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Applied Linear Algebra

Applied Linear Algebra - 06 edition

ISBN13: 978-0131473829

Cover of Applied Linear Algebra 06 (ISBN 978-0131473829)
ISBN13: 978-0131473829
ISBN10: 0131473824
Cover type:
Edition/Copyright: 06
Publisher: Prentice Hall, Inc.
Published: 2006
International: No
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Applied Linear Algebra - 06 edition

ISBN13: 978-0131473829

Peter Olver and Cheri Shakiban

ISBN13: 978-0131473829
ISBN10: 0131473824
Cover type:
Edition/Copyright: 06
Publisher: Prentice Hall, Inc.

Published: 2006
International: No
Summary

For in-depth Linear Algebra courses that focus on applications.

This text aims to teach basic methods and algorithms used in modern, real problems that are likely to be encountered by engineering and science students--and to foster understanding of why mathematical techniques work and how they can be derived from first principles. No text goes as far (and wide) in applications. The authors present applications hand in hand with theory, leading students through the reasoning that leads to the important results, and provide theorems and proofs where needed. Because no previous exposure to linear algebra is assumed, the text can be used for a motivated entry-level class as well as advanced undergraduate and beginning graduate engineering/applied math students.

Table of Contents

Chapter 1. Linear Algebraic Systems

1.1. Solution of Linear Systems
1.2. Matrices and Vectors
1.3. Gaussian Elimination--Regular Case
1.4. Pivoting and Permutations
1.5. Matrix Inverses
1.6. Transposes and Symmetric Matrices
1.7. Practical Linear Algebra
1.8. General Linear Systems
1.9. Determinants

Chapter 2. Vector Spaces and Bases

2.1. Vector Spaces
2.2. Subspaces
2.3. Span and Linear Independence
2.4. Bases
2.5. The Fundamental Matrix Subspaces
2.6. Graphs and Incidence Matrices

Chapter 3. Inner Products and Norms

3.1. Inner Products
3.2. Inequalities
3.3. Norms
3.4. Positive Definite Matrices
3.5. Completing the Square
3.6. Complex Vector Spaces

Chapter 4. Minimization and Least Squares Approximation

4.1. Minimization Problems
4.2. Minimization of Quadratic Functions
4.3. Least Squares and the Closest Point
4.4. Data Fitting and Interpolation

Chapter 5. Orthogonality

5.1. Orthogonal Bases
5.2. The Gram-Schmidt Process
5.3. Orthogonal Matrices
5.4. Orthogonal Polynomials
5.5. Orthogonal Projections and Least Squares
5.6. Orthogonal Subspaces

Chapter 6. Equilibrium

6.1. Springs and Masses
6.2. Electrical Networks
6.3. Structures

Chapter 7. Linearity

7.1. Linear Functions
7.2. Linear Transformations
7.3. Affine Transformations and Isometries
7.4. Linear Systems
7.5. Adjoints

Chapter 8. Eigenvalues

8.1. Simple Dynamical Systems
8.2. Eigenvalues and Eigenvectors
8.3. Eigenvector Bases and Diagonalization
8.4. Eigenvalues of Symmetric Matrices
8.5. Singular Values
8.6. Incomplete Matrices and the Jordan Canonical Form

Chapter 9. Linear Dynamical Systems

9.1. Basic Solution Methods
9.2. Stability of Linear Systems
9.3. Two-Dimensional Systems
9.4. Matrix Exponentials
9.5. Dynamics of Structures
9.6. Forcing and Resonance

Chapter 10. Iteration of Linear Systems

10.1. Linear Iterative Systems
10.2. Stability
10.3. Matrix Norms
10.4. Markov Processes
10.5. Iterative Solution of Linear Systems
10.6. Numerical Computation of Eigenvalues

Chapter 11. Boundary Value Problems in One Dimension

11.1. Elastic Bars
11.2. Generalized Functions and the Green's Function
11.3. Adjoints and Minimum Principles
11.4. Beams and Splines
11.5. Sturm-Liouville Boundary Value Problems
11.6. Finite Elements

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