Advanced Calculus of a Single Variable By Tunc Geveci – eBook PDF
This advanced undergraduate textbook, Advanced Calculus of a Single Variable, (PDF), is centered on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for several years. The goal of this classroom-tested book is to deliver a complicated discussion of the concepts and theorems that are dealt with casually in the first two semesters of a beginning calculus course. As such, students are expected to attain a deeper understanding of the basic concepts of calculus, for example, limits (with stress on ε-δ definitions), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule), continuity (including an appreciation of the difference between mere pointwise and uniform continuity and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests).
Success in this program is expected to prepare students for more advanced courses in real and complex analysis, and this ebook will help accomplish this. The first semester of advanced calculus can be followed by a thorough course in an introductory real analysis course and multivariable calculus that treats the Lebesgue integral and metric spaces, emphasizing Banach and Hilbert spaces.
NOTE: The product only includes the ebook, Advanced Calculus of a Single Variable in PDF. No access codes are included.