Table of contents

  1. Front Matter
    Pages i-xi
  2. David M. Bressoud
    Pages 1-28
  3. David M. Bressoud
    Pages 29-52
  4. David M. Bressoud
    Pages 53-76
  5. David M. Bressoud
    Pages 77-110
  6. David M. Bressoud
    Pages 111-138
  7. David M. Bressoud
    Pages 139-170
  8. David M. Bressoud
    Pages 171-210
  9. David M. Bressoud
    Pages 211-232
  10. David M. Bressoud
    Pages 233-278
  11. David M. Bressoud
    Pages 279-332
  12. David M. Bressoud
    Pages 333-360
  13. Back Matter
    Pages 361-388

About this book

Introduction

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book carries us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Keywords

calculus differential calculus integral integration

Authors and affiliations

  • David M. Bressoud
    • 1
  1. 1.Mathematics and Computer Science DepartmentMacalester CollegeSaint PaulUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0959-1
  • Copyright Information Springer-Verlag, New York, Inc. 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-97606-8
  • Online ISBN 978-1-4612-0959-1
  • Series Print ISSN 0172-6056
  • About this book