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開講年度 2019年度 開講箇所 先進理工学部
Ordinary Differential Equations (2)

IPSE Course

担当教員 ボーウェン マーク
学期曜日時限 秋学期  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 54-404教室 キャンパス 西早稲田(旧大久保)
科目キー 28G0210010 科目クラスコード 02
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:2019/03/06 13:24:47

We first learn in calculus that derivatives can be used to represent the rate of change of one variable (height, temperature,....) with the change in another (space, time,...).  At the simplest level, a differential equation is just an equation containing a derivative.  Consequently, any physical phenomena that involves a rate of change leads to a differential equation, and an understanding of solution methods for differential equations is therefore essential for studies of phenomena in physics, biology, chemistry and engineering.

This course focusses on the solution of ordinary differential equations (those depending on a single independent variable) and as well as teaching solution methodologies, also includes various applications of the methods to problems from the natural sciences and engineering.
授業の到達目標 Learn methods that can be used to solve a wide variety of ordinary differential equations

Learn how some ordinary differential equations can be derived from modelling physical phenomena
事前・事後学習の内容 Students should review their notes after every class.
Basic concepts and first order ordinary differential equations (ODE)

October 2nd: First order, homogeneous, linear equations: Population models, terminology

October 9th: First order, linear, non-homogeneous equations: Population models, Newton's Law of Cooling, Integrating factors, particular solutions, variation of parameters

October 16th: First order, nonlinear equations: Logistic growth, separable equations and existence/uniqueness

Second order ODE

October 23rd: Second order, constant coefficient, homogeneous equations: LRC circuits, Newton's Second Law

October 30th: Second order, non-homogeneous equations: Forced-systems, Resonance, Particular solutions (non-homogeneous)

November 6th: Second order, homogeneous equations: Reduction of order, general theory, the Wronskian

November 13th: Second order, non-homogeneous equations: Variation of parameters

November 20th:  Midterm in-class examination [there may be schedule changes due to class progress]

November 27th: Laplace transforms for ODE I: Heaviside functions, switches

December 4th: Laplace transforms for ODE I: Dirac delta functions, impulses

Systems of ODE

December 11th: Higher order equations and constant coefficient systems (I): eigenvalues, eigenvectors (distinct and complex roots of the characteristic equation)

December 18th: Higher order equations and constant coefficient systems (II): repeated roots of the characteristic equation, matrix exponential form 

Geometric theory

January 8th: 2x2 linear constant coefficient systems (I) : Phase lines and phase planes

January 15th: 2x2 linear constant coefficient systems (II) : Null-clines, direction fields; Applications: mechanical systems, 

[If time allows, we may also study some series solutions to ordinary differential equations]

January 22nd: Final in-class examination and review
教科書 There is no required textbook for this course
参考文献 The instructor will recommend reference texts in the first week of class
割合 評価基準
試験: 70% Midterm (30%)
Final examination (40%)

Provisionally, the in-class examinations are set for week 8 and week 15 of the regular class period. Please be aware that there may be schedule changes due to class progress.
その他: 30% Homework (30%)
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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