IA ideas library
Differential equation IA ideas for HL (and ambitious SL)
Differential equations describe how something changes, which makes them perfect for epidemics, populations, cooling, falling objects and chemical reactions. They are in both HL courses: AA HL solves them analytically (separation of variables, integrating factors) and AI HL builds coupled systems, slope fields and Euler's method.
A strong DE exploration sets up the equation from assumptions you state, solves or simulates it, compares the result with data, and reflects on which assumption is doing the most damage when the model and reality disagree.
Differential equations & dynamics ideas (10)
- How long does a skydiver take to reach terminal velocity?AA HLAI HLAmbitious
- Linear or quadratic drag? Testing air resistance with falling coffee filtersAA HLAI HLSolid
- How much of cycling effort goes on air resistance? A coast-down testAA HLAI HLAmbitious
- How fast would flu spread through my school? An SIR modelAI HLAA HLAmbitious
- How long would a lake take to flush out a pollutant?AA HLAI HLSolid
- Can the Lotka–Volterra model explain the lynx and hare cycles?AI HLAA HLAmbitious
- Can mathematics predict a battle? Lanchester's laws and Iwo JimaAI HLAA HLAmbitious
- How does bread dough rise? A logistic model in the kitchenAA SLAA HLAI SLAI HLAccessible
- How fast does news spread through a year group?AI SLAI HLAA SLAA HLSolid
- Does caffeine build up if you drink coffee every few hours?AA SLAA HLAI SLAI HLSolid
Also relevant (7)
- How long does a bottle take to drain? Testing Torricelli's lawAA SLAA HLAI SLAI HLSolid
- Exponential or logistic? Modelling my country's populationAA SLAA HLAI SLAI HLSolid
- Which mug keeps tea hot longest? Newton's law of cooling, comparedAA SLAA HLAI SLAI HLAccessible
- Radioactive decay with dice: does chance produce an exponential curve?AA SLAI SLAA HLAI HLAccessible
- How much vaccination is enough to stop measles?AI SLAI HLAA SLSolid
- Modelling bacterial growth in the biology labAA SLAA HLAI SLAI HLSolid
- How fast did COVID-19 spread at the start? Comparing doubling timesAA SLAA HLAI SLAI HLSolid
Frequently asked questions
Can an SL student write about differential equations?
Yes, if you explain the new mathematics carefully and keep it at a level you fully understand. Euler's method on a spreadsheet is a good route. Criterion E rewards mathematics that is relevant and correct, not the hardest mathematics possible.
What data can I compare a differential equation model with?
Your own cooling or draining measurements, public epidemic data (for example the archived Johns Hopkins COVID-19 repository), population series from the UN or Our World in Data, or motion data from a video tracked in Tracker.
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