Differential equations /
Blanchard, Paul, 1951-
Differential equations / Paul Blanchard, Robert L. Devaney, Glen R. Hall. - 2nd ed. - Pacific Grove, CA : Brooks/Cole Thomson Learning, c2002. - xx, 786 p. : ill. ; 24 cm.
Includes index.
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. TOC
0534385141 9780534385149 0534228585
2001056095
Differential equations.
QA371 / .B63 2002
515.35 / BLD 2002
Differential equations / Paul Blanchard, Robert L. Devaney, Glen R. Hall. - 2nd ed. - Pacific Grove, CA : Brooks/Cole Thomson Learning, c2002. - xx, 786 p. : ill. ; 24 cm.
Includes index.
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. TOC
0534385141 9780534385149 0534228585
2001056095
Differential equations.
QA371 / .B63 2002
515.35 / BLD 2002