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Short course in ordinary differential equations / Qingkai Kong.

By: Material type: TextTextSeries: UniversitextPublication details: Switzerland : Springer, 2014.Description: xii, 267 p. : illustrations ; 24 cmISBN:
  • 9783319112381
Subject(s): DDC classification:
  • 515.352 23 K82
Contents:
Preface -- Notation and Abbreviations -- 1. Initial Value Problems -- 2. Linear Differential Equations -- 3. Lyapunov Stability Theory -- 4. Dynamic Systems and Planar Autonomous Equations -- 5. Introduction to Bifurcation Theory -- 6. Second-Order Linear Equations -- Answers and Hints -- Bibliography -- Index.
Summary: This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré?Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm?Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.352 K82 (Browse shelf(Opens below)) Available 135833
Total holds: 0

Includes bibliographical references and index.

Preface --
Notation and Abbreviations --
1. Initial Value Problems --
2. Linear Differential Equations --
3. Lyapunov Stability Theory --
4. Dynamic Systems and Planar Autonomous Equations --
5. Introduction to Bifurcation Theory --
6. Second-Order Linear Equations --
Answers and Hints --
Bibliography --
Index.

This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré?Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm?Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.

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