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:
- First-Order 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
- First-order separable differential equations
- Using definite integrals for separable differential equations
- Direction fields
- Existence and uniqueness
- Euler's numerical method (optional)
- First-order linear differential equations
- Form of the general solution
- Solutions of homogeneous first-order linear differential equations
- Integrating factors for first-order linear differential equations
- Linear first-order 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 Higher-Order Differential Equations
- General solution of second-order 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 (nth-order)
- 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 (second-order)
- Variation of parameters (nth-order)
- 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 First-Order Differential Equations
- First-order differential equations
- Equilibria and stability
- Equilibrium
- Stability
- Review of linearization
- Linear stability analysis
- One-dimensional 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
- Predator-prey population models
- Mechanical systems
- Nonlinear pendulum
- Linearized pendulum
- Conservative systems and the energy integral
- The phase plane and the potential
- Answers to odd-numbered exercises.