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A textbook on ordinary differential equations

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概要 This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercise...s that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. --続きを見る
目次 First order linear differential equations
Theory of first order differential equations
First order nonlinear differential equations
Existence and uniqueness for systems and higher order equations
Second order equations
Higher order linear equations
Systems of first order equations
Qualitative analysis of 2x2 systems and nonlinear second order equations
Sturm Liouville eigenvalue theory
Solutions by infinite series and Bessel functions
Laplace transform
Stability theory
Boundary value problems
Appendix A. Numerical methods
Answers to selected exercises.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2015 English/International

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登録日 2020.06.27
更新日 2020.10.21