The mathematical formulations of problems in physics economics biology and other sciences are usually embodied in differential equations the analysis of the resulting equations then provides new insight into the original problems. The old classic by smale and hirschdifferential equationsdynamical systems and linear algebra is best balanced by the second edition coauthored with robert devaney differential equationsdynamical systems and an introduction to chaos the second edition is more applied and less mathematically rigorousbut it contains much more information on . This textbook is designed for a one year course covering the fundamentals of partial differential equations geared towards advanced undergraduates and beginning graduate students in mathematics science engineering and elsewhere. This treatment is more detailed than that in most differential equations texts and provides a solid foundation for the next two chapters chapter 3 studies linear systems of differential equations it starts with the matrix exponential melding material from chapters 1 and 2 and uses this exponential as a key tool in the linear theory. Introduction to differential equations michael e taylor university of north carolina chapel hill nc mathematical analysis of ordinary th e ams pure and applied undergraduate texts series is a collection of fi rst class undergraduate textbooks made available at moderate prices th e intent behind the series
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