Summary and Info
This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed by students to continue to the next level in applying the methods to more advanced problems. There is a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics, chemical reactors, and other areas. Moreover, the text contains a new, elementary chapter on systems of differential equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent chapters treat systems in a more formal way. Briefly, the topics include: First-order equations: separable, linear, autonomous, and bifurcation phenomena; Second-order linear homogeneous and non-homogeneous equations; Laplace transforms; and Linear and nonlinear systems, and phase plane properties Introduction -- Lyapunov's Direct Method for Uncertain Systems -- Stability of Uncertain Controlled Systems -- Stability of Quasilinear Uncertain Systems -- Stability of Large-Scale Uncertain Systems -- Interval and Parametric Stability of Uncertain Systems -- Stability of Solutions of Uncertain Impulsive Systems -- Stability of Solutions of Uncertain Dynamic Equations on a Time Scale -- Singularly Perturbed Systems with Uncertain Structure -- Qualitative Analysis of Solutions of Set Differential Equations -- Set Differential Equations with a Robust Causal Operator -- Stability of a Set of Impulsive Equations
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