Differential equations / Paul Blanchard, Robert L. Devaney, Glen R. Hall.

By: Blanchard, Paul, 1951-
Contributor(s): Devaney, Robert L, 1948- | Hall, Glen R
Material type: TextTextLanguage: English Publisher: Pacific Grove, CA : Brooks/Cole Thomson Learning, c2002Edition: 2nd edDescription: xx, 786 p. : ill. ; 24 cmISBN: 0534385141; 9780534385149; 0534228585 Subject(s): Differential equationsDDC classification: 515.35 LOC classification: QA371 | .B63 2002Online resources: WorldCat details
Contents:
Table of contents 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.
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Includes index.

Table of contents 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.

Applied Physics & Electronics

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