TY - BOOK AU - Blanchard,Paul AU - Devaney,Robert L. AU - Hall,Glen R. TI - Differential equations SN - 0534385141 AV - QA371 .B63 2002 U1 - 515.35 PY - 2002/// CY - Pacific Grove, CA PB - Brooks/Cole Thomson Learning KW - Differential equations N1 - Includes index; TOC; 1 First-order differential equations -- Modeling via differential equations -- Analytic technique: separation of variables -- Qualitative technique: slope fields -- Numerical techniques: Euler's method -- Existence and uniqueness of solutions -- Equilibria and the phase line -- Bifurcations -- Linear differential equations -- Changing variables -- Labs for chapter 1 -- 2 First order systems -- Modeling via systems -- The geometry of systems -- Analytic methods for special systems -- Euler's method for systems -- The Lorenz equations -- Labs for chapter 2 -- 3 Linear systems -- Properties of linear systems and linearity principle -- Straight-line solutions -- Phase planes for linear systems with Eigenvalues -- Complex Eigenvalues -- Special cases: repeated and Eigenvalues -- Second-order linear equations -- The trace-determinant plane -- Linear systems in three dimensions -- 4 Forcing and resonance -- Forced harmonic oscillators -- Sinusoidal forcing -- Undamped forcing and resonance -- Amplitude and phase of the steady state -- The Tacoma Narrows Brodge 5 Nonlinear systems -- Equilibrium point analysis -- Qualitative analysis -- Hamiltonian systems -- Dissipative systems -- Nonlinear systems in three dimensions -- Periodic forcing of nonlinear systems and chaos -- Labs for chapter 5 -- 6 Laplace Transformes -- Laplace Transforms -- Discontinuous functions -- Second-order equations -- Delta functions and impulse forcing -- Convolutions -- The qualitative theory of Laplace Transforms -- Labs for chapter 6 -- 7 Numerical methods -- Numerical Error in Euler's Method -- Improving Euler's method -- The Runge-Kutta method -- The effects of finite arithmetic -- Labs for chapter 7 -- 8 Discrete dynamical systems -- the discrete logistic equation -- Fixed points and periodic points -- Bifurcations -- Chaos -- Chaos in the Lorenz system -- Labs for chapter 8; APE UR - http://www.worldcat.org/title/differential-equations/oclc/48449686&referer=brief_results ER -