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 important research method that is widely applied to the natural sciences and, in recent years, the social sciences. The goal of this course is to understand the basics of multivariable calculus and to become familiar with and apply it to various calculations in the latter half of the year-round lecture. In particular, we emphasize understanding associated with geometric and spatial images. |
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授業の達成目標 【英語】
Objectives of the Course [ENG] | | | The aim of the second half of this one-year course is to provide a solid understanding of functions of several real variables. The students will become familiar with the various tools necessary for the analysis of such functions. |
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授業の内容や構成
Course Content or Plan | | The course will cover basic notions related to the study of functions of several variables. These include:
- Functions of several variables: partial derivatives, maximum and minimum
- Vector-valued functions of several variables: Jacobian matrix, implicit function theorem
- Integration: curve integrals of vector fields, volume integrals, surface integrals
- Green's theorem, divergence theorem, Stokes theorem
Throughout the course, we consider connections to and examples from the natural sciences. |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | | Some notions on functions of one variable, as seen in Calculus I. A basic knowledge of linear algebra will be an asset. It is strongly encouraged to attend the Mathematics Tutorial IIa which is linked to this course. |
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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 homework questions (40%), quizzes (10%), the midterm and final exam (50%) |
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教科書
Textbook | | | Lecture notes will be provided to students |
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参考書
Reference Book | | | Serge Lang, Calculus of Several Variables. Third Edition, Springer, 1987. |
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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 lectures of Calculus II before each tutorial sessions. |
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注意事項
Notice for Students | | |
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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 | | | It is easy to fall behind in this course without continual effort. I am always available to help you understand the content. |
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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 | | B-3）Face-to-face course（both simultaneous interactive and on-demand methods will be provided when necessary)
* Classrooms for face-to-face classes can be found in Timetable B on the ILAS website. |
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