Ordinary Differential Equations

One of the few books on Ordinary Differential Equations (ODEs), this book contains both qualitative theory, allowing students to analyze the solutions without obtaining formulas, and methods and techniques for obtaining formulas. It features friendly explanations of theorems on top of their formal proofs, expressed in examples, questions, figures, exercises, fun models related to various aspects of life, and even Math Theater explaining, using ODEs, the advantage of optimization by feedback versus a rigid plan. Exercises, both simple and more advanced levels, can be found within.

This will allow students to deal with ODEs with a full understanding of what they are doing rather than manipulating with symbols, and even to extend themselves some theorems and techniques. The book is designed for students, teachers, and researchers. It can be used straightforwardly for a one-semester course on ODEs; alternatively, teachers might find it worthwhile to include some of the chapters in their course.

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• Welcome to ODEs
• Theorems on Existence, Uniqueness, and Prolongation of Solutions
• First Order Autonomous ODEs
• Math Theater Regarding Fish in a Lake and Love Between B and G
• Separable ODEs
• Linear First Order ODEs
• First Order ODEs Which Can Be Solved by a Change of Variables
• Main Theorems for System of First Order ODEs and kth Order ODEs
• Equations x''= f(x)
• Homogeneous Systems of Linear First Order ODEs with Constant Coefficients
• Non-Homogeneous Systems of Linear First Order ODEs with Constant Coefficients
• Linear nth Order ODEs with Constant Coefficients
• Linear nth Order ODEs with Non-Constant Coefficients
• Stability of Equilibrium Points
• ODEs with a Small Parameter
• Series Solution of ODEs
• Proof of Peano Existence Theorem