## Mathematical Description of Natural Phenomena

 シラバスID la_27014 開講年度・開講期 前期 授業形態 講義 対象回生 主として１回生 対象学生 Undergraduate 使用言語 英語 曜時限 火3 教員 CHANG，Kai-Chun(工学研究科) 授業の概要・目的 One of the major reasons of providing this course is the noticeable gap between high school mathematics and college mathematics. The gap has led to a marked decline in the students' ability not only to grasp physical phenomena observed in engineering disciplines but also to explain principles behind the phenomena - e.g. to describe and analyze natural phenomena by means of differential equations. This course aims at bridging the gap between high school mathematics and college mathematics. Through this course, students learn how the physical phenomena in engineering disciplines - e.g. vibration of a structure, wave propagation, fluid dynamics and so on - are described in differential equations. They also learn how those physical phenomena are solved by differential equations. 到達目標 ・To understand the relationship between scientific observation and mathematics. ・To understand how the physical phenomena in engineering disciplines are described in differential equations, as well as how to solve them. 授業計画と内容 * To achieve the goal, this lecture will cover the following topics. 1. Sets and Maps 2. Basics of differentiation and integration 3. e, the basis of the natural logarithm 4. Complex numbers, exponential function, logarithmic function and trigonometric function 5. Differential equation and modeling physical phenomena * The lecture is designed to cover following topics, in detail. - Basics of calculus (3 weeks) The lecture focuses on rational numbers, irrational numbers such as √2 and the basis of the natural logarithm, limit, series, complex numbers, which are fundamental to understand the calculus. - Application of linear algebra (4 weeks) The lecture discusses linear combinations of variables in multidimensional space to understand system of linear equations. The lecture also covers vector and matrix, and how to use a computer to solve higher order linear equations. - Basics of multivariate functions and multiple integration (3 weeks) The lecture provides basics on multivariable calculus, such as partial differentiation, total differentiation, directional derivatives and the concept of the multiple integration, which is the extension of single variable calculus. - Basics of differential equations (4 weeks) Many physical phenomena are expressed in the form of infinitesimal quantity, which usually directly links to differential equations. The lecture focuses on widening students understanding on the differential equation as a useful tool to express physical phenomena. It also introduces the way to solve differential equations by linear algebra and a computer. 成績評価の方法・観点及び達成度 Quizzes and exercises (50%) and final examination (50%) 履修要件 特になし 授業外学習（予習・復習）等 Students are expected to spend at least 2 hours on this course for preview and review. More than half of that time is spent preparing for class and doing assignments. 教科書 Handouts distributed in class or uploaded to PandA 参考書等 Calculus (College Review Series), E.C. Gootman, (Barron's Educational Series), Linear Algebra, G. Shilov, (Dover),