Skip to main content
SpringerLink
Log in
Book cover

Advanced Calculus of a Single Variable

  • Textbook
  • © 2016

Overview

Authors:
  1. Tunc Geveci

    1. Mathematics, San Diego State University, SAN DIEGO, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Carefully dissects key concepts such as limits of sequence, convergence & divergence of monotone sequences, infinite limits, derivatives, integrals, and series of real numbers

  • Contextualizes subtle, commonly-misunderstood topics such as the notion of an infinite limit, the e-d definitions (for a better command of uniform versus pointwise continuity), error in local linear approximations, and integrability criteria

  • Includes more than 120 exercises, with a solution manual available to instructors

  • Includes supplementary material: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Real Numbers, Sequences, and Limits

    • Tunc Geveci
    Pages 1-59

  3. Limits and Continuity of Functions

    • Tunc Geveci
    Pages 61-108

  4. The Derivative

    • Tunc Geveci
    Pages 109-168

  5. The Riemann Integral

    • Tunc Geveci
    Pages 169-259

  6. Infinite Series

    • Tunc Geveci
    Pages 261-311

  7. Sequences and Series of Functions

    • Tunc Geveci
    Pages 313-379

  8. Back Matter

    Pages 381-382
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

“This is a textbook for a single variable advanced calculus course … . This is a very traditional text on single variable advanced calculus, very readable. If I were teaching such a course this is a text to which I would give serious consideration.” (G. A. Heuer, Mathematical Reviews, October, 2016)

“This volume is devoted to a thorough discussion of some basic concepts and theorems related to a beginning calculus course. … The presentation is thorough and clear with many comments on the historical context of the problems and concepts. Requiring only basic knowledge of elementary calculus, this book presents the necessary material for students and professionals in various mathematics-related fields, such as engineering, statistics, and computer science, to explore real analysis.” (Teodora-Liliana Rădulescu, zbMATH 1339.26001, 2016)

Authors and Affiliations

  • Mathematics, San Diego State University, SAN DIEGO, USA

    Tunc Geveci

About the author

Tunc Geveci is Professor Emeritus in the Department of Mathematics & Statistics at San Diego State University. His main publications have been in the fields of partial differential equations, numerical analysis, and the calculus of variations and optimal control.

Bibliographic Information

  • Book Title: Advanced Calculus of a Single Variable

  • Authors: Tunc Geveci

  • DOI: https://doi.org/10.1007/978-3-319-27807-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-27806-3Published: 08 April 2016

  • Softcover ISBN: 978-3-319-80220-6Published: 25 April 2018

  • eBook ISBN: 978-3-319-27807-0Published: 30 March 2016

  • Edition Number: 1

  • Number of Pages: XII, 382

  • Number of Illustrations: 11 b/w illustrations, 77 illustrations in colour

  • Topics: Integral Transforms, Operational Calculus, Functional Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation