Perturbations: Theory and Methods
This is a course in perturbation theory for the solution of algebraic and differential equations, especially ordinary differential equations. It covers all of the methods commonly used in both regular and singular perturbations: Taylor series,
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actually appear applied approach approximate solution approximation asymptotic averaging becomes bifurcation bifurcation theory boundary bounded calculation called Chapter close coefficients compact complete compute consider constant continuous coordinates correction course curve defined depend derivatives determining differential equation difficult discussion equal error exact solution exactly example Exercise exist expansion expression fact fixed forcing formal function gauges given gives holds important initial initial conditions inner instance integral interval introduce leading limit linear matching means method necessary obtained original oscillator outer parameter partial periodic solutions perturbation positive possible present problem proof prove reduced problem remains requires resonance rest result roots satisfy scales Section solved standard form step Substituting Theorem theory tion turn uniform uniformly valid value problem variables vector zero