2021 Differential Equations II

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Academic unit or major
Undergraduate major in Mathematics
Yanagida Eiji 
Course component(s)
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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.


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

Competencies that will be developed

Specialist skills Intercultural skills Communication 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

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.


Theory of differential equations, Eiji Yanagida and Ei Shin-Ichiro, Asakura Shoten (Japanese)

Reference books, course materials, etc.

to be announced

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.)

Students are expected to have passed Differential Equations I.

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