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Introductory Linear Algebra: An Applied First Course, 8/E
Bernard Kolman, Drexel University
David R. Hill, Temple University

ISBN-10: 0131437402
ISBN-13:  9780131437401

Publisher:  Pearson
Copyright:  2005
Format:  Cloth; 768 pp
Published:  08/02/2004
Status: Out of Print


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Description

For freshman/sophomore-level courses in Linear Algebra.

This book provides an applied introduction to the basic ideas, computational techniques, and applications of linear algebra. The most applied of our basic books in this market, this text has a superb range of problem sets. Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled “Calculus Required.”) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors) and introduce applications of linear algebra in a one-semester course.


Features

  • NEW - New sections–Includes An Introduction to Coding, Matrix Transformations, and More on Coding. (see pp. 119-124, 390-403)

    • Provides students with an enhanced text that introduces geometric applications and coding.

  • Exanded End-of-Chapter Review material- The key ideas section empahsizes the verbal/language aspects of linear algebra. (see pp. 179-181, 211-213, 371-374)

 

  • Flexibility- The lengthy Applications are grouped into separate chapters that are quite optional. So this lengthy text collapses to just under 400 pages if the applications chapters aren't assigned.

 

  • NEW - More geometry–Adds more figures to increase the geometrical aspects of linear algebra. (see pp. 52-60)

    • Gives students a strong emphasis on linear transformations and geometry.

  • NEW - More exercises at all levels. (see pp. 49-52, 105-107)

    • Provides students with more opportunities to enhance understanding.

  • NEW - Upgraded MATLAB chapter. (see Chapter 12)

    • Gives students more modern versions of MATLAB, preparing them for higher-level courses.

  • NEW - Key terms–Added to the end of each section.

    • Provides students with an increased empahsis on communication skills in mathematics. (pp. 165, 178)

  • NEW - New Glossary. (see p. A35)

    • Enables students to use this text for reference in the future.

  • Strong, clear presentation of Eigenvalues and Eigenvectors–Defines Eigenvalues in terms of real and complex numbers.

    • Provides students with a firm foundation in this important topic.

  • Strong supplement package–Includes a Student Solutions Manual, and an Instructor's Solutions Manual. Any one of the following supplements can be ordered free of charge when shrinkwrapped with the text: Linear Algebra Labs with MATLAB, Visualizing Linear Algebra with Maple, ATLAST Computer Exercises for Linear Algebra, and Understanding Linear Algebra with MATLAB.

    • Enables students to check their answers to all odd-numbered computational and theoretical exercises, providing enhanced review. Gives instructors valuable course support.


New To This Edition

  • Enhanced and reorganized chapters and many new sections—Includes An Introduction to Coding, Matrix Transformations, and More on Coding.

    • Provides students with an enhanced text that introduces geometric applications and coding.

  • More geometry—More figures increase the geometrical aspects of linear algebra.

    • Gives students a strong emphasis on linear transformations and geometry.

  • More exercises at all levels.

    • Provides students with more opportunities to work problems that enhance understanding.

  • Upgraded MATLAB chapter.

    • Gives students more modern versions of MATLAB, preparing them for higher-level courses.

  • Key terms—Added to the end of each section.

    • Helps students master mathematical vocabulary.

  • Enhanced true/false questions—Students are asked to justify their answers; an additional 25 true/false questions have been added to the Cumulative Review at the end of the first ten chapters.

    • Encourages reading and develops mathematical reasoning.

  • New Glossary.

    • Enables students to use this text for reference in the future.


Table of Contents



1. Linear Equations and Matrices.

Linear Systems. Matrices. Dot Product and Matrix Multiplication. Properties of Matrix Operations. Matrix Transformations. Solutions of Linear Systems of Equations. The Inverse of a Matrix. LU-Factorization (Optional).



2. Applications of Linear Equations and Matrices (Optional).

An Introduction to Coding. Computer Graphics. Graph Theory. Electrical Circuits. Markov Chains. Linear Economic Models. Introduction to Wavelets.



3. Determinants.

Definition and Properties. Cofactor Expansion and Applications. Determinants from a Computational Point of View.



4. Vectors in Rn .

Vectors in the Plane. n-Vectors. Linear Transformations.



5. Applications of Vectors in R2 and R3 (Optional).

Cross Products in R3. Lines and Planes.



6. Real Vector Spaces.

Real Vector Spaces. Subspaces. Linear Independence. Basis and Dimension. Homogeneous Systems. The Rank of a Matrix and Applications. Coordinates and Change of Basis. Orthonormal Bases in Rn. Orthogonal Complements.



7. Applications of Real Vector Spaces (Optional).

QR-Factorization. Least Square Lines. More on Coding.



8. Eigenvalues, Eigenvectors, and Diagonalization.

Eigenvalues and Eigenvectors. Diagonalization and Similar Matrices. Diagonalization of Symmetric Matrices.



9. Applications of Eigenvalues and Eigenvectors (Optional).

The Fibonacci Sequence. Differential Equations (Calculus Required). Dynamical Systems (Calculus Required). Quadratic Forms. Conic Sections. Quadric Surfaces.



10. Linear Transformations and Matrices.

Definition and Examples. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Introduction to Fractals (Optional).

Cumulative Review of Introductory Linear Algebra.

11. Linear Programming (Optional).

The Linear Programming Problem; Geometric Solution. The Simplex Method. Duality. The Theory of Games.

12. MATLAB for Linear Algebra.

Input and Output in MATLAB. Matrix Operations in MATLAB. Matrix Powers and Some Special Matrices. Elementary Row Operations in MATLAB. Matrix Inverses in MATLAB. Vectors in MATLAB. Applications of Linear Combinations in MATLAB. Linear Transformations in MATLAB. MATLAB Command Summary.

Appendix A: Complex Numbers.

Complex Numbers. Complex Numbers in Linear Algebra.

Appendix B: Further Directions.

Inner Product Spaces (Calculus Required). Composite and Invertible Linear Transformations.

Answers to Odd-Numbered Exercises and Chapter Tests. Index.



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Instructor's Manual for Introductory Linear Algebra: An Applied First Course, 8/E
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