Differential equations - Blanchard, Paul 1951-; Devaney, Robert L. 1948-; Hall, Glen R. (Pacific Grove, CA Brooks/Cole Thomson Learning, 2002)
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.
Includes index.
Keywords: Differential equations