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Linear Functions and Matrix Theory

  • Bill┬áJacob

Part of the Textbooks in Mathematical Sciences book series

Table of contents

  1. Front Matter
    Pages i-xi
  2. Bill Jacob
    Pages 1-39
  3. Bill Jacob
    Pages 40-71
  4. Bill Jacob
    Pages 72-116
  5. Bill Jacob
    Pages 117-154
  6. Bill Jacob
    Pages 155-187
  7. Bill Jacob
    Pages 188-214
  8. Bill Jacob
    Pages 215-245
  9. Bill Jacob
    Pages 246-276
  10. Bill Jacob
    Pages 277-302
  11. Back Matter
    Pages 303-330

About this book

Introduction

Courses that study vectors and elementary matrix theory and introduce linear transformations have proliferated greatly in recent years. Most of these courses are taught at the undergraduate level as part of, or adjacent to, the second-year calculus sequence. Although many students will ultimately find the material in these courses more valuable than calculus, they often experience a class that consists mostly of learning to implement a series of computational algorithms. The objective of this text is to bring a different vision to this course, including many of the key elements called for in current mathematics-teaching reform efforts. Three of the main components of this current effort are the following: 1. Mathematical ideas should be introduced in meaningful contexts, with formal definitions and procedures developed after a clear understanding of practical situations has been achieved. 2. Every topic should be treated from different perspectives, including the numerical, geometric, and symbolic viewpoints. 3. The important ideas need to be visited repeatedly throughout the term, with students' understanding deepening each time. This text was written with these three objectives in mind. The first two chapters deal with situations requiring linear functions (at times, locally linear functions) or linear ideas in geometry for their understanding. These situations provide the context in which the formal mathematics is developed, and they are returned to with increasing sophistication throughout the text.

Keywords

Eigenvalue Eigenvector Matrix Matrix Theory linear algebra

Authors and affiliations

  • Bill┬áJacob
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-59277-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-78055-7
  • Online ISBN 978-3-642-59277-5
  • Series Print ISSN 1431-9381
  • Buy this book on publisher's site
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