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開講年度 2019年度 開講箇所 基幹理工学部
Calculus B

IPSE Course

担当教員 ボーウェン マーク
学期曜日時限 春学期  01:火5時限/02:木4時限
科目区分 数学 必修 配当年次 1年以上 単位数 4
使用教室 01:52-204教室/02:52-204教室 キャンパス 西早稲田(旧大久保)
科目キー 26G0210007 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 MATX13ZL
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 初級レベル(入門・導入) 授業形態 講義


最終更新日時:2019/02/20 14:16:20

In the real-world, quantities of interest (such as temperature, location, stock prices,...) depend on more than one variable.  We will see how to extend the ideas of single variable calculus to tackle these multi-variable problems.
授業の到達目標 Learning Goals:

1) Gain an understanding of methods of (primarily) multi-variable calculus

2) Understand how to apply methods from differential and integral calculus to solving problems arising in applications.

3) Expand English language science/engineering vocabulary
事前・事後学習の内容 Students are expected to review their notes after each class.
授業計画 Week 1:
April 9th: Introduction
April 11th: Parametric curves in the plane

Week 2:
April 16th: Functions of several variables
April 18th: Partial derivatives

Week 3:
April 23rd: Applications of the chain rule
April 25th Normals to curves

Week 4:
May 7th: Directional derivatives
May 9th: Example class 1

Week 5:
May 14th: Normals to surfaces 
May 16th: Extrema

Week 6:
May 21st: Extrema (part 2)
May 23rd: Lagrange Multipliers

Week 7:
May 28th: Example class 2
May 30th: Double integrals

Week 8:
June 4th: Double integrals over non-rectangular domains
June 6th: Triple integrals in Cartesian coordinates

Week 9:
June 11th: Examples class 3
June 13th: Midterm (in-class exam) [Exam schedule may change due to class progress]

Week 10:
June 18th: Polar coordinates
June 20th: Double integrals in polar coordinates

Week 11:
June 25th: Triple integrals in cylindrical and spherical coordinates
June 27th: Moments and centres of mass

Week 12:
July 2nd: Change of variables in double integrals
July 4th: Examples class 4

Week 13:
July 9th: Arclength and curvature
July 11th: Line integrals

Week 14:
July 16th: Theorems of Pappus
July 18th: Integration through vector fields

Week 15:
July 23rd: Conservative vector fields and potential functions
July 25th: Final (in-class examination) and review

教科書 There is no required textbook for this class.
参考文献 The lecturer will discuss useful reference textbooks in the first class.
割合 評価基準
試験: 60% Mid-term 30%
Final Exam 30%

Provisionally, the examinations will be held in week 9 and week 15 of the regular class period. Please be aware that there may be schedule changes due to class progress.
その他: 40% Continuous assessment (Quizzes, homework and so on)
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 transport problems, please see me. 


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