Graduate Lecture in Partial Differential Equations

Numbering Code G-SCI11 90406 LJ55 Year/Term 2022 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Master's students Target Student
Language Japanese Day/Period
Instructor name NAKANISHI KENJI (Research Institute for Mathematical Sciences Professor)
Outline and Purpose of the Course Partial differential equations (PDE) arise as models to describe various phenomena in physics, chemistry, biology, informatics, finance, etc.. The analysis of PDE is the primary mathematical means to understand, predict and control those phenomena as well as the mechaism, and also to solve problems in abstract mathematical theories. The main goal of this course is to understand properties of solutions for typial PDEs and basic methods of analysis. More recent topics will be introduced from time to time and around the end of the course.
Course Goals -To understand basic properties of solutions and methods of analysis for partial differential equations.
-To understand the roles and positions of partial differential equations in various fields of sciences.
Schedule and Contents 15 lectures in total will be given on the following items (including the feedback). The plan is to spend the number of weeks in () for each item in order, but it may be changed according to requests and status of the students, as well as the progress of lectures.
Course Requirements The knowledge of the calculus and the linear algebra is assumed. Basic knowledge will be used without notice from the set theory, the general topology and the Lebesgue integration, too. It is desirable that the students also know the ordinary differential equations and the functional analysis to some extent.
Study outside of Class (preparation and review) Work actively on report assignments etc.
Textbooks Textbooks/References No textbook is used, but lecture notes (in Japanese) will be posted on KULASIS before each lecture. English versions may be provided upon request.
References, etc. Partial Differential Equations, F. John, (Springer), ISBN:978-0-387-90609-6
Partial Differential Equations, L. C. Evans, (American Mathematical Society), ISBN:978-0-8218-4974-3
Elliptic Partial Differential Equations of Second Order, D. Gilbarg and N. S. Trudinger , (Springer), ISBN:978-3-540-41160-4
Functional Analysis, Sobolev Spaces and Partial Differential Equations, H. Brezis , (Springer), ISBN:978-0-387-70913-0
Distributions, Partial Differential Equations, and Harmonic Analysis, D. Mitrea, (Springer), ISBN:978-1- 4614-8207-9
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