### 2019　Applied Mathematics for Physicists and Scientists I

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Physics
Instructor(s)
Ito Katsushi
Course component(s)
Lecture
Mode of instruction

Day/Period(Room No.)
Mon1-2(H135)  Thr1-2(H135)
Group
-
Course number
ZUB.M201
Credits
2
2019
Offered quarter
1Q
Syllabus updated
2019/4/3
Lecture notes updated
-
Language used
Japanese
Access Index ### 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.

### Keywords

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

The complex function theory is learned in the class in terms of the textbook. 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 Compute the Fourier coefficients
Class 15 Fourier transformation Perform the Fourier transformation

none specified

### Reference books, course materials, etc.

R. V. Churchill and J. W. Brown, Complex valuables and applications, Sugaku Shobo (Japanese)
Shinichi Oishi Fourier Analysis Iwanami Shoten

### Assessment criteria and methods

Students’ course scores are based on final exams.

### Related courses

• ZUB.M210 ： Exercises in Applied Mathematics I

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

No prerequisites are necessary, but enrolment in the related exercises is desirable. 