2016 Advanced topics in Analysis B

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Yanagida Eiji 
Course component(s)
Lecture     
Day/Period(Room No.)
Mon3-4(H201)  
Group
-
Course number
MTH.C402
Credits
1
Academic year
2016
Offered quarter
2Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
Japanese
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Course description and aims

This course follows Advanced topics in Analysis A.

This course begins with nonlinear differential equations and continuous dynamical systems, local properties, especially the notion of stability. Also, this course discusses the existence of various orbits and their geometric properties.

Student learning outcomes

Students will understand fundamental notions and methods of nonlinear analysis, and apply them to some examples.

Keywords

Nonlinear differential equation, continuous dynamical system, stability, orbit

Competencies that will be developed

Specialist skills Intercultural skills Communication 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 differential equation Details will be provided during each class session.
Class 2 Theory of continuous dynamical systems Details will be provided during each class session.
Class 3 Stability Details will be provided during each class session.
Class 4 Stable manifold and unstable manifold Details will be provided during each class session.
Class 5 Homoclinic orbit Details will be provided during each class session.
Class 6 Periodic orbit Details will be provided during each class session.
Class 7 Homotopy method Details will be provided during each class session.
Class 8 Bifurcation theory 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

  • MTH.C401 : Advanced topics in Analysis A

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

Students are required to have completed Advanced topics in Analysis A (MTH.C401).

Other

None in particular

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