Special Mathematics Lecture (Differential equations and dynamical systems)

Goals of the Course

【Standardized across all programs】 In a global and interconnected society, mathematics play a central role. They are at the root of all communications tools, and serve as a universal language for natural and social sciences. All current technological developments are based on them. Mathematics can also be learned, enjoyed, and shared by everybody. Studying mathematics is also learning humility, tolerance, and diversity.

The aim of these Special Mathematics Lectures is to provide a solid knowledge on various mathematical topics. Concomitantly, students will develop a rigorous argumentation and a critical thinking. Each semester, a new subject is proposed, and these lectures are accessible to all students of Nagoya University, independently of their major and of their academic age. These special lectures also offer a unique opportunity to study in an international, transdisciplinary, and friendly environment.

Objectives of the Course

Differential equations and dynamical systems are playing an essential role in many research fields, and in particular for describing the evolution of time dependent systems. Our goal is to provide the necessary background information for understanding these evolutions and their asymptotic behaviors. The presentation will be accessible to all students, independently of their major. Students will learn the abstract theory of differential equations and dynamical systems, and will be able to apply this knowledge to their respective field of expertise.

Course Contents or Plan

Program :

1. Introduction through examples
2. Linear differential equations or systems
3. Initial value problems
4. Dynamical systems
5. Examples in 2D
6. Dynamical systems in any dimension
7. Discrete time evolution processes
8. Cellular automata

Course Prerequisites and Related Courses

Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but need an approval from the instructor.

Course Evaluation Method and Criteria

The final grade will be based on the active participation during the lectures and on some written reports. Students will be encouraged to work on applications related to their major during the semester. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course during the semester.

Study Load (Self-directed Learning Outside Course Hours)

Students are expected to read their notes, and to be familiar with the content of the previous lectures before each new lecture.

Notice for students

It is expected that the students show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions might be organized on a weekly basis.

Textbook

Lecture Notes

Additional information

Reference Website

This lecture is provided under Creative Commons Attribution-Non Commercial-ShareAlike 4.0 International.

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