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Addison-Wesley / Prentice Hall

Mathematics

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Linear Algebra with Applications, 2/E
Otto BretscherColby College

ISBN-10: 0130198579
ISBN-13:  9780130198570

Publisher:  Pearson
Copyright:  2001
Format:  Cloth; 440 pp
Published:  12/29/2000

For courses in Introductory Linear Algebra and Matrix Methods.

With the most geometric presentation now available, this text emphasizes linear transformations as a unifying theme, and enables students to “do” both computational and abstract math in each chapter. A second theme is introduced half way through the text—when eigenvectors are reached—on dynamical systems. It also includes a wider range of problem sets than found in any other text in this market.

  • NEW - Earlier introduction to vector spaces (“linear spaces”).
    • Now introduced in chapter 4. Ex.___

  • Extensive visualization and geometrical interpretations throughout—E.g., the determinant; the Gram-Schmidt process; the singular value of decomposition; the QR-factorization; and the use of phase portraits for dynamical systems.
    • Allows students to see a visual depiction of equations and processes. Ex.___

  • Avoidance of the “wall of vector spaces.”
    • Keeps students from becoming overwhelmed and confused, and prevents them from getting lost and discouraged early in the course. Ex.___

  • Early, strong introduction to linear transformation. This becomes an underlying theme of the text. All chapters have some theory.
    • Makes the discussion of matrix manipulations more meaningful, and easier for students to visualize. Ex.___

  • More and better problems and exercises than in any other linear algebra text.
    • Gives students opportunities to solve routine problems, and more thought-provoking exercises—some abstract and some focusing on applications. Ex.___

  • After Eigenvalue chapter, a running theme in applying dynamical systems.
    • Unifies the presentation and provides motivation for students. Ex.___

  • Extensive historical references throughout.
    • More history in textbook for student relief and motivation. Ex.___

  • Earlier introduction to vector spaces (“linear spaces”).
    • Now introduced in chapter 4. Ex.___



1. Systems of Linear Equations.


2. Linear Transformations.


3. Subspaces of Rn and Their Dimension.


4. Linear Spaces.


5. Orthogonality and Least Squares.


6. Determinants.


7. Eigenvalues and Eigenvectors.


8. Symmetric Matrices and Quadratic Forms.


9. Linear Differential Equations.

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    Linear Algebra with Applications, 4/E
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