AMS 212B Lecture Notes, Spring 2015
WARNING: downloading the lecture notes
and putting them under your pillow at night will not help you learn the material.
Preparation for each class : You must come to class prepared - just "showing up" is not sufficient. Graduate studies involve progressively more independent working practices, and this class will slowly get you used to this. Prior to each class, you must:
- Read the material from the last lecture, and come prepared with questions on what you do not understand. You must be ready to be able to summarize the previous lecture in front of the class.
- Read the assigned material, and work through it. Come prepared with questions on material you did not understand. The class will assume that you have read the assigned chapters, and you must be prepared to answer questions on them.
Week 1:
Lecture notes:
- Lecture 1: Introduction to perturbation methods 1.
- Further reading for Lecture 1: sections 1.1 and 1.3 od textbook
- Lecture 2: Introduction to perturbation methods 2.
- Lecture 2.5: Introduction to perturbation methods 3
- Futher reading for Lecture 2: section 1.2 and 1.4 of textbook
Week 2:
Lecture notes:
- Lecture 3: Asymptotics 1.
- Further reading for lecture 3: sections 2.1 of textbook.
- Lecture 4: Asymptotics 2.
- Further reading for lecture 4: rest of Chapter 2.
Week 3:
Lecture notes:
- Lecture 5: The Linsted-Poincare method for perturbed periodic systems
- Further reading for lecture 5: sections 3.1 and 3.2 of textbook.
- Lecture 6: Lighthill's generalization and renormalization.
- Further reading for lecture 6: section 3.3 of textbook
Week 4:
Lecture notes:
- Lecture 7: Renormalization for non-periodic systems
- Lecture 8: Multi-scale methods (part 1)
- Further reading for lecture 8: sections 4.1 to 4.3 of textbook. Note that 4.1 and 4.2 are a bit repetitive, skip if you are pressed for time, but do read 4.3.
Week 5:
Lecture notes:
- Lecture 9: Multi-scale methods (part 2)
- Lecture 10: Boundary Layers (part 1)
- Further reading: section 5.1 of the textbook.
Week 6:
Lecture notes:
- Lecture 11: Boundary layers (part 2)
- Lecture 12: Boundary layers (part 3)
- Further reading: sections 5.2 and 5.3 of the textbook
Week 7:
Lecture notes:
- Lecture 13: The method of dominant balance and the WKB approximation (part 1)
- Further reading: Chapter 6.1
Week 8:
Lecture notes:
- Lecture 14: The method of dominant balance and the WKB approximation (part 2)
- Lecture 15: The method of dominant balance and the WKB approximation (part 3)
- Further reading: Chapter 6.2-6.3
Week 9:
Lecture notes:
- Lecture 16: The method of dominant balance and the WKB approximation (part 4)
- Further reading: Chapter 6.4-6.5
- Lecture 17: Asymptotic theory of integrals (part 1)
- Further reading: Chapter 7.1-7.3
Week 10:
Lecture notes:
- Lecture 18: Asymptotic theory of integrals (part 2)
- Further reading: rest of Chapter 7.