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2021　Mathematical Methods in Physics I(Exercise) A

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Academic unit or major
Undergraduate major in Physics
Instructor(s)
Yoshimura Takato  Imamura Yosuke 
Class Format
Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(H112)  Thr3-4(H112)  
Group
A
Course number
PHY.M214
Credits
1
Academic year
2021
Offered quarter
1Q
Syllabus updated
2021/4/8
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
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.

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.

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.

Assessment criteria and methods

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

Enrollment in PHY.M204 Mathematical Methods in Physics I(Lecture) is desirable.

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