授業の目的 【英語】
Goals of the Course [ENG] | | | 【Standardized across all programs】 The field of mathematics that describes and analyzes quantitative changes is analysis, and its central method is calculus. It is an essential research method in the natural sciences, but in recent years it has been widely applied to the social sciences. The goal of this course is to understand the basics of one-variable differentiation and integration as the first half of the year-round lecture. In particular, it is important to understand the essence of the limit and to be able to handle elementary functions such as logarithmic functions and trigonometric functions freely. |
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授業の達成目標 【英語】
Objectives of the Course [ENG] | | | The aim of the first half of this one-year course is to provide a solid understanding of functions of one real variable. The students will become familiar with the various tools necessary for the analysis of such functions and for their applications. |
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授業の内容や構成
Course Content or Plan | | 1. Limits and continuity: Basic properties of limits of sequences and functions, continuous functions and their basic properties, maxima and minima, asymptotic properties of functions.
2. Differentiation: Basic properties of the derivative and its interpretation, mean value theorem, higher derivatives, Taylor series.
3. Integration: Riemann integral and its properties, improper integrals, the fundamental theorem of calculus. |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | | Some basic knowledge on calculus from high school is assumed, including differentiation and integration of polynomial functions. Students are encouraged to attend the related Math Tutorial Ia. |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | The final grade will be determined by quizzes (30%), the midterm (30%) and a final exam (40%). The grading scale will be A+, A, B, C, C-, F. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course during the semester. |
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教科書
Textbook | | | Free reference books and lecture notes will be available on the website of the course. |
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参考書
Reference Book | | | Free reference books will be available on the website of the course. |
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課外学修等
Study Load (Self-directed Learning Outside Course Hours) | | | Students are expected to read their notes, and to be familiar with the content of the previous lecture of Calculus I before attending the next lecture. |
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注意事項
Notice for Students | | | Check the website mentioned below for updated information. |
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本授業に関するWebページ
Reference website for this Course | | |
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担当教員からのメッセージ
Message from the Instructor | | |
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実務経験のある教員等による授業科目（大学等における修学の支援に関する法律施行規則に基づくもの）
Courses taught by Instructors with practical experience | | |
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授業開講形態等
Lecture format, etc | | A-1）Face-to-face course （Only face-to-face classes）
* Classrooms for face-to-face classes can be found in Timetable B on the ILAS website. |
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