0: Introduction
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- 0.1: Notes About These Notes
- This page discusses a book that originated from the author's class notes for differential equations courses taught at various universities, including UIUC, UCSD, and OSU. The book is positioned as a potential replacement for traditional texts by Edwards and Penney or Boyce and DiPrima. It is organized to allow flexible course structures, covering topics like ODEs and PDEs, with resources available online. Acknowledgments are given to various individuals for their contributions and support.
- 0.2: Introduction to Differential Equations
- The page discusses the significance of differential equations in science and engineering, highlighting their role as the mathematical language of physical laws. It emphasizes the importance of understanding differential equations for success in related studies. Examples of solving these equations, such as Newton???s law of cooling and population growth models, are provided.
- 0.3: Classification of Differential Equations
- This page discusses the classification of differential equations into ordinary (ODE) and partial (PDE), provides examples of each, and explains the concept of systems of differential equations. It further delves into classifications based on order, linearity, homogeneity, and whether the equations have constant coefficients or are autonomous.
- 0.E: Introduction (Exercises)
- The page provides introductory exercises related to differential equations from a book for engineers. It includes a series of exercises requiring verification and classification of differential equations, solution finding, and initial condition problems. Various equations, both ordinary and partial, are discussed with specific problems addressing linearity, homogeneity, and order of the equations.