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First Course in the Qualitative Theory of Differential Equations, A
James H. Liu, James Madison University

ISBN-10: 0130083801
ISBN-13: 9780130083807

Publisher: Prentice Hall
Copyright: 2003
Format: Cloth; 558 pp
Status: Out of Print

Suggested retail price: $111.00
This item is out of print and is no longer available for purchase.

For upper-level undergraduate and beginning graduate-level courses in Qualitative Theory of Differential Equations.

Striking a unique balance between advanced and elementary material, this text is perfect for a second course in differential equations or a first theory course in differential equations. Liu provides a complete analysis of those subjects that are of fundamental importance and related to current research—including details that other texts in the field tend to overlook. As a result, students gain a solid understanding of the topics covered then challenge their creativity with exercises, reading, and/or research projects.

  • Chapters 1-7 are targeted to undergraduates, while Chapters 8-12 are more focused on graduate level presentation.

    • Chapters 1-7 provide an elementary approach so students can apply their mathematical knowledge and Chapters 8-12 strengthen students' analysis skills.

  • Topics chosen are of fundamental importance, accessible, and related to current research.

    • Provides accessible and rigorous treatment of most important subjects that leads to current research.

  • A review of the subjects covered in an Elementary Differential Equations course—Appears in Chapter 1.

    • Describes for students some qualitative properties of differential equations that will be covered in the rest of the book.

  • End-of-section exercises.

    • Gives students ample opportunity to practice the material just learned.

  • Open-ended exercises.

    • Provides direction toward graduation theses and research in qualitative theory of differential equations.



 1. A Brief Description.


 2. Existence and Uniqueness.


 3. Linear Differential Equations.


 4. Autonomous Differential Equations in R2.


 5. Stability. Part I.


 6. Bifurcation.


 7. Chaos.


 8. Dynamical Systems and Poincare—Bendixson Theorem in R2.


 9. Stability. Part II.


10. Bounded Solutions.


11. Periodic Solutions.


12. Remarks on Some New Types of Differential Equations.


Appendix.


References.


Index.

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