Differential equations and models
Change you can see.
Explore integration, differential equations, series, and geometry through physical models.
Follow the real situation, derive the mathematics, and test it with interactive graphs and worked practice.
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Differential equations and models
A differential equation specifies how a state changes.
A population rate law links growth to the current amount. Instead of prescribing the curve, the equation prescribes its slope.
Explore the idea ↗Interactive lessonA hot cup approaches the room temperature.
Cooling depends on the temperature gap. Change the initial temperature and rate constant to see a family of physical solutions.
Explore the idea ↗Interactive lessonApproximate a trajectory by following short tangents.
An Euler solver predicts the next temperature using the present cooling rate. Compare its line segments with the exact curve.
Explore the idea ↗Interactive lessonGrowth changes when resources become limited.
An exponential model grows forever, but a carrying capacity makes growth slow and can pull an oversized population downward.
Explore the idea ↗Interactive lessonAn integrating factor turns a sum into a product derivative.
A system with constant input and proportional loss approaches a balance where input equals loss.
Explore the idea ↗Interactive lessonA tank can keep its volume while changing its contents.
Clean water can become salty while equal inlet and outlet flows keep the level fixed. The mass balance must track solute separately from total liquid.
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