Math 130A: Ordinary Differential Equations, part I.
Homework solutions.Below are links to homework solutions; the
topics of the problems are indicated.
- Homework
1. Equilibrium points; sinks and sources; phase-lines;
bifurcation-diagrams and bifurcation. Separation of variables.
- Homework
2. Eigenvalues and general solutions to linear systems. Converting
the harmonic oscillator equation to a system or first order equations.
- Homework
3. Eigenvalues, Jordan normal form; solutions to linear systems.
Bifurcation in linear systems.
- Homework
4. Trace and determinant. Eigenvalues and general solutions.
- Homework
5. Jordan normal form; block matrices.
- Homework
6. Point-set topology; general solutions for linear systems.
- Homework
7. A pair of harmonic oscillators; exponentials of matrices. Do the
exponentials of matrices commute?
- Homework
9. Linearising non-linear systems. Behaviours of linearised systems
around stationary points.
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