Bernard Kolman, Drexel University

Published December, 1996 by Prentice Hall Engineering/Science/Mathematics

Copyright 1997, 696 pp.
Cloth
ISBN 0-13-266313-9

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    Introductory Linear Algebra-Mathematics

    Linear Algebra-Mechanical Engineering

This book provides an introduction to the basic ideas, computational techniques, and applications of linear algebra at the college sophomore level. The most applied of our basic books in this market, this text has a superb range of problem sets. Also, this is the most technology-friendly text on the market.




Emphasizes the computational and geometrical aspects of linear algebra, while keeping abstraction to a minimum and illustrating every idea with examples.
Groups exercises into three classes. Exercises contains routine exercises. Theoretical Exercises includes exercises that fill in gaps in some of the proofs and can be used to raise the level of the course and to challenge the more capable and interested student. The third class consists of MATLAB exercises.
A MATLAB disk is available that introduces more pedagogy, thereby making it more courseware than software.
The end of every chapter contains a summary of Key Ideas for Review, a set of Supplementary Exercises, and a Chapter Test.
NEW— Incorporates recommendations from The Linear Algebra Curriculum Study Group on developing ways to improve the teaching of linear algebra, such as a greater emphasis on geometry.
NEW—An introduction to the language of vectors and linear transformations now comes much earlier in the text.
NEW—New sections have been added on:

• Dot product and Matrix Multiplication.
• Introduction to Linear Transformation. Early introduction to this material in the new chapter on Vectors in R^2 and R^n.
• Subspaces. Now treated separately from vector spaces.
• Orthogonal Complements.
• Inner Product Spaces (Optional).
• Composite and Invertible Linear Transformations (Optional).
• Electrical Circuits.
• QR-Factorization (Optional).
• Appendix A on complex numbers has been expanded and now consists of two sections.
• Many new exercises at all levels have been added.
• Many of these additional exercises are qualitative, rather than quantitative, and their solutions require discussion rather than more computation.
• The section on least squares has been expanded.
• More material on computational techniques has been incorporated. In particular, the QR-factorization of a matrix is now discussed.
• The Cumulative Review of Part I has been expanded.
  
  

I. INTRODUCTORY LINEAR ALGEBRA.

1. Linear Equations and Matrices.
2. Determinants.
3. Vectors in R^2 and R^n.
4. Real Vector Spaces.
5. Eigenvalues and Eigenvectors.
6. Linear Transformations and Matrices.
Cumulative Review of Part I.

II. APPLICATIONS.

7. Linear Programming.
8. Applications.

III. NUMERICAL LINEAR ALGEBRA.

9. Numerical Linear Algebra.

IV. MATLAB FOR LINEAR ALGEBRA.

10. MATLAB for Linear Algebra.
Appendix A: Complex Numbers.
Appendix B: Further Directions.
Answers to Odd-Numbered Exercises and Chapter Tests.
Index.

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