Title:
Linear algebra and differential equations
Personal Author:
Publication Information:
Boston, Mass. : Addison Wesley, 2002
ISBN:
9780201662122
Added Author:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010050537 | QA184.2 P47 2002 | Open Access Book | Book | Searching... |
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Summary
Summary
This book has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including courses that cover differential equations first. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest.
KEY TOPICS: Matrices and Determinants; Vector Spaces; First Order Ordinary Differential Equations; Linear Differential Equations; Linear Transformations and Eigenvalues and Eigenvectors; Systems of Differential Equations; The Laplace Transform; Power Series Solutions to Linear Differential Equations; Inner Product Spaces MARKET: For all readers interested in linear algebra and differential equations.Table of Contents
| 1 Matrices and Determinants |
| Systems of Linear Equations |
| Matrices and Matrix Operations |
| Inverses of Matrices |
| Special Matrices and Additional Properties of Matrices |
| Determinants |
| Further Properties of Determinants |
| Proofs of Theorems on Determinants |
| 2 Vector Spaces |
| Vector Spaces |
| Subspaces and Spanning Sets |
| Linear Independence and Bases |
| Dimension; Nullspace, Rowspace, and Column Space |
| Wronskians |
| 3 First Order Ordinary Differential Equations |
| Introduction to Differential Equations |
| Separable Differential Equations |
| Exact Differential Equations |
| Linear Differential Equations |
| More Techniques for Solving First Order Differential Equations |
| Modeling With Differential Equations |
| Reduction of Order |
| The Theory of First Order Differential Equations |
| Numerical Solutions of Ordinary Differential Equations |
| 4 Linear Differential Equations |
| The Theory of Higher Order Linear Differential Equations |
| Homogenous Constant Coefficient Linear Differential Equations |
| The Method of Undetermined Coefficients |
| The Method of Variation of Parameters |
| Some Applications of Higher Order Differential Equations |
| 5 Linear Transformations and Eigenvalues and Eigenvectors |
| Linear Transformations |
| The Algebra of Linear Transformations; Differential Operators and Differential Equations |
| Matrices for Linear Transformations |
| Eigenvectors and Eigenvalues of Matrices |
| Similar Matrices, Diagonalization, and Jordan Canonical Form |
| Eigenvectors and Eigenvalues of Linear Transformations |
| 6 Systems of Differential Equations |
| The Theory of Systems of Linear Differential Equations |
| Homogenous Systems with Constant Coefficients: The Diagonalizable Case |
| Homogenous Systems with Constant Coefficients: The Nondiagonalizable Case |
| Nonhomogenous Linear Systems |
| Converting Differential Equations to First Order Systems |
| Applications Involving Systems of Linear Differential Equations |
| 2x2 Systems of Nonlinear Differential Equations |
| 7 The Laplace Transform |
| Definition and Properties of the Laplace Transform |
| Solving Constant Coefficient Line |
