Quest for Mathematics I-E2
|科目ナンバリング||U-LAS10 10023 LE55||開講年度・開講期||2021 ・ 前期|
|教員||Arseniy Aleksandrovich，Kuzmin (工学研究科 講師)|
|授業の概要・目的||In the "Quest for Mathematics", complex numbers and their applications are introduced. At first, we will follow some of the steps of their invention and learn to understand their basic properties. This numbers are very important in many different fields, such as quantum mechanics or electric engineering. In this course we explore geometrical applications of complex numbers, geometrical transformations, and complex functions.|
- To understand the origins and importance of complex numbers
- Understanding of the geometric representation of complex numbers
- Learn the complex numbers arithmetic
- Learn the relation between trigonometric and exponential functions
- Acquire the ability to use complex numbers
In this course the following topics are covered:
1. Introduction and history of complex numbers. Geometric definition of complex numbers.
2. From geometric definition to Bombelli's "wild thought". The Argand plane and modern definitions.
3. Simple complex arithmetic and De Moivre's formula.
4. Equivalence of symbolic and geometric arithmetic.
5. Euler's formula: moving particle argument.
6. Euler's formula: power series argument.
7. Applications: trigonometry.
8. Applications: geometry.
9. Applications: calculus.
10. Applications: algebra.
11. Applications: vector operations.
12. Complex numbers and Euclidean geometry: transformations.
13. Motions and reflections.
14. Similarities and complex arithmetic. Spatial complex numbers.
14 lectures in total and one feedback class.
Evaluation will be based on:
10% attendance and participation
50% final exam
|履修要件||No knowledge of complex numbers is required to join this class. All necessary concepts are introduced during the lecture.|
|授業外学習（予習・復習）等||Preparation for lectures will include revision of class materials and homework assignments. The work during the semester is most important, it helps to build up the understanding. If you have no problems with homework, there will be no problem solving the tests.|
|参考書等||Mathematics and its history, John Stillwell, (Springer), ISBN:978-1-4419-6052-8|