Introduction to differential equations with dynamical systems / Stephen L. Campbell and Richard Haberman.
Saved in:
Main Author:  

Other Authors:  
Format:  Book 
Language:  English 
Published: 
Princeton, N.J. :
Princeton Univ. Press,
c2008.

Subjects:  
Online Access:  Table of contents Contributor biographical information Publisher description 
Table of Contents:
 FirstOrder Differential Equations and Their Applications
 Introduction to ordinary differential equations
 The definite integral and the initial value problem
 The initial value problem and the indefinite integral
 The initial value problem and the definite integral
 Mechanics I: elementary motion of a particle with gravity only
 Firstorder separable differential equations
 Using definite integrals for separable differential equations
 Direction fields
 Existence and uniqueness
 Euler's numerical method (optional)
 Firstorder linear differential equations
 Form of the general solution
 Solutions of homogeneous firstorder linear differential equations
 Integrating factors for firstorder linear differential equations
 Linear firstorder differential equations with constant coefficients and constant input
 Homogeneous linear differential equations with constant coefficients
 Constant coefficient linear differential equations with constant input
 Constant coefficient differential equations with exponential input
 Constant coefficient differential equations with discontinuous input
 Growth and decay rroblems
 A first model of population growth
 Radioactive decay
 Thermal cooling
 Mixture problems
 Mixture problems with a fixed volume
 Mixture problems with variable volumes
 Electronic circuits
 Mechanics II: including air Rrsistance
 Orthogonal trajectories (optional)
 Linear Second and HigherOrder Differential Equations
 General solution of secondorder linear differential equations
 Initial value problem (for homogeneous equations)
 Reduction of order
 Homogeneous linear constant coefficient differential equations (second order)
 Homogeneous linear constant coefficient differential equations (nthorder)
 Mechanical vibrations I: formulation and free response
 Formulation of equations
 Simple harmonic motion (no damping, 8 = 0)
 Free response with friction (8 > 0)
 The method of undetermined coefficients
 Mechanical vibrations II: forced response
 Friction is absent (8 = 0)
 Friction is present (8 > 0) (damped forced oscillations)
 Linear electric circuits
 Euler equation
 Variation of parameters (secondorder)
 Variation of parameters (nthorder)
 The Laplace Transform
 Definition and basic properties
 The shifting theorem (multiplying by an exponential)
 Derivative theorem (multiplying by t)
 Inverse laplace transforms (roots, quadratics, and partial fractions)
 Initial value problems for differential equations
 Discontinuous forcing functions
 Solution of differential equations
 Periodic functions
 Integrals and the convolution theorem
 Derivation of the convolution theorem (optional)
 Impulses and distributions
 An Introduction to Linear Systems of Differential Equations and Their Phase Plane
 Introduction
 Introduction to linear systems of differential equations
 Solving linear systems using eigenvalues and eigenvectors of the matrix
 Solving linear systems if the eigenvalues are real and unequal
 Finding general solutions of linear systems in the case of complex eigenvalues
 Special systems with complex eigenvalues (optional)
 General solution of a linear system if the two real eigenvalues are equal (repeated) roots
 Eigenvalues and trace and determinant (optional)
 The phase plane for linear systems of differential equations
 Introduction to the phase plane for linear systems of differential equations
 Phase plane for linear systems of differential equations
 Real eigenvalues
 Complex eigenvalues
 General theorems
 Mostly Nonlinear FirstOrder Differential Equations
 Firstorder differential equations
 Equilibria and stability
 Equilibrium
 Stability
 Review of linearization
 Linear stability analysis
 Onedimensional phase lines
 Application to population dynamics: the logistic equation
 Nonlinear Systems of Differential Equations in the Plane
 Introduction
 Equilibria of nonlinear systems, linear stability analysis of equilibrium, and the phase plane
 Linear stability analysis and the phase plane
 Nonlinear systems: summary, philosophy, phase plane, direction field, nullclines
 Population models
 Two competing species
 Predatorprey population models
 Mechanical systems
 Nonlinear pendulum
 Linearized pendulum
 Conservative systems and the energy integral
 The phase plane and the potential
 Answers to oddnumbered exercises.