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| 001 | 978-3-031-02395-8 | ||
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_aWeintraub, Steven H. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981178 |
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| 245 | 1 | 0 |
_aJordan Canonical Form _h[electronic resource] : _bApplication to Differential Equations / _cby Steven H. Weintraub. |
| 250 | _a1st ed. 2008. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2008. |
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| 300 |
_aVII, 85 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 |
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| 505 | 0 | _aJordan Canonical Form -- Solving Systems of Linear Differential Equations -- Background Results: Bases, Coordinates, and Matrices -- Properties of the Complex Exponential. | |
| 520 | _aJordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it-eigenvalues, eigenvectors, and chains of generalized eigenvectors. We begin with the diagonalizable case and then proceed to the general case, but we do not present a complete proof. Indeed, our interest here is not in JCF per se, but in one of its important applications. We devote the bulk of our attention in this book to showing how to apply JCF to solve systems of constant-coefficient first order differential equations, where it is a very effective tool. We cover all situations-homogeneous and inhomogeneous systems; real and complex eigenvalues. We also treat the closely related topic of the matrix exponential. Our discussion is mostly confined to the 2-by-2 and 3-by-3 cases, and we present a wealth of examples that illustrate allthe possibilities in these cases (and of course, exercises for the reader). Table of Contents: Jordan Canonical Form / Solving Systems of Linear Differential Equations / Background Results: Bases, Coordinates, and Matrices / Properties of the Complex Exponential. | ||
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_iPrinted edition: _z9783031012679 |
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