授業科目名 年度 学期 開講曜日・時限 学部・研究科 全担当教員 単位数
34757:Computing Mathematics(G1) 2019 春セメスター 月2 情報理工学部 白 楊 2

キャンパス

BKC

授業施設

プリズムハウス１０９号教室

授業で利用する言語

英語

授業の概要と方法

The goal of this course is to bring fundamental knowledge of differentiation and integration to students. Specifically, this course covers some basic contents of Calculus, including limit, continuity, derivative and its applications, indefinite integral and definite integral, multiple integral, curvilinear integral, surface integral, series, and so on. This course lays the foundation for learning future courses such as differential equation.

受講生の到達目標

After this course, students should understand the importance of Calculus as one of the fundamental subjects for most of the engineering programs. Also, students will be able to explain the basic concepts of limit, differentiation and integration. At the same time, they will gain the skills of computing derivatives and integrals, as well as applying these skills to solve concrete problems such as calculating areas and volumes, or optimization problems.

事前に履修しておくことが望まれる科目

Pre-calculus: limits, continuity, and derivatives

授業スケジュール

授業回数/
担当教員（複数担当の場合） 		テーマ
キーワード・文献・補足事項等
1

Preliminaries

Limits and continuity, tangents and the derivative at a point
2

Differentiation (1)

The derivative as a function, differentiation rules, the derivative as a rate of change
3

Differentiation (2)

Derivatives of trigonometric functions, derivatives of transcendental functions
4

Differentiation (3)

The chain rule, implicit differentiation, linearization and differentials
5

Differentiation (4)

Applications of derivatives: indeterminate forms and L’Hôpital’s Rule, extreme values of functions
6

Differentiation (5)

Applications of derivatives: the mean value theorem, optimization
7

Mid-term Exam

Lasts 90 min. and covers topics of Weeks 1 through 6
8

Integration (1)

Pre-calculus: area and estimating with finite sums, the definite integral, indefinite integrals
9

Integration (2)

Techniques of integration: substitution, integration by parts, trigonometric Integrals, etc.
10

Integration (3)

Applications of definite integrals: calculation of area, volume, and arch length, etc.
11

Integration (4)

Multiple integrals: double integrals, triple integrals, moments and centers of mass
12

Integration (5)

Integrals and vector fields: line integrals, surface integrals, etc.
13

Infinite Sequences and Series (1)

Infinite series, the integral test, comparison tests, the ratio and root tests
14

Infinite Sequences and Series (2)

Power series, Taylor and Maclaurin series, the binomial series
15

Course Overview

Covers topics of Weeks 1 through 14

授業実施形態

授業外学習の指示

Students are recommended to read relevant chapters before class. This will be helpful for them to better and faster understand the contents of the lecture. Homework will be assigned within each lecture and is due on the next lecture. Collaboration on homework is encouraged because discussion with other students is an efficient way of solving challenging problems. However, it is not allowed to copy solutions from other students directly.

成績評価方法

種別 割合(%) 評価基準等
定期試験（筆記） 50

Ability to solve the questions provided in the final exam
レポート試験
（統一締切日を締切とするレポート）		 0

上記以外の試験・レポート、平常点評価
（日常的な授業における取組状況の評価）		 50

Attendance, assignments and the mid-term exam

成績評価方法(備考)

Software such as Mathematica, Matlab, and so on, is recommended to use for checking the answers to your homework problems. However, solutions to these problems need to be clearly understood and written in steps by yourself.

受講および研究に関するアドバイス

Students are recommended to review the contents of the lecture after each class. Although the slides used in the lecture will be provided, taking notes is considered to be necessary, since the slides may not cover everything in the lecture. The example problems given during the class are recommended to be re-studied by yourselves after class.

教科書

書名 著者 出版社 ISBNコード 備考
Thomas’ Calculus 13th Ed. George B. Thomas, Jr., Maurice D. Weir, Joel Hass, Christopher Heil Pearson Education 978-0-321-87896-0

教科書(使用頻度、その他補足)

参考書

参考書(使用頻度、その他補足)

参考になるwwwページ

授業内外における学生・教員間のコミュニケーションの方法

学生との直接対話,その他(教員より別途指示）

備考

This course describes the theory of some very practical and immensely useful parts of computer science. Students are encouraged to deepen their understanding of the principles learned by implementing those principles as working programs. For example, understanding binary arithmetic makes possible the implementation of functions providing arbitrary-precision arithmetic (where overflow never occurs). Understanding state machines makes possible the implementation of pattern recognisers. These are challenging, but realistic, projects to undertake while studying the 'Introduction to Programming' course. Your instructors will be more than happy to help you attempt any such project that you feel is at, or even just beyond, your level of programming competence.