2016 Advanced courses in Analysis A

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Academic unit or major
Mathematics
Instructor(s)
Yanagida Eiji 
Course component(s)
Lecture
Day/Period(Room No.)
Mon3-4(H201)  
Group
-
Course number
ZUA.C331
Credits
1
Academic year
2016
Offered quarter
1Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
Japanese
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Course description and aims

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.

Student learning outcomes

Students are expected to understand fundamental notions and methods of nonlinear analysis, and apply them to some examples. This course is followed by Advanced courses in Analysis B.

Keywords

Nonlinear operator, nonlinear analysis, reduction

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Standard lecture course.

Course schedule/Required learning

  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.

Textbook(s)

None in particular

Reference books, course materials, etc.

None in particular

Assessment criteria and methods

Based on overall evaluation of the results for report and final examinations. Details will be announced during a lecture.

Related courses

  • ZUA.C332 : Advanced courses in Analysis B

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are required to complete Advanced courses in Analysis B (ZUA.C332).

Other

None in particular

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