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開講年度 2019年度 開講箇所 基幹理工学部
Calculus A

IPSE Course

担当教員 ボーウェン マーク
学期曜日時限 秋学期  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 01:51-10―06(共通ゼミ室)/02:51-10―06(共通ゼミ室) キャンパス 西早稲田(旧大久保)
科目キー 26G0210004 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 14:11:32

授業概要 [ISPE Subject]
Important: Depending on the number of registered students, this may be an active learning class in which students are expected to do pre-class reading in order to aid their understanding of the material.

This is an introductory calculus course taught in English.  The course covers single-variable (differential and integral) calculus and assumes no previous knowledge of the subject.  We will build step-by-step from basic principles up to more advanced results.  We will also consider applications of the results to various fields of science and engineering.

This course also aims to increase the students' academic/scientific English vocabulary.

This course meets twice a week for 15 weeks.
授業の到達目標 Learning Goals:

1) Gain an understanding of methods of (primarily) single variable differentiation and integration

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:
October 1st: Functions, Limits and Continuity
October 3rd: Differentiation toolbox

Week 2:
October 8th: Rigorous limits
October 10th: Radians, Sandwich Theorem, and the derivatives of trigonometric functions

Week 3:
October 15th: Composite functions and the chain ruke
October 17th: Examples class 1

Week 4: 
October 24th: Rolle's Theorem, Mean-Value Theorem 
October 29th: Applications: Related rates, orthogonal trajectories, power rule

Week 5:
October 31st: Extrema
November 5th: Curve sketching

Week 6:
November 7th: Examples class 2
November 12th: Definite integrals

Week 7:
November 14th: Fundamental Theorems of Calculus
November 19th: Logarithms

Week 8:
November 21st: Exponentials
November 26th: Indeterminate forms and L'Hopital

Week 9:
November 28th: Inverse functions, inverse trigonometric functions
December 3rd: Example class 3

Week 10:
December 5th: Midterm (in-class examination) [there may be schedule changes due to class progress]
December 10th: Integration substitutions

Week 11:
December 12th: Partial Fractions
December 17th: Integration by parts

Week 12:
December 19th: Infinite series I
January 7th: Infinite series II

Week 13:
January 9th: Improper integrals
January 14th: Examples class 4

Week 14:
January 16th: Taylor polynomials
January 21st: Power series

Week 15:
January 23rd: Taylor series
January 28th: In-class examination (final) and review
教科書 There is no required textbook for this course.
参考文献 The instructor will recommend books for reference in the first lecture.
割合 評価基準
試験: 70% Midterm 30%
Final exam 40%

Provisionally, the in-class exams will be held in the 10th and 15th week of classes. Please be aware that there may be schedule changes due to class progress.
その他: 30% 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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