This textbook offers an engaging account of the theory of ordinary
differential equations intended for advanced undergraduate students of
mathematics. Informed by the author's extensive teaching experience, the
book presents a series of carefully selected topics that, taken
together, cover an essential body of knowledge in the field. Each topic
is treated rigorously and in depth.
The book begins with a thorough treatment of linear differential
equations, including general boundary conditions and Green's functions.
The next chapters cover separable equations and other problems solvable
by quadratures, series solutions of linear equations and matrix
exponentials, culminating in Sturm-Liouville theory, an indispensable
tool for partial differential equations and mathematical physics. The
theoretical underpinnings of the material, namely, the existence and
uniqueness of solutions and dependence on initial values, are treated at
length. A noteworthy feature of this book is the inclusion of project
sections, which go beyond the main text by introducing important further
topics, guiding the student by alternating exercises and explanations.
Designed to serve as the basis for a course for upper undergraduate
students, the prerequisites for this book are a rigorous grounding in
analysis (real and complex), multivariate calculus and linear algebra.
Some familiarity with metric spaces is also helpful. The numerous
exercises of the text provide ample opportunities for practice, and the
aforementioned projects can be used for guided study. Some exercises
have hints to help make the book suitable for independent
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