and Joel E. Keizer
| A.1 |
Matrix and Vector Manipulation |
| A.2 |
A Brief Review of Power Series |
| A.3 |
Linear ODEs |
| A.3.1 |
Solution of Systems of Linear ODEs |
| A.3.2 |
Numerical Solutions of ODEs |
| A.3.3 |
Eigenvalues and Eigenvectors |
| A.4 |
Phase Plane Analysis |
| A.4.1 |
Stability of Linear Steady States |
| A.4.2 |
Stability of Nonlinear Steady States |
| A.5 |
Bifurcation Theory |
| A.5.1 |
Bifurcation at a Zero Eigenvalue |
| A.5.2 |
Bifurcation at a Pair of Imaginary Eigenvalues |
| A.6 |
Perturbation Theory |
| A.6.1 |
Regular Perturbation |
| A.6.2 |
Resonances |
| A.6.3 |
Singular Perturbation Theory |
| A.7 |
Exercises |
