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Advanced Calculus of a Single Variable

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This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests).

Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.

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Detail Information

Series Title

-

Call Number

515.4 GEV a

Publisher

Cham, Switzerland : Springer., 2016

Collation

XII, 382

Language

English

ISBN/ISSN

978-3-319-27807-0

Classification

515.4

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

Functional Analysis
Integral Transforms and Operational Calculus

Specific Detail Info

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Statement of Responsibility

Tunc Geveci

Other Information

Cataloger

umi

Source

https://link.springer.com/content/pdf/10.1007/978-3-319-27807-0.pdf?pdf=button

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