© 2014

Calculus With Applications

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Peter D. Lax, Maria Shea Terrell
    Pages 1-49
  3. Peter D. Lax, Maria Shea Terrell
    Pages 51-116
  4. Peter D. Lax, Maria Shea Terrell
    Pages 117-169
  5. Peter D. Lax, Maria Shea Terrell
    Pages 171-216
  6. Peter D. Lax, Maria Shea Terrell
    Pages 217-244
  7. Peter D. Lax, Maria Shea Terrell
    Pages 245-289
  8. Peter D. Lax, Maria Shea Terrell
    Pages 291-332
  9. Peter D. Lax, Maria Shea Terrell
    Pages 333-345
  10. Peter D. Lax, Maria Shea Terrell
    Pages 347-373
  11. Peter D. Lax, Maria Shea Terrell
    Pages 375-434
  12. Peter D. Lax, Maria Shea Terrell
    Pages 435-473
  13. Back Matter
    Pages 475-503

About this book


This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of  functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.


approximation of integrals complex valued functions convergence of Newton’s method differentiability discrete probability least upper bound theorem

Authors and affiliations

  1. 1.Courant Institute of Math. SciencesNew York University Department of MathematicsNew YorkUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

About the authors

Peter D. Lax is currently an Emeritus Professor of Mathematics at the Courant Institute of Mathematical Sciences.
Maria Shea Terrell is currently a Senior Lecturer of Mathematics and Director of Teaching Assistant Programs at Cornell University.

Bibliographic information

  • Book Title Calculus With Applications
  • Authors Peter D. Lax
    Maria Shea Terrell
  • Series Title Undergraduate Texts in Mathematics
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-7945-1
  • Softcover ISBN 978-1-4939-3688-5
  • eBook ISBN 978-1-4614-7946-8
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 2
  • Number of Pages XII, 503
  • Number of Illustrations 220 b/w illustrations, 0 illustrations in colour
  • Topics Calculus
  • Buy this book on publisher's site


From the book reviews:

“The book under review, a little over 500 pages co-authored with Maria Terrell, is a first-approximation to Lax’s dream come true: a ‘thorough revision’ of the 1976 Lax-Burstein-Lax. … This reviewer will attempt to use them as a pedagogical tool when teaching single-variable calculus or introductory analysis in the future. … It is filled with beautiful ideas that are elegantly explained and chock-full with problems that will enchant both the experienced teacher and the curious novice.” (Tushar Das, MAA Reviews, December, 2014)

“The text starts with introductory facts on real numbers, sequences and limits, followed by chapters aimed at differential and integral calculus. … The text is accompanied by a lot of worked examples, figures and applications. Together with detailed proofs of theorems this makes the text suitable also for self-study.” (Vladimír Janiš, zbMATH, 2014)