トップページへ

2022 Students Enrolled in or before 2015 School of Science Physics

Exercises in Applied Mathematics I

Academic unit or major
Physics
Instructor(s)
Takehito Yokoyama / Akihisa Koga
Class Format
Exercise (Face-to-face)
Media-enhanced courses
-
Day of week/Period
(Classrooms)
3-4 Mon (W241) / 3-4 Thu (W241)
Class
-
Course Code
ZUB.M210
Number of credits
020
Course offered
2022
Offered quarter
1Q
Syllabus updated
Jul 10, 2025
Language
Japanese

Syllabus

Course overview and goals

In this course, students will practice solving problems related to complex function theory and Fourier series that are widely applicable in science and engineering.

The aim of this course is to aid students’ understanding of Applied Mathematics for Physicists and Scientists I by solving exercise problems.

Course description and aims

By the end of this course, students will be able to:
1) Understand the basic concepts and properties of complex functions, such as holomorphicity.
2) Do differentiation and integration of complex functions, as well as integration
of real function by the residue theorem.
3) Solve the boundary value problem of 2-D Laplace’s equation by using conformal mapping technique.

Keywords

complex function, holomorphy, Cauchy’s internal 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

This course follows the progress of Applied Mathematics for Physicists and Scientists I, and will take place online using Zoom. Exercise problems will be assigned every class meeting and will be due the next class. Some problems are to be submitted as written assignments, based on which the grade will be decided.

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 defined for complex numbers.
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 theorem and residue theorem.
Class 8 Complex integration 1 To learn how to perform complex integration.
Class 9 Complex integration 2 To learn how to perform complex integration.
Class 10 Conformal mapping To understand the concept of conformal map and learn conformal map of elementary functions.
Class 11 Application of conformal mapping To learn how conformal mapping can be used in physics.
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 surfaces for several types of 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 Applied Mathematics for Physicists and Scientists I.

Reference books, course materials, etc.

See the page of Applied Mathematics for Physicists and Scientists I.

Evaluation methods and criteria

The course evaluation is based on in-class assignment, take-home written assignment and a term-end examination.

Related courses

  • ZUB.M201 ： Applied Mathematics for Physicists and Scientists I

Prerequisites

Enrollment in Applied Mathematics for Physicists and Scientists I is desirable.