Matter -- Advanced Calculus in One Variable. Real Numbers and Limits of Sequences -- Continuous Functions -- Riemann Integral -- The Derivative -- Infinite Series -- Advanced Topics in One Variable. Fourier Series -- The Riemann₆Stieltjes Integral -- Advanced Calculus in Several Variables. Euclidean Space -- Continuous Functions on Euclidean Space -- The Derivative in Euclidean Space -- Riemann Integration in Euclidean Space -- Appendix A: Set Theory -- Problem Solutions -- References -- Index.

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Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra. Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis. Following an introdu.

Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL

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