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Ordinary Differential Equations: Analysis, Qualitative Theory and Control
Paperback
Series: Springer Undergraduate Mathematics
Technology & EngineeringGeneral MathematicsGeneral Science
ISBN13: 9781447163978
Publisher: Springer Nature
Published: Mar 19 2014
Pages: 333
Weight: 1.07
Height: 0.72 Width: 6.14 Depth: 9.21
Language: English
The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature.
The following topics are particularly emphasised:
- existence, uniqueness and continuation of solutions,
- flows,
- qualitative behaviour of solutions,
- limit sets,
- stability theory,
- invariance principles,
- introductory control theory,
- feedback and stabilization.
The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability.
Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.
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