Linear Algebra for Engineers and Scientists Using Matlab,9780139067280

Linear Algebra for Engineers and Scientists Using Matlab

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Edition: 1st
ISBN13: 9780139067280
ISBN10: 0139067280
Format: Paperback
Pub. Date: 2004-07-23
Publisher(s): Pearson
List Price: $128.38

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Summary

This short book integrates the use of MATLAB in a unique, innovative way. Linear transformations are integrated throughout the book.The book uses MATLAB as the chosen computational software. It may be used without the need form machine computation, although exposure to some use of MATLAB is recommended. Worked examples illustrating every important concept or main point. At the end of each example the reader is asked to work one (or more) routine exercises which are of the same type.Although the book has been developed in the context of engineering and computer science, it is also suitable for other audiences.

Table of Contents

(NOTE: A (historic) profile and introduction are keynotes to each chapter.)
1. Linear Systems.

Linear Equations. Linear Systems, Solving Linear Systems. Echelon Forms. Rank of a Matrix. Numerical Analysis. Review.

2. Applications of Linear Systems.
Descriptive Problems. Networks. Electrical Circuits. Polynomial Curve-Fitting. Balancing Chemical Equations.

3. Spaces of Column Vectors.
Spaces of Vectors, Subspaces. Linear Combinations. Linear Independence, Bases, Dimension. Introduction to Linear Transformations. Row Space, Column Space, Null Space. Review.

4. Matrices.
Matrices, Submatrices. Matrix Addition, Scalar Multiplication. Matrix Multiplication. Special Matrices. Inverses. Matrix Factorization. Review.

5. Applications of Matrices.
Graph Theory. Discrete Dynamical Systems. Markov Chains.

6. Orthogonality.
Dot Product, Norm. Statistics. Orthogonal and Orthonormal Sets. Gram-Schmidt and QR. Orthogonal Projections. Method of Least Squares. Applications of Least Squares. Review.

7. Determinants.
Defining a Determinant. Properties of Determinants. Inverses, Cramer's Rule. Review.

8. The Eigenvalue Problem.
The Basic Theory. Diagonalization. Systems of Differential Equations. Linear Recurrence Relations. Review.

9. Vector Spaces.
Definition and Examples. Subspaces. Linear Independence. Bases. Coordinates. Dimension. Change of Basis. Linear Transformations Revisited. Review.

10. Complex Numbers.
Introducing Complex Numbers. Properties of the Modulus. The Complex Plane. Polar Form. Solving Polynomial Equations. Polynomials. Linear Algebra with Complex Numbers. Review.

11. Linear Programming.
A Geometrical Approach. The Simplex Method. Mixed Constraints. Review.

Answers to Odd-Numbered Exercises.
Appendix A: Geometry of Space.
Appendix B: MATLAB.
Appendix C: Toolbox.
Glossary.
References.
Index.

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