シラバス詳細照会

シラバス詳細照会

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授業情報

開講年度 開講箇所 科目名 2019年度 創造理工学部 Partial Differential EquationsIPSE Course ボーウェン　マーク 春学期  水２時限 数学　必修 ２年以上 2 ５３-４０３教室 西早稲田（旧大久保） 27G0210012 01 英語 MATX23ZL 数学 数学 解析学 中級レベル（発展・応用） 講義

最終更新日時：2019/02/20 14:19:33

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.

Learn how some partial differential equations can be derived from modelling physical phenomena.

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

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

Take-home exam: 20%
その他: 40％ Homework

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