2019 Differential Equations II

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Onodera Michiaki 
Course component(s)
Lecture
Day/Period(Room No.)
Tue7-8(W242)  
Group
-
Course number
MTH.C342
Credits
1
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
2019/7/22
Language used
Japanese
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Course description and aims

The main topic of this course is nonlinear differential equation. Other topics cover existence and uniqueness of initial value problem, continuous dependence on parameters and theory of finite dimensional dynamical system. This course is a continuation of Differential Equations I.


Differential equations are fundamental notions appearing in all fields of mathematics. Space of solutions have algebraic structure, existence theorems of solutions give various geometric and analytic objects of great interests. This course is an entry to these paths.

Student learning outcomes

The main topic of this course is a basic theory and its applications of ordinary differential equations of one unknown variable. Ordinary differential equations describe various natural phenomena and physical laws, thus, method of solving equations and its theory are important mathematically as well as for applications. Method of solving ordinary differential equation and theory for analyzing qualitative properties of solutions are to be discussed. Applications to science and engineering will be also discussed.

Keywords

nonlinear ordinary differential equation, existence and uniqueness of solution, stability

Competencies that will be developed

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

Class flow

Standard course lecture.

Course schedule/Required learning

  Course schedule Required learning
Class 1 nonlinear ordinary differential equation Details will be provided during each class session
Class 2 existence and uniqueness of solution Details will be provided during each class session
Class 3 dependence of solution on initial value and parameter Details will be provided during each class session
Class 4 vector field and its flow Details will be provided during each class session
Class 5 stability Details will be provided during each class session
Class 6 phase space Details will be provided during each class session
Class 7 Hamilton flow, gradient flow Details will be provided during each class session
Class 8 examples and applications of nonlinear ordinary differential equations, comprehension check-up Details will be provided during each class session

Textbook(s)

Introduction to differential equations, Koji Kasahara, Asakura Shoten (Japanese)

Reference books, course materials, etc.

to be determined

Assessment criteria and methods

Evaluation based on mid-term and final exam. Details will be provided in the class.

Related courses

  • MTH.C341 : Differential Equations I

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

Differential Equations I

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