Discrete vs Continuous

Mathematical Modeling · Axiom Academy

Two fundamentally different ways to model change in the world Step 1: Two Ways to See Change Explore the difference between discrete and continuous models by watching how population grows in each approach. Population counted at specific moments (generations) Population flows smoothly at every instant Drag each example to the correct category. Think about whether the quantity changes in jumps or flows smoothly. Step 3: How Time Works Differently Click each model type to see how they represent the same changing quantity over time. Discrete: Values exist only at specific time points (t = 0, 1, 2, 3, ...) Step 4: Choosing Your Approach Answer the question to determine which modeling approach fits your situation. Counted items, scheduled events, generations Flowing quantities, smooth changes Difference equations, sequences, iteration Differential equations, calculus, smooth curves Here is what you have discovered about discrete and continuous modeling. Good for: populations, transactions, counts Good for: temperature, velocity, pressure In this unit, you will learn to build and analyze discrete models using difference equations . You will explore population dynamics, financial models, and discover how simple discrete rules can lead to complex behavior - including chaos!

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.