Applied Linear Algebra / Edition 1

Applied Linear Algebra / Edition 1

by Peter J. Olver, Cheri Shakiban
     
 

This book describes basic methods and algorithms used in modern, real problems likely to be encountered by engineers and scientists - and fosters an understanding of why mathematical techniques work and how they can be derived from first principles. Assumes no previous exposure to linear algebra. Presents applications hand in hand with theory, leadingSee more details below

Overview

This book describes basic methods and algorithms used in modern, real problems likely to be encountered by engineers and scientists - and fosters an understanding of why mathematical techniques work and how they can be derived from first principles. Assumes no previous exposure to linear algebra. Presents applications hand in hand with theory, leading readers through the reasoning that leads to the important results. Provides theorems and proofs where needed. Features abundant exercises after almost every subsection, in a wide range of difficulty. A thorough reference for engineers and scientists.

Product Details

ISBN-13:
9780131473829
Publisher:
Pearson
Publication date:
12/10/2004
Edition description:
New Edition
Pages:
736
Sales rank:
285,511
Product dimensions:
8.20(w) x 10.20(h) x 1.20(d)

Related Subjects

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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