Qualitative Theory of Differential Equations
A First Course
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Beschreibung
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.
Qualitative Theory of Differential Equations 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.
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.
Qualitative Theory of Differential Equations 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.
Provides a concise introduction to the fundamentals of ODEs with an emphasis on qualitative analysis Focuses on equipping students with the tools to answer critical questions rather than specific solution techniques Offers numerous worked examples, applications, homework exercises, and sample exams
Autor*in
Slobodan Simić
Themen in »Qualitative Theory of Differential Equations«
Differential equations Ordinary differential equations ODEs Phase portrait Phase line Qualitative analysis of differential equations Linear equations Eigenvalues Laplace transform Harmonic oscillator Phase plan First order systems Linear systems Nonlinear systems