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開講年度 2019年度 開講箇所 創造理工学部
Partial Differential Equations

IPSE Course

担当教員 ボーウェン マーク
学期曜日時限 春学期  水2時限
科目区分 数学 必修 配当年次 2年以上 単位数 2
使用教室 53-403教室 キャンパス 西早稲田(旧大久保)
科目キー 27G0210012 科目クラスコード 01
授業で使用する言語 英語
  コース・コード MATX23ZL
大分野名称 数学
中分野名称 数学
小分野名称 解析学
レベル 中級レベル(発展・応用) 授業形態 講義


最終更新日時:2019/02/20 14:19:33

授業概要 Partial differential equations can be used to model various physical phenomena such as heat flow and wave motion.  Consequently, partial differential equations arise throughout nature, science, engineering and industry (as well as being useful in finance and the social sciences).

This introductory course will show how to derive partial differential equations modelling heat flow and wave motion (as well as other phenomena) and introduce some powerful methods of solution for the resulting equations.  Students will learn to interpret the behaviour of solutions in terms of the original physical problem and in a wider mathematical context.
授業の到達目標 Understand how to solve basic linear partial differential equations

Learn how some partial differential equations can be derived from modelling physical phenomena.
事前・事後学習の内容 Students show review their notes after every class.
April 10th: Introduction

Infinite domain problems
April 17th: First order equations and the method of characteristics

April 24th: Quasilinear problems and shocks

May 8th: The wave equation on an infinite domain

May 15th: Fourier transforms

May 22nd: Fourier transforms -- the heat equation on an infinite domain (and introduction to boundary conditions)

May 29th: Laplace transforms

Finite domain problems

June 5th: The heat equation and the method of separation of variables

June 12th: Fourier series

June 19th: Sturm-Liouville Theory

June 26th: Sturm-Liouville Theory -- worked example

July 3rd: The wave equation and separation of variables

Laplace's Equation

July 10th: Solution of Laplace's equation in rectangular and radially symmetric domains

July 17th: Maximum principle, existence and uniqueness

July 24th: Final in-class examination and review
教科書 There is no assigned textbook for this course.
参考文献 The lecturer will discuss relevant textbooks for reference in the first lecture.
割合 評価基準
試験: 60% Final in-class examination: 40%

The final examination will be held in the last week of the regular class period.

Take-home exam: 20%
その他: 40% Homework
備考・関連URL In general, late homework will not be accepted.  If you are late turning in a homework due to special circumstances such as illness, emergencies, or public transportation problems, please see me.


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