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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
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School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Takiguchi Takashi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(W521)
- Group
- -
- Course number
- MTH.U212
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 2Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Based on [Applied Mathematics for Engineers Ia] in the first quarter, this course focuses on basic part of complex analysis. First, we explain Cauchy's integral theorem and Cauchy's integral formula after reviewing complex line integrals. Then, we explain the Laurent expansion of meromorphic functions after classifying isolated singularities of complex functions. Finally, we explain the residue theorem and its application to the calculation of definite integrals.
Complex analysis is an absolutely essential mathematical basis of science and engineering. The aim of this lecture is to explain the basic theory and practical way to use of complex analysis by an efficient way.
Student learning outcomes
・Students are expected to understand Cauchy's integral theorem.
・Students are expected to be familiar with the classificationof isolated singularities of complex functions.
・Students are expected to be able to calculate the Laurent expansion of basic complex functions.
・Students are expected to be able to apply the residue theorem to the calculation of definit integrals.
Keywords
Cauchy's integral theorem, isolated singularities, the Laurent expansion, meromorphic functions, the residue theorem
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course mixed with recitation.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Cauchy's integral theorem | Details will be announced during each lecture |
| Class 2 | Cauchy's integral formula | |
| Class 3 | power series expansions and its applications | |
| Class 4 | isolated singularities | |
| Class 5 | the Laurent expansion | |
| Class 6 | meromorphic functions and the residue theorem | |
| Class 7 | evaluation of integrals using the residue theorem | |
| Class 8 | evaluation of progress |
Textbook(s)
H. Shiga, Theory of complex functions to learn in 15 weeks (Japanese), Sugakushobo, 2008
Reference books, course materials, etc.
None in particular
Assessment criteria and methods
Based on overall evaluation of the results for quizzes, report and final examination. Details will be announced during a lecture.
Related courses
- MTH.U211 ： Applied Mathematics for Engineers Ia
- MTH.U213 ： Applied Mathematics for Engineers Iia
- MTH.U214 ： Applied Mathematics for Engineers Iib
Prerequisites (i.e., required knowledge, skills, courses, etc.)
The prerequisite to take this course is that you have acquired the credits of "Applied Mathematics for Engineers Ia".
Without having acquired the credits of the above course, the credits of this course will not be counted as the necessary number of credits for graduation.
Students are expected to have completed [Calculus I / Recitation], [Calculus II]and [Calculus Recitation II] .
In particular, students are expected to understand partial differentiation, definite integral and multiple integral clearly.
