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The Ordinary Differential Equations Project
Thomas W. Judson
Contents
Index
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Contents
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Front Matter
Colophon
Dedication
Preface
Acknowledgements
1
A First Look at Differential Equations
Modeling with Differential Equations
Separable Differential Equations
Geometric and Quantitative Analysis
Analyzing Equations Numerically
First-Order Linear Equations
Existence and Uniqueness of Solutions
Bifurcations
Projects for First-Order Differential Equations
2
Systems of Differential Equations
Modeling with Systems
The Geometry of Systems
Numerical Techniques for Systems
Solving Systems Analytically
Projects for Systems of Differential Equations
3
Linear Systems
Linear Algebra in a Nutshell
Planar Systems
Phase Plane Analysis of Linear Systems
Complex Eigenvalues
Repeated Eigenvalues
Changing Coordinates
The Trace-Determinant Plane
Linear Systems in Higher Dimensions
The Matrix Exponential
Projects Systems of Linear Differential Equations
4
Second-Order Linear Equations
Homogeneous Linear Equations
Forcing
Sinusoidal Forcing
Forcing and Resonance
Projects for Second-Order Differential Equations
5
Nonlinear Systems
Linearization
Hamiltonian Systems
More Nonlinear Mechanics
The Hopf Bifurcation
Projects
6
The Laplace Transform
The Laplace Transform
Solving Initial Value Problems
Delta Functions and Forcing
Convolution
Projects for Laplace Transforms
Reference
A
GNU Free Documentation License
B
Hints and Answers to Selected Exercises
Readings and References
C
Notation
Index
Colophon
Authored in PreTeXt
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Section
3.10
Projects Systems of Linear Differential Equations
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Projects go here.
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Project
3.10.1
.
Project 1.
First project.