List price: $210.00
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.
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
Peter Olver and Cheri Shakiban
ISBN13: 978-0131473829For 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