Ordinary Differential Equations with Applications

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Focusing on ordinary differential equations, this book offers a comprehensive, student-friendly introduction based on a year-long course at the University of Missouri. It emphasizes the Implicit Function Theorem and later explores perturbation theory applications. Unique to this text is the inclusion of the Fiber Contraction Principle, which proves the smoothness of functions derived from fixed points of contractions. These concepts are also applicable to infinite dimensions, providing a broader context for advanced studies in mathematics.