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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Laplace transform
An integral transform converts time-domain derivatives into algebraic relations under convergence conditions.
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Resonance
Forcing near a natural frequency can produce large oscillatory responses depending on damping.
Variation of parameters
Variable coefficients multiplying homogeneous solutions construct a particular solution of a forced linear ODE.
Bernoulli equations
A power substitution converts a suitable nonlinear first-order Bernoulli equation into a linear one.
Characteristic equations
An exponential trial converts a constant-coefficient homogeneous linear ODE into a polynomial equation.
Equilibria and stability
Stability describes whether nearby trajectories remain close to or approach an equilibrium.
Knowledge connections
- Variation of parameters · Related · Map context
- Resonance · Related · Map context