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Mathematics - Dynamical Systems & Differential Equations | Ordinary Differential Equations

Ordinary Differential Equations

Analysis, Qualitative Theory and Control

Logemann, Hartmut, Ryan, Eugene P

2014, XIII, 333 p. 40 illus.

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  • Provides a self-contained, rigorous and analytical treatment of initial-value problems for ordinary differential equations
  • Includes an introduction to mathematical control theory which sets this text apart from others on the subject
  • Allows for discontinuous time dependence in differential equations, but does not require Lebesgue integration theory
  • Accessible to undergraduate students

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 the current textbook literature.

The following topics are particularly emphasised:

• existence, uniqueness and continuation of solutions,
• continuous dependence on initial data,
• 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.

Content Level » Lower undergraduate

Keywords » Control Theory - Feedback - Lyapunov Stability - Ordinary Differential Equations - Stability Theory

Related subjects » Applications - Dynamical Systems & Differential Equations - Mechanics

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Distribution rights for India: Researchco Book Centre, New Delhi, India

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