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 ofthis 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 study.fsfsfsscs
