Differential Equations

Unit 5: Qualitative Descriptions of Systems

Week 12

Class 54: Topic 27: Linear Phase Portraits

• Reading: Topic 27: Qualitative Behavior of Linear Systems: Phase-Plane (PDF)
• In-Class Notes: Linear Phase Portraits (PDF)
• Class 54 Problems (PDF)
• Class 54 Solutions (PDF)

Class 55: Topic 27:  Linear Phase Portraits (cont.)

• Reading: Topic 27: Qualitative Behavior of Linear Systems: Phase-Plane (PDF)
• In-Class Notes: Linear Phase Portraits (cont.) (PDF)
• Class 55 Problems (PDF)
• Class 55 Solutions (PDF)

Class 56: Recitation 12

• Recitation 12 Problems (PDF)
• Recitation 12 Solutions (PDF)

Class 57: Topic 28: Nonlinear Systems

• Reading: Topic 28: Qualitative Behavior of Non-Linear Systems, Linearization (PDF)
• In-Class Notes: Nonlinear Systems (PDF)
• Class 57 Problems (PDF)
• Class 57 Solutions (PDF)

Class 58: Review and Catch-Up 

Week 13

Class 59: Topic 29: Structural Stability [no problems]

• Reading: Topic 29: Structural Stability (PDF)
• In-Class Notes: Structural Stability (PDF)

Class 60: Topic 30: Population Models

• Reading: Topic 30: Applications to Population Biology: Volterra’s Principle (PDF)
• In-Class Notes: Population Models (PDF)
• Class 60 Problems (PDF)
• Class 60 Solutions (PDF)

Class 61: Recitation 13

• Recitation 13 Problems (PDF)
• Recitation 13 Solutions (PDF)

Class 62: Quiz 6 (Topics 24–26) (see Quizzes page)

Class 63: Review 

Week 14

Classes 64–65: Review 

Class 66: Recitation 14

• Recitation 14 Problems (PDF)
• Recitation 14 Solutions (PDF)

Week 15 (Final Exam Week)

Quiz 7 (four problems from unit 1, four problems from unit 5, and two problems of your choice from units 2, 3, or 4) (see Quizzes page)

Optional Reading for Enrichment

• Reading: Topic 31: Application to Physics: the Pendulum (PDF)