2018 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  Terashima Yuji  Murofushi Toshiaki  Suzuki Sakie 
Course component(s)
Lecture
Day/Period(Room No.)
Mon3-4(W351)  Thr3-4(W351)  
Group
-
Course number
MCS.T401
Credits
2
Academic year
2018
Offered quarter
1Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
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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

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
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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 Stable, unstable and center manifolds Understand the contents covered by the lecture.
Class 12 Asymptotic analysis by center manifold theorem Understand the contents covered by the lecture.
Class 13 Introduction to bifurcation theory Understand the contents covered by the lecture.
Class 14 Limit Cycle Understand the contents covered by the lecture.
Class 15 Poincaré–Bendixson theorem Understand the contents covered by the lecture.

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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