This course begins with the notion of differentiation of nonlinear operators, and discusses the existence of fixed points and its application, and the reduction to finite dimensions. This course is followed by Advanced topics in Analysis B.
Students are expected to understand fundamental notions and methods of nonlinear analysis, and apply them to some examples.
Students are expected to understand fundamental notions and methods of nonlinear analysis, and apply them to some examples.
Nonlinear operator, nonlinear analysis, reduction
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course.
Course schedule | Required learning | |
---|---|---|
Class 1 | Nonlinear operator | Details will be provided during each class session. |
Class 2 | Gateaux derivative, Frechet derivative | Details will be provided during each class session. |
Class 3 | Contraction mapping principle | Details will be provided during each class session. |
Class 4 | Banach's perturbation theorem | Details will be provided during each class session. |
Class 5 | Newton's method | Details will be provided during each class session. |
Class 6 | Implicit function theorem | Details will be provided during each class session. |
Class 7 | Nonlinear compact operator | Details will be provided during each class session. |
Class 8 | Lyapunov-Schmidt reduction | Details will be provided during each class session. |
None in particular
None in particular
Based on overall evaluation of the results for report and final examinations. Details will be announced during a lecture.
Students are required to complete Advanced topics in Analysis A (MTH.C402).
None in particular