2020 | Analysis on Continuous Systems

2020　Analysis on Continuous Systems

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Academic unit or major: Graduate major in Mathematical and Computing Science

Instructor(s): Nishibata Shinya Miura Hideyuki Umehara Masaaki Murofushi Toshiaki Suzuki Sakie

Class Format: Lecture (ZOOM)

Media-enhanced courses

Day/Period(Room No.): Mon3-4(W832) Thr3-4(W832)

Group: -

Course number: MCS.T401

Credits: 2

Academic year: 2020

Offered quarter: 1Q

Syllabus updated: 2020/9/18

Lecture notes updated: -

Language used: Japanese

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Syllabus

Course description and aims

Differential equations are utilized to analyze the mathematical structure of nonlinear phenomena, In this lecture we introduce methods to handle differential equations. In the first half of lectures, we study basic theories such existence theorem. In the second half, we study more advanced theories to analyze the large time behavior of solutions.

Student learning outcomes

In this lecture, we study the basic concepts and methods to study the mathematical structure of nonlinear phenomena, We show the existence of solutions to ordinary differential equations. Then we discuss asymptotic analysis, bifurcation theory and limit cycle as special topics.

Keywords

Ordinary differential equations

Competencies that will be developed

✔ Specialist skills

Intercultural skills

Communication skills

Critical thinking skills

Practical and/or problem-solving skills

Class flow

The lectures provide the fundamentals of ordinary differential equations.

Course schedule/Required learning

	Course schedule	Required learning
Class 1	Existence of time local solution	Understand the contents covered by the lecture.
Class 2	Uniqueness of solution	Understand the contents covered by the lecture.
Class 3	Dependence of solution on parameter	Understand the contents covered by the lecture.
Class 4	Existence of time global solution	Understand the contents covered by the lecture.
Class 5	Linear approximation of autonomous system	Understand the contents covered by the lecture.
Class 6	Stability and instability of equilibrium point	Understand the contents covered by the lecture.
Class 7	Asymptotic analysis by linearization	Understand the contents covered by the lecture.
Class 8	Lyapunov’ｓ method	Understand the contents covered by the lecture.
Class 9	Asymptotic analysis by Lyapunov’ｓ method	Understand the contents covered by the lecture.
Class 10	Stable, instable and center manifolds	Understand the contents covered by the lecture.
Class 11	Asymptotic analysis by center manifold theorem	Understand the contents covered by the lecture.
Class 12	Introduction to bifurcation theory	Understand the contents covered by the lecture.
Class 13	Limit Cycle	Understand the contents covered by the lecture.
Class 14	Poincaré–Bendixson theorem	Understand the contents covered by the lecture.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

None

Reference books, course materials, etc.

None.

Assessment criteria and methods

By scores of　reports.

Related courses

MCS.T211 ： Applied Calculus
MCS.T301 ： Vector and Functional analysis
MCS.T311 ： Applied Theory on Differential Equations

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

None.

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