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37953 results in Cambridge Textbooks

Page 1799 of 1898

  • Preface

  • C. D. Cantrell, University of Texas, Dallas
  • Book:
    Modern Mathematical Methods for Physicists and Engineers
    Published online:
    14 September 2019
    Print publication:
    09 October 2000, pp xix-xx

  • Summary

    The purpose of Modern Mathematical Methods for Physicists and Engineers is to help graduate and advanced undergraduate students of the physical sciences and engineering acquire a sufficient mathematical background to make intelligent use of modern computational and analytical methods. This book responds to my students’ repeated requests for a mathematical methods text with a modern point of view and choice of topics.

    For the past fifteen years I have taught graduate courses in computational and mathematical physics. Before introducing the course on which this book is based, I found it necessary, in courses ranging from numerical methods to the applications of group theory in physics, to summarize the rudiments of linear algebra and functional analysis before proceeding to the ostensible subjects of the course. The questions of the students who studied early drafts of this work have helped to shape the presentation. Some students working concurrently in nearby telecommunication, semiconductor, or aerospace, industries have contributed significantly to the substance of portions of the book.

    The following is an example of the situations that motivated me to take the time to write a mathematical methods text that breaks significantly with the past: Every semester, students come to my office, puzzled over numerical modeis in which minor changes in the data produce drastic changes in the Outputs. Unfortunately most of these students lack the mathematical background needed to conceptualize some of the most common problems of numerical computation. For an engineer, and for the increasingly large fraction of physics graduates who make careers in numerical modeling or electrical engineering, conceptual understanding of analytical and numerical modeis is an absolutely essential ingredient of successful designs. A Computer can be a tool for understanding, and not merely a means for obtaining a numerical answer of unknown reliability and significance, only in the hands of those who understand the foundations and potential shortcomings of numerical methods. Yet the traditional mathematical methods taught to students in engineering and physics for most of the twentieth Century do not provide a sufficient background even for introductory graduate texts on many important contemporary topics, of which numerical computation is only one.

    What upper-level undergraduate and first-year graduate students in physics and engineering tend consistently to lack is an understanding of basic mathematical structures - groups, rings, fields, and vector Spaces - and of mappings that preserve these structures.

Page 1799 of 1898