## A second course in elementary differential equationsFocusing on applicable rather than applied mathematics, this text is appropriate for advanced undergraduates majoring in any discipline. The author emphasizes basic real analysis as well as differential equations. 1986 edition. Includes 39 figures. |

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### Contents

Systems of Linear Differential Equations 1 Introduction | 1 |

Some Elementary Matrix Algebra | 2 |

The Structure of Solutions of Homogeneous Linear Systems | 14 |

Copyright | |

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### Common terms and phrases

apply asymptotically stable behavior boundary conditions boundary value problem called Chapter complete computation Consider the system constant coefficient continuous functions contraction mapping theorem corresponding cosh curve definition denote diagonal matrix eigenfunctions eigenvalues eigenvector elements example Exercise existence and uniqueness existence theorem Figure Floquet multipliers fundamental matrix given Hence Hint initial conditions initial value problem integral interval Lemma Liapunov limit cycle linear combination linear system linearly independent linearly independent solutions Lipschitz condition mathematics metric space n x n nonlinear system nonsingular nontrivial solution norm Note omega limit set ordinary differential equations origin orthogonal parameter pendulum periodic solutions phase plane polar polynomial proof properties Putzer algorithm real numbers satisfies a Lipschitz scalar equation Section Show sinh solution of 9.1 solve stability Sturm-Liouville problem Suppose system of differential takes the form Theorem 5.1 theory trajectory trivial solution unique solution variables vector Wronskian xn(t yields