Differential Equations for Modeling

~60 min · 15 stations

Start reading — Station 01

Conductor

The Conductor

Welcome aboard the express route to understanding change. We are mapping the invisible forces that shape our world, from cooling coffee to population growth. Mind the gap as we accelerate.

What you will learn

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FOUNDATION

Establishes the core vocabulary and essential context you need before going further.

• Define the nature of rates within dynamic systems

Station 01: The Language of Change▶

• Distinguish between independent variables and dependent variables

Station 02: Variables and Constants▶

• Map relationships between input values and output values

Station 03: Introduction to Functions▶

CORE CONCEPTS

Unpacks the ideas and principles that the subject is built on.

• Explain the geometric meaning of a derivative

Station 04: Defining Derivatives▶

• Solve first-order equations through basic integration

Station 05: Solving Simple Equations▶

• Construct models for exponential population growth

Station 06: Modeling Growth Patterns▶

• Formulate models for heat transfer over time

Station 07: Rate of Cooling Laws▶

MECHANICS

Examines how things actually work — the processes, rules, and systems in action.

• Combine different rates into a single model

Station 08: Integrating Multiple Rates▶

• Determine steady states within a dynamic system

Station 09: Equilibrium Point Analysis▶

• Sketch phase portraits for simple systems

Station 10: Visualizing Phase Spaces▶

APPLICATION

Puts knowledge to use through real-world scenarios and practical problems.

• Adjust growth models for limited environmental resources

Station 11: Resource Limitation Models▶

• Model the interaction between two competing species

Station 12: Predator Prey Dynamics▶

• Predict the spread of disease within populations

Station 13: Epidemic Spread Modeling▶

SYNTHESIS

Connects everything together and explores broader implications and open questions.

• Compare theoretical models against real world data

Station 14: Validating Complex Models▶

• Forecast future system states using established models

Station 15: Future Predictive Modeling▶

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General Public / 9th GradeAI Generated · gemini-3.1-flash-lite

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