Practical Analysis in One Variable

  • Donald Estep

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Introduction

    1. Pages 1-3
  3. Numbers and Functions, Sequences and Limits

  4. Differential and Integral Calculus

  5. You Want Analysis? We’ve Got Your Analysis Right Here

  6. Back Matter
    Pages 605-621

About this book


This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majors.
Donald Estep is Professor of Mathematics at Colorado State University. He is the author of Computational Differential Equations, with K. Eriksson, P. Hansbo and C. Johnson (Cambridge University Press 1996) and Estimating the Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. Memoirs, 2000), and recently co-edited Collected Lectures on the Preservation of Stability under Discretization, with Simon Tavener (S.I.A.M., 2002), as well as numerous research articles. His research interests include computational error estimation and adaptive finite element methods, numerical solution of evolutionary problems, and computational investigation of physical models.


Derivative Newton's method Taylor's theorem advanced calculus calculus differential equation logarithm mean value theorem real analysis

Authors and affiliations

  • Donald Estep
    • 1
  1. 1.Department of MathematicsColorado State UniversityFort CollinsCOUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95484-4
  • Online ISBN 978-0-387-22644-6
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site