2025 (Current Year) Faculty Courses School of Materials and Chemical Technology Common courses
Applied Mathematics for Engineers Ib
- Academic unit or major
- Common courses
- Instructor(s)
- Masahiko Shimojo
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue
- Class
- -
- Course Code
- XMC.A202
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers the contents following Applied Mathematics for Engineers Ia.
Based on [Applied Mathematics for Engineers Ia] in the first quarter, this course focuses on basic part of complex analysis. After reviewing complex line integrals, we explain the Taylor expansion of holomorphic function and the Laurent expansion of meromorphic functions after classifying isolated singularities of complex functions. Finally, we explain the residue theorem and its application to the calculation of definite integrals.
Complex analysis is an absolutely essential mathematical basis of science and engineering. The aim of this lecture is to explain the basic theory and practical way to use of complex analysis by an efficient way.
Course description and aims
・Students are expected to be able to calculate the Taylor expansion of basic complex functions.
・Students are expected to be familiar with the classification of isolated singularities of complex functions.
・Students are expected to be able to calculate the Laurent expansion of basic complex functions.
・Students are expected to be able to apply the residue theorem to the calculation of definite integrals.
Keywords
Cauchy's integral theorem, isolated singularities, the Laurent expansion, meromorphic functions, the residue theorem
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course mixed with recitation.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Fundamental theorem of algebra | Students will be able to solve the exercises in Chapter 4 of the textbook (pp. 100–101). |
| Class 2 | Taylor expansion of a holomorphic function | Students will be able to solve the exercises in Chapter 4 of the textbook (pp. 100–101). |
| Class 3 | Uniqueness theorem for holomorphic functions | Students will be able to solve the exercises in Chapter 4 of the textbook (pp. 100–101). |
| Class 4 | The Laurent expansion of meromorphic functions | Students will be able to solve the exercises in Chapter 5 of the textbook (pp. 128–129). |
| Class 5 | Isolated singularity, residue, and the residue theorem | Students will be able to solve the exercises in Chapter 5 of the textbook (pp. 128–129). |
| Class 6 | Evaluation of definite integrals using the residue theorem | Students will be able to solve the exercises in Chapter 5 of the textbook (pp. 128–129). |
| Class 7 | Evaluation of definite integrals using the residue theorem | Students will be able to solve the exercises in Chapter 5 of the textbook (pp. 128–129). |
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)
Hara and Matsunaga, Introduction to Complex Analysis, 2nd ed., Kyoritu Pub. (In Japanese)
Reference books, course materials, etc.
None in particular
Evaluation methods and criteria
Grades will be based on 20% for class participation, quizzes, and reports, and 80% for the final exam. The minimum passing grade is 60%.
Related courses
- XMC.A201 ： Applied Mathematics for Engineers Ia
- XMC.A203 ： Applied Mathematics for Engineers Ila
- XMC.A204 ： Applied Mathematics for Engineers Ilb
Prerequisites
The prerequisite to take this course is that you have acquired the credits of "Applied Mathematics for Engineers Ia".
Without having acquired the credits of the above course, the credits of this course will not be counted as the necessary number of credits for graduation.
Students are expected to have completed [Calculus I / Recitation], [Calculus II]and [Calculus Recitation II] .
In particular, students are expected to understand partial differentiation, definite integral and multiple integral clearly.