Learn Differential Equations I

Description

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.

Syllabus :

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

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