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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
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- School of Science
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Mechanical Engineering
- Instructor(s)
- Suekane Tetsuya Yamamoto Takatoki
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H121)
- Group
- -
- Course number
- MEC.B212
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 1Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
A complex number is a combination of real and imaginary numbers and is an indispensable mathematical tool to understand the various phenomena in mechanical engineering. In this lecture, you study the fundamentals and application of the complex function theory, which is required by a mechanical engineer. In addition to understanding the basics of the differentiation of complex functions, you acquire mathematical skills to solve various engineering problems by studying the second-order partial differential equations and the application to the integral calculation of real functions.
The lecture is focused on the following points.
1. By learning the calculus of the complex function in comparison with that of the real function, you understand the characteristics of the complex function and acquire the calculating ability.
2. You learn that many of the important techniques in the integral evaluation of complex functions are developed from Cauchy's integral theorem and Cauchy's integral formula by learning the Cauchy-Riemann equation, Laplace equation, Cauchy's integral theorem.
3. Learn about the advanced integral methods using Taylor and Laurent series expansion and the use of residue theory.
Student learning outcomes
By the end of this course, students will be able to:
1) Have an understanding of an overview of a complex number and complex function, and gain an ability to solve the basic problem.
2) Understand the advantage of complex functions, and gain an ability to solve real problems in various engineering.
Keywords
Complex derivative, linear second-order partial differential equation, Laplace equation, complex integration, residues.
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
After devoting the classes to fundamentals, the course advances to applications. To allow students to get a good understanding of the course contents and practice application, problems related to the contents of this course are provided.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Differentiation and integral in the complex plane, Cauchy-Riemann equation | Derivation of Cauchy-Riemann equation |
| Class 2 | Basics of the second-order partial differential equation, Laplace equation | Relation to an elliptic second-order partial differential equation |
| Class 3 | Integral in the complex plane, Integral theorem of Cauchy, | Set-up of the integration path in the integration of complex functions |
| Class 4 | The integral theorem of Cauchy | Integration method using Cauchy's integral formula |
| Class 5 | Taylor and Laurent series expansion | Derivation of series expansion |
| Class 6 | Residue theorem, evaluation of the integrals using the residue theorem | Examples of integrals using the residue theorem |
| Class 7 | Application to Real function integration | Examples of the integral of a real function |
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 afterward (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
See Japanese site.
Reference books, course materials, etc.
To be announced
Assessment criteria and methods
Learning achievement is evaluated by the assignment and exercise.
Related courses
- MEC.B213 ： Partial Differential Equations
Prerequisites (i.e., required knowledge, skills, courses, etc.)
It is desirable to have knowledge in the partial differential equation.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
T. Yamamoto、yamamoto.t.ba[at]m.titech.ac.jp, ex) 3182
T. Suekane: suekane.t.aa[at]m.titech.ac.jp, ex) 5494
Other
In fiscal 2022, we give lectures on ZOOM.
