2025 (Current Year) Faculty Courses School of Materials and Chemical Technology Common courses
Applied Mathematics for Engineers Ia
- 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.A201
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course allows students to learn the basics for mathematical analysis of phenomena captured through experiments and observation on the basis of the calculus and linear algebra completed in the first year.
This lecture covers complex function theory, which is the calculus of functions with complex numbers as their domain. First , we will discuss differentiable complex functions (holomorphic functions) and explain functions such as the exponential function, trigonometric functions, and the logarithmic function. Second, we will focus on complex line integrals, Cauchy's integral theorem, and Cauchy's integral formula. In addition, as part of complex analysis, we review contents of [Calculus I / Recitation] and [Calculus II]. This course will be succeeded by [Applied Mathematics for Engineers Ib] in the second quarter.
Complex analysis is an absolutely essential mathematical basis of science and engineering. The aim of this course 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 understand the differentiability of complex functions.
・Students are expected to be familiar with elementary functions as complex functions.
・Students are expected to be able to calculate basic complex line integrals.
・Students are expected to understand the Green's theorem and Stokes' theorem, and be able to apply them to a calculation of an integral.
Keywords
complex functions, holomorphic functions, complex line integral, Cauchy's integral theorem, Cauchy's integral formula
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 | Complex elementary functions | Students will be able to solve the exercises in Chapter 1 of the textbook (pp. 12–13). |
| Class 2 | Complex function | Students will be able to solve the exercises in Chapter 2 of the textbook (pp. 50–51). |
| Class 3 | Complex differentiation | Students will be able to solve the exercises in Chapter 2 of the textbook (pp. 50–51). |
| Class 4 | Cauchy-Riemann equations | Students will be able to solve the exercises in Chapter 2 of the textbook (pp. 50–51). |
| Class 5 | Complex line integrals | Details will be announced during each lecture. |
| Class 6 | Cauchy's integral theorem | Students will be able to solve the exercises in Chapter 3 of the textbook (pp. 74–75). |
| Class 7 | Cauchy's integral formula | Students will be able to solve the exercises in Chapter 3 of the textbook (pp. 74–75). |
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.A202 ： Applied Mathematics for Engineers Ib
- XMC.A203 ： Applied Mathematics for Engineers Ila
- XMC.A204 ： Applied Mathematics for Engineers Ilb
Prerequisites
This is the prerequisite course to take "Applied Mathematics for Engineers Ib".
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.