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授業科目
Course Title

Ｔｏｐｉｃｓ　ｉｎ　Ａｎａｌｙｓｉｓ 担当者
Instructor
 講師　　 瀬戸　道生 後学期　月曜日4時限
単 位
Credit
2
 関連するディプロマポリシー　Related Diploma Policy 時代の課題と社会の要請に応えた専門的知識と技能/Expert knowledge and skills to address the issues of the age and the demands of society 到達目標　Target to be Reached After the course, the students are expected to be able to:  understand the basic concept of Fourier series and integrals, use and apply the famous formulas (Fourier inversion formula, Parseval's formula, Plancherel's formula, etc.), understand the role of the theory of Lebesgue integral in Fourier analysis. 授業内容　Course Content Fourier analysis is not only useful in many fields, but also interesting as a theory in mathematics. The pourpose of this lecture is to introduce its basic theory and applications, and also this course is intended to be support to understand functional analysis. The course covers the following topics: Fourier series, Dirichlet's theorem, heat equation on the circle, Fejer's theorem, L^2 space, Parseval formula, Fourier integrals, Schwartz class, inversion formula, heat equation on the real line, Plancherel's theorem, and various applications. 授業計画　Course Planning 01. Introduction 02. Fourier coefficients 03. L^2-geometry 04. Dirichlet kernel 05. Dirichlet's theorem 06. Heat equation on the circle 07. Fejer's theorem 08. Parseval's formula 09. Fourier integrals 10. Schwartz class 11. Fourier inversion formula 12. Heat equation on the real line 13. Plancherel's theorem 14. Various applications Lecture notes will be given in the first lecture. Homework will be given in ``almost every" lecture. Your solutions to the assigned homework will be graded and returned to you. 授業運営　Course Management Lecture 評価方法　Evaluation Method The final grade will be based on the homework. オフィスアワー　Office Hour (s) The students may ask questions by e-mail. 参考書　Book (s) for Reference H. Dym and H. P. Mckean,,FOURIER SERIES AND INTEGRALS,Academic Press

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