First-Order Differential Equations: Theory, Methods and Applications provides comprehensive treatment of first-order ordinary differential equations for undergraduates and graduate students in mathematics, physics, engineering, and the applied sciences. The presentation balances theoretical foundations with practical solution techniques and scientific modeling.
Five chapters develop the existence and uniqueness theory for initial value problems including the Picard-Lindel鐪 theorem, Picard iteration, Peano's theorem, interval of definition, and Gr霵wall's inequality. This framework provides essential preparation for advanced study in differential equations and dynamical systems. The text systematically presents standard techniques for solving first-order equations: separable equations, linear equations, exact equations, homogeneous equations, and the method of integrating factors. Each chapter is developed through clear exposition, worked-out examples, and progressive exercises with answers. Dedicated chapters demonstrate how differential equations arise from fundamental physical principles. Topics include population dynamics (exponential, logistic, Gompertz, threshold, Allee effect, and harvesting models), Newton's law of cooling, mixing problems and chemical kinetics, radioactive decay, motion under gravity with air resistance, and electrical circuit analysis.外文書商品之書封，為出版社提供之樣本。實際出貨商品，以出版社所提供之現有版本為主。部份書籍，因出版社供應狀況特殊，匯率將依實際狀況做調整。
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