### 2016　Exercises in Applied Mathematics I

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Academic unit or major
Physics
Instructor(s)
Koga Akihisa  Toyoda Masayuki
Course component(s)
Exercise
Day/Period(Room No.)
Mon3-4(H136)  Thr3-4(H136)
Group
b
Course number
ZUB.M210
Credits
2
2016
Offered quarter
1Q
Syllabus updated
2017/1/11
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

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.

### Student learning outcomes

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 that will be developed

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

This course follows the progress of Applied Mathematics for Physicists and Scientists I. Exercise problems will be assigned every class meeting and will be due the next class. Problems are to be solved at the blackboard in the classroom, or submitted as written assignments.

### 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 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 1 To understand the properties of Fourier series and learn how to perform Fourier transformation.
Class 15 Fourier series and Fourier transformation 2 To understand the properties of Fourier series and learn how to perform Fourier transformation.

### 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.

### Assessment criteria and methods

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

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