Qualitative Theory of Differential Equations

A First Course
Erscheinungsjahr 2027
ISBN: 978-3-032-41966-8
Verlag: Birkhäuser

Buch, Englisch, 256 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Compact Textbooks in Mathematics

This textbook provides a concise introduction to the fundamentals of ordinary differential equations with an emphasis on qualitative analysis. Rather than presenting techniques to solve specific differential equations, the author focuses instead on equipping students with the tools to answer questions they will likely encounter, such as: Are there any equilibrium or periodic solutions? How do solutions behave near them? What is the asymptotic behavior of typical solutions as time moves to infinity? Chapters highlight first-order linear and nonlinear equations, planar linear systems with constant coefficients, and second-order linear differential equations. Numerous worked examples and applications appear, including a sustained examination of the forced harmonic oscillator. The appendices offer several sample exams as well as a discussion of the Picard method of successive approximations and the matrix exponential.

is an ideal text for an introductory course in ordinary differential equations. Assuming only a background in multivariable calculus, this will be particularly suitable for students in engineering and science.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Simic, Slobodan

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

First order differential equations.- First order systems.- Linear systems.- Nonlinear systems.-  Laplace transform.- Appendix A. Old Exams.

Über Autor(innen)

Slobodan Simic is a professor of mathematics at San José State University. He received his PhD at the University of California at Berkeley in 1995, and has held positions at the University of Illinois, Chicago, University of Southern California, and UC Berkeley before joining San José State. Broadly speaking, his main research interests are dynamical systems and differential geometry.