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Advanced Calculus of a Single Variable

  • Tunc Geveci

Table of contents

  1. Front Matter
    Pages i-xii
  2. Tunc Geveci
    Pages 1-59
  3. Tunc Geveci
    Pages 61-108
  4. Tunc Geveci
    Pages 109-168
  5. Tunc Geveci
    Pages 169-259
  6. Tunc Geveci
    Pages 261-311
  7. Tunc Geveci
    Pages 313-379
  8. Back Matter
    Pages 381-382

About this book

Introduction

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.

Keywords

Single Variable Advanced Calculus Riemann Integral Banach Spaces Hilbert Spaces Cauchy Sequence

Authors and affiliations

  • Tunc Geveci
    • 1
  1. 1.MathematicsSan Diego State UniversitySAN DIEGOUSA

Bibliographic information

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