This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.
Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations
is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations.
Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained. "This book provides a thorough and mathematically rigorous presentation of the basic theory of differential equations. ... The author has a style and approach that makes the book quite readable. There is, also, given explanatory and motivational material, associated with carefully chosen examples and exercises (with hints). This is an excellent book ... by means of which an undergraduate student can be introduced to ordinary and partial differential equations." (George Karakostas, zbMATH 1370.34001, 2017)
Introduction.- Existence and uniqueness for the Cauchy problem.- Systems of linear differential equations.- Stability theory.- Prime integrals and first-order partial differential equations.