F
by C. Henry Edwards,
David E. Penney,
David T. Calvis,
Differential Equations and Linear Algebra, 4th Edition
- Differential Equations & Linear Algebra
- Contents
- Application Modules
- Preface
- 1 First-Order Differential Equations
- 2 Mathematical Models and Numerical Methods
- 2.1 Population Models
- 2.2 Equilibrium Solutions and Stability
- 2.3 Acceleration–Velocity Models Acceleration–Velocity Models
- 2.4 Numerical Approximation: Euler’s Method Numerical Approximation: Euler’s Method
- 2.5 A Closer Look at the Euler Method
- An Improvement in Euler’s Method
- 2.6 The Runge–Kutta Method The Runge–Kutta Method
- 3 Linear Systems and Matrices
- 4 Vector Spaces
- 5 Higher-Order Linear Differential Equations
- 5.1 Introduction: Second-Order Linear Equations
- 5.2 General Solutions of Linear Equations
- 5.3 Homogeneous Equations with Constant Coefficients
- 5.4 Mechanical Vibrations
- 5.5 Nonhomogeneous Equations and Undetermined Coefficients
- 5.6 Forced Oscillations and Resonance
- 6 Eigenvalues and Eigenvectors
- 7 Linear Systems of Differential Equations
- 7.1 First-Order Systems and Applications
- 7.2 Matrices and Linear Systems
- 7.3 The Eigenvalue Method for Linear Systems
- 7.4 A Gallery of Solution Curves of Linear Systems
- Systems of Dimension n=2
- Real Eigenvalues
- Saddle Points
- Nodes: Sinks and Sources
- Zero Eigenvalues and Straight-Line Solutions
- Repeated Eigenvalues; Proper and Improper Nodes
- The Special Case of a Repeated Zero Eigenvalue
- Complex Conjugate Eigenvalues and Eigenvectors
- Pure Imaginary Eigenvalues: Centers and Elliptical Orbits
- Complex Eigenvalues: Spiral Sinks and Sources
- A 3-Dimensional Example
- 7.4 Problems
- 7.4 Application Dynamic Phase Plane Graphics
- 7.5 Second-Order Systems and Mechanical Applications*
- 7.6 Multiple Eigenvalue Solutions
- 7.7 Numerical Methods for Systems
- 7.7 Application Comets and Spacecraft
- 8 Matrix Exponential Methods
- 9 Nonlinear Systems and Phenomena
- 9.1 Stability and the Phase Plane
- 9.2 Linear and Almost Linear Systems
- 9.3 Ecological Models: Predators and Competitors
- 9.4 Nonlinear Mechanical Systems
- 10 Laplace Transform Methods
- 11 Power Series Methods
- References for Further Study
- APPENDIX A Existence and Uniqueness of Solutions
- APPENDIX B Theory of Determinants
- Answers to Selected Problems
- Index
F
Finite-dimensional vector space, 237
First-order equation, 7
FitzHugh, Richard (1922–2007), 555
FitzHugh-Nagumo equations, 555
Flight trajectories, 63
Flywheel on cart, 327
Folia of Descartes, 524
Forced motion, 303
Forced oscillations:
Forced vibrations, 266
Formal multiplication of series, 606
Fox-rabbit example, 357
Fps units, 13
Free motion, 303
Free oscillations, 428
Free vibrations, 266
Frequency, 305
resonance, 432
Frobenius, Georg (1848–1919), 631
Frobenius series, 631
Frobenius series solutions, 633
From the Earth to the Moon, 100
Function space, 259
Fundamental matrix, 469
Funnel, 89
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