Ordinary Differential Equations
Explore first-order equations; linear equations and forcing; systems and phase space. Concepts and connections are available independently of video coverage.
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Systems of ODEs
Coupled differential equations describe interacting state variables.
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Derivatives
A derivative is the limit of a difference quotient, measuring local rate of change when that limit exists.
Eigenvalues and eigenvectors
A nonzero eigenvector is scaled by a linear operator; the scale factor is its eigenvalue.
Phase portraits
A phase portrait displays trajectories in state space rather than against time.
Second-order linear ODEs
A second-order linear ODE combines a function and its first two derivatives linearly.
Bernoulli equations
A power substitution converts a suitable nonlinear first-order Bernoulli equation into a linear one.
Knowledge connections
- Phase portraits · Related · Map context
- Eigenvalues and eigenvectors · Related · Map context
- Second-order linear ODEs · Related · Map context
- Derivatives · Related · Map context
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