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Linear Functions and Matrix Theory

Author: Bill Jacob
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1995.
Series: Textbooks in mathematical sciences.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Bill Jacob
ISBN: 9783642592775 3642592775
OCLC Number: 851772466
Description: 1 online resource (xi, 330 pages).
Contents: 1 Linear Functions --
2 Linear Geometry --
3 Systems of Linear Equations --
4 Basic Matrix Algebra --
5 Key Concepts of Linear Algebra in Rn --
6 More Vector Geometry --
7 Eigenvalues and Eigenvectors of Matrices --
8 Matrices as Linear Transformations --
9 Orthogonality and Least-Squares Problems --
Answers to Odd-Numbered Problems.
Series Title: Textbooks in mathematical sciences.
Responsibility: by Bill Jacob.

Abstract:

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.

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