Kenneth Hardy, Carleton University

Coming March, 2000 by Prentice Hall Engineering/Science/Mathematics

Copyright 2000, 420 pp.
Cloth
ISBN 0-13-906728-0

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    Introductory Linear Algebra-Mathematics

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For a one-semester course in Introductory Linear Algebra. Although the text has been developed in the context of engineering and computer science, it is also suitable for science students and other audiences. This short text integrates the use of MATLAB in a unique, innovative way. An early applications chapter is intended to motivate the study of abstract ideas by the client audience—engineering, computer science, math, and science students. Linear transformations are integrated throughout the text.




The most applications-based text in this market—Each chapter pivots from a well chosen application as well as having Chapter 2 filled with applications.
Strong Matlab ties—While the text may be used without the need of machine computation, Matlab materials are found in each chapter, as well as Matlab exercises and projects.
Complex numbers are covered more thoroughly than in other linear algebra texts—Engineers and physics students need strong coverage of this topic.
Linear transformations are integrated throughout the text.
Gentle introduction to linear independence and spanning sets in R^n—An overview is presented in Chapter 1 and the real meat in Chapter 5.

1. Systems of Linear Equations.

Solution of Linear Systems. Echelon Forms. Rank. Vectors in R^n. Vector Equations. Spanning Sets. Linear Independence.

2. Applications Systems of Linear Systems.

Scheduling and Optimization, Network Flows. Electrical Circuits. Curve Fitting.

3. Matrices.

Matrix Algebra. Elementary Matrices. Inverses. LU-Factorization. Applications. Graph Theory. Discrete Dynamical Systems. Markov Chains.

4. Determinants.
5. Vector Spaces.

Subspace. Spanning Sets. Linear Independence. Basis. Coordinates. Dimension. Change of Basis. Row Space. Column Space. Null Space.

6. Eigenvalues.

Eigenvalues. Eigenvectors. Diagonalization. Powers of Matrices. Linear Systems of Differential Equations. Linear Recurrence Relations.

7. Orthogonality.

Length and Distance. Orthogonal and Orthonormal Vectors. Orthogonal Projections. The Gram Schmidt Algorithm. Least Squares.

8. Complex Numbers.

Introduction to Complex Numbers with Applications to Linear Systems.

9. MATLAB.

Introduction to MATLAB Commands and Graphics.

10. The Tool Chest.

A compilation of useful results and background material.

Glossary.
Index.
Answers to Selected Exercises.

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