Differential Equations

Linearization Near Critical Points

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In this session we learn how to use a technique called linearization. This technique allows us to apply the qualitative methods we developed for linear systems (in the session on Phase Portraits) to the qualitative sketching of the phase portraits of autonomous nonlinear systems.

Session Activities

Read the course notes:

• Linearization Near Critical Points: Introduction (PDF)
• Sketching Non-linear Systems (PDF)

Watch the lecture video clip:

• The Nonlinear Pendulum

Read the course notes:

• Structural Stability (PDF)
• The Borderline Geometric Types (PDF)

Watch the lecture video clip:

• Example: Predator-Prey and Volterra’s Principle

Read the course notes:

• Structural Stability for Non-linear Systems (PDF)

Watch the problem solving video:

• Linearization

Check Yourself

Complete the problem sets:

• Problem Set Part I Problems (PDF)

• Problem Set Part I Solutions (PDF)

• Problem Set Part II Problems (PDF)

• Problem Set Part II Solutions (PDF)

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