In this course, you will :
- What are differential equations and how do they work?
- By completing this chemistry challenge, you will be able to sketch integral curves like a pro.
- Investigate the meaning of the integrating factor in physics.
- Learn how to visualise the essential characteristics of equation pairs.
- Learn how to use vector geometry to explore linear systems as a powerful tool.
- Discover the intricate relationship between higher-order equations and systems.
1. First-Order Separable Equations
- Modeling: The Drag Equation
- Separate and Integrate
- Application: Molecular Motor
- The Phase Portrait
2. Advanced First-Order Equations
- Direction Fields
- Integrating Factor
- Application: A Mixing Problem
- The Potential
3. Basics of Linear Systems
- The Phase Plane
- The Matrix Exponential
- Application: Underdamped Springs
- Non-Diagonalizable Matrices
4. Higher-Order Equations
- Equations of Order Two
- Application: RLC Filter
- Challenge: Higher-Order Equations