2022 Faculty Courses School of Science Undergraduate major in Physics
Mathematical Methods in Physics I（Exercise) B
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Takehito Yokoyama / Akihisa Koga
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon (W351) / 3-4 Thu (W351)
- Class
- B
- Course Code
- PHY.M214
- Number of credits
- 010
- Course offered
- 2022
- Offered quarter
- 1Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This exercise course covers complex analysis (the theory of functions of complex variables) and the basics of Fourier series. Both topics are important mathematical tools to describe various phenomena in the field of science and engineering. The aim of this course is to help students understand the counterpart lecture course Mathematical Methods in Physics I through solving exercises.
Course description and aims
By the end of this course, you will be able to:
1) Understand the basic concepts and properties of complex functions, such as holomorphy.
2) Perform differentiation and integration of complex functions, as well as integration
of real function by using the residue theorem.
3) Solve the boundary value problem of 2-D Laplace's equation by using conformal mapping technique.
Keywords
complex functions, holomorphy, Cauchy’s integral theorem, residue theorem, conformal map, analytic continuation, Fourier series
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The classes will be provided via Zoom. We will give you exercise questions at each class meeting. You are expected to solve all the questions by the beginning of the next class. Some questions are required to be submitted as written assignments, according to which your grade will be calculated.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Complex numbers | To understand the concept of complex numbers. |
| Class 2 | Holomorphic functions | To understand the properties of holomorphic functions. |
| Class 3 | Elementary functions | To learn about elementary functions for complex arguments. |
| Class 4 | Complex integration 1 | To learn how to perform complex integration. |
| Class 5 | Complex integration 2 | To learn how to perform complex integration. |
| Class 6 | Power series | To understand power series expansion of complex functions. |
| Class 7 | Residue theorem | To understand Cauchy's integration theorem and residue theorem. |
| Class 8 | Application of complex integration 1 | To learn how to find various real definite integrals by using complex integration. |
| Class 9 | Application of complex integration 2 | To learn how to perform integration of functions with poles on the real axis. |
| Class 10 | Conformal map | To understand the concept of conformal map and learn conformal mapping by elementary functions. |
| Class 11 | Application of conformal mapping | To learn how to use conformal mapping in solving physical problems. |
| Class 12 | Analytic continuation | To understand the concept of analytic continuation. |
| Class 13 | Riemann surface | To understand the concept of Riemann surface and learn the structures of Riemann surface for multi-valued functions. |
| Class 14 | Fourier series and Fourier transformation | To understand the properties of Fourier series and learn how to perform Fourier Transformation. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
See the page of Mathematical Methods in Physics I.
Reference books, course materials, etc.
See the page of Mathematical Methods in Physics I.
Evaluation methods and criteria
Your final grade will be calculated based on in-class presentation, submission of written assignments and quarter end examination.
Related courses
- PHY.M204 ： Mathematical Methods in Physics I(Lecture)
Prerequisites
Enrollment in PHY.M204 Mathematical Methods in Physics I(Lecture) is desirable.