2016 Applied Analysis I

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Yoneda Tsuyoshi  Onodera Michiaki  Yoneda Tsuyoshi 
Course component(s)
Lecture
Day/Period(Room No.)
Wed3-4(H112)  
Group
-
Course number
MTH.C211
Credits
1
Academic year
2016
Offered quarter
3Q
Syllabus updated
2017/1/11
Lecture notes updated
-
Language used
Japanese
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Course description and aims

The main subject of this course is basic concepts of complex analysis and Fourier series. After introducing such basic facts, we explain some typical examples of Fourier series. This course will be followed by Applied Analysis II.

Complex analysis is one of the fundamental tools in mathematics, and is applicable to a wide variety of objects. On the other hand, it is not easy to comprehend without suitable training. To that end, rigorous proofs will be given for most propositions, lemmas and theorems. Moreover, we study typical examples of complex series.

Student learning outcomes

Students are expected to study basic concepts of complex analysis. More precisely, we study Fourier series, Fourier transform, these definitions, properties and method of these calculations. These have important roles in science and technology.

Keywords

complex number, holomorphic function, Cauchy-Riemann relations, d'Alembert's ratio test, power series, trigonometric series, Fourier series expansion

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 Introductory to Complex Analysis, Four arithmetic operations, complex plane, Euler's formula Details will be provided during each class session
Class 2 Power series, trigonometric series Details will be provided during each class session
Class 3 Fourier series expansion Details will be provided during each class session
Class 4 Convergence, Gibbs phenomenon Details will be provided during each class session
Class 5 sine and cosine series expansions Details will be provided during each class session
Class 6 Fourier series expansion of complex form Details will be provided during each class session
Class 7 Fourier series on general interval Details will be provided during each class session
Class 8 Fourier series of multi-variable function, comprehension check-up Details will be provided during each class session

Textbook(s)

to be determined

Reference books, course materials, etc.

None required

Assessment criteria and methods

Students' course scores are based on final exam 50% and midterm exam 50%.

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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