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Linear Algebra with Applications, 3/E
Otto Bretscher

ISBN-10: 0131453343
ISBN-13: 9780131453340

Publisher: Prentice Hall
Copyright: 2005
Format: Cloth; 496 pp
Published: 06/28/2004

Suggested retail price: $137.33
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For courses in Introductory Linear Algebra.

This text offers the most geometric presentation now available, emphasizes linear transformations as a unifying theme, and is recognized for its extensive and thought-provoking problem sets. While preserving the same table of contents as the previous edition, this revision is the outcome of a careful reflection (and appropriate change) on the wording of each idea.

  • No text in this market has more, or a wider range of, problem sets. Over 400 new exercises have been added to the problem sets, ranging in difficulty from the elementary to the challenging.

    • See pp. 89-97 for one section of problems.    

    • Each chapter ends with 50-60 True-False questions that test conceptual understanding and ehlp force students TO READ. (see pp. 97 and 183)

  • NEW - Historical problems have been added, taken from ancient Chinese, Indian, Arabic, and early European sources. (see pp. 25-26)
  • NEW - The text with the strongest geometric presentation has been strengthened.

    • There is an even greater emphasis on the geometric representation of linear transformations, starting in Chapter 2.

    • Rotations, reflections, projections, and shears are used throughout to illustrate new ideas.

  • NEW - Multiple perspectives on the kernel of a matrix are presented, with a stronger emphasis on the relations among the columns.
  • NEW - Commutative diagrams are used more extensively to enhance the students' conceptual understanding of the matrix of a linear transformation. These diagrams enable students to visualize the relations between linear transformations.
  • NEW - A more conceptual approach to the QR factorization is presented, in terms of a change-of-basis.
  • NEW - The determinant is introduced in terms of Laplace expansion rather than permutations, with Gaussian elimination and permutations still presented as alternative methods.
  • NEW - These innovations have been class-tested for several semesters, and they have proven to enhance the students' learning and understanding.

 

  • Strong emphasis on Linear Transformations.

    • Serves as a unifying theme for the text.

    • Makes discussion of matrix manipulations more meaningful and easier for students to visualize.



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.

    Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous edition.

  • 0136009263Linear Algebra with Applications, 4/E
    Bretscher
    © 2009 | Prentice Hall | Cloth; 504 pages | Estimated Availability: 10/01/2008
    ISBN-10: 0136009263 | ISBN-13: 9780136009269
    Brief Description

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