A first look at perturbation theory
This introductory text explains methods for obtaining approximate solutions to mathematical problems by exploiting the presence of small, dimensionless parameters. For engineering and physical science undergraduates.
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ROOTS OF POLYNOMIALS
SINGULAR PERTURBATIONS IN ORDINARY
PERIODIC SOLUTIONS OF THE SIMPLEST
7 other sections not shown
algebraic analysis approximate solution associated polynomial assume asymptotic BC's behavior boundary layer calcium Catenary change of variable Chapter compute consider convergence damping denote determine differential equations dimensionless domain drill string equating to zero error exact solution example Exercise 5.1 exponents expression finding the roots follows force function Fundamental Theorem graph Hence IC's identical implies independent variable initial conditions integration introduce linear membrane non-zero roots Nondimensionalization nonlinear ODE's Ordinary Differential Equations pendulum period of oscillation perturbation methods perturbation theory physical Poincare's Method proper values protein quadratic formula radius of convergence reduces regular expansion regular perturbation expansion result right side roots of z2 singular perturbation singular perturbation problem Singular Problem small parameter solution of 7.8 solve spring-mass system Substituting sufficiendy small sufficiently small takes the form Theorem of Perturbation trigonometric identity two-scale method uniformly valid upper bound WKB approximation yields Young's modulus