2021 Mathematical Methods in Physics I(Lecture)

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Academic unit or major
Undergraduate major in Physics
Imamura Yosuke 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Mon1-2(W621)  Thr1-2(H115)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course focuses on the complex function theory and Fourier series widely applicable to the field of science and engineering.

This course has two aims. The first is to understand the derivative and integral of the complex functions. The other is to understand the basic of the Fourier analysis.

Student learning outcomes

By the end of this course, students will be able to:
1) explain the basic concept of the complex function theory.
2) understand the derivative and integral of the complex functions and calculate the integral of the real function by means of the residue theorem.
3) explain the conformal map for the holomorphic function and solve two-dimensional Laplace equations.
4) explain the concept of the analytic continuation.
5) explain the concept of the Fourier series for the periodic functions and obtain the series coefficients.


complex function, holomorphy, Cauchy's integral theorem, residue theorem, conformal map, analytic continuation, Fourier series

Competencies that will be developed

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

Class flow

To prepare for class, students should read the course schedule section 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 complex variables Compute the operations of complex variables.
Class 2 holomorphic function Understand the holomorphic functions
Class 3 elementary functions Understand the elementary functions.
Class 4 complex integral 1 Understand the contour integral in the Gauss plane
Class 5 complex integral 2 Understand the Cauchy's theorem
Class 6 power series Compute the series coefficients.
Class 7 residue theorem Understand the residue theorem
Class 8 application of complex integral 1 Compute the integral for the real function by means of the complex integral.
Class 9 application of complex integral 2 Compute the integral for the real function by means of the complex integral.
Class 10 Conformal map Understand the conformal map
Class 11 application of conformal map Solve the two-dimensional Laplace equations
Class 12 analytic continuation Understand the identity theorem and analytic continuation.
Class 13 Riemann surface Understand the Riemann surface
Class 14 Fourier series and Fourier transformation Compute the Fourier coefficients and Fourier transformations

Out-of-Class Study Time (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.


物理数学I (古賀昌久著) 丸善出版

Reference books, course materials, etc.

none specified

Assessment criteria and methods

Students’ course scores are based on final exams.

Related courses

  • PHY.M211 : Mathematical Methods in Physics II
  • PHY.M330 : Mathematical Methods in Physics III

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

No prerequisites are necessary

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