2019 Applied Analysis I

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Kawahira Tomoki 
Course component(s)
Lecture
Day/Period(Room No.)
Wed3-4(H112)  
Group
-
Course number
MTH.C211
Credits
1
Academic year
2019
Offered quarter
3Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course is intended to introduce basic concepts in the Fourier analysis, in particular, the Fourier series.
The course is followed by Applied Analysis II.

The main objective is to understand the mathematical treatment of Fourier series, which was originally introduced by Fourier himself for the purpose of solving the heat equation.
We study fundamental properties of Fourier series and its convergence, and applications to several fields in mathematics.

Student learning outcomes

Students are expected to understand basic concepts in Fourier series, in particular, mathematical treatment of Fourier series.
We also focus on computations of Fourier series expansion of given functions and applications to differential equations.

Keywords

Series of functions, Fourier series, Bessel's inequality, Riemann-Lebesgue lemma, Dirichlet kernel

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - - -

Class flow

Before coming to class, students should read the course schedule and check what topics will be covered.
Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Fourier's idea and trigonometric series Details will be provided during each class session
Class 2 Complex-valued functions and series of functions Details will be provided during each class session
Class 3 Fourier series of a periodic function Details will be provided during each class session
Class 4 Convergence theorem Details will be provided during each class session
Class 5 Regularity of a function and the behavior of Fourier coefficients Details will be provided during each class session
Class 6 Fourier series on intervals Details will be provided during each class session
Class 7 Applications of Fourier series Details will be provided during each class session
Class 8 Evaluation of understanding Details will be provided during each class session

Textbook(s)

None required

Reference books, course materials, etc.

Elias Stein, Rami Shakarchi "Fourier analysis" Nippon Hyoron sha

Assessment criteria and methods

In-class exercises (25 %) and homeworks (75 %)

Related courses

  • ZUA.C201 : Advanced Calculus I
  • ZUA.C203 : Advanced Calculus II
  • MTH.C212 : Applied Analysis II
  • MTH.C301 : Complex Analysis I
  • MTH.C302 : Complex Analysis II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed Calculus I/Recitation and Calculus II/Recitation.

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