Course title
ベクトル解析   [Vector Analysis]
Course category	technology speciality courses	Requirement		Credit	2
Department		Year	2～4	Semester	1st
Course type	1st	Course code	022353
Instructor(s)
合田 洋   [GODA Hiroshi]
Facility affiliation	Faculty of Engineering	Office	afjgxte/L1151	Email address

Course description

Vector Calculus provides indispensable tools to analyze changes of states of spaces appearing in dynamics, electromagnetism and fluid dynamics. In this course, we will learn properties of vector fields, curves and surfaces, using Calculus and Linear Algebra.

Expected Learning

The goals of this course are (1) to understand the basis of scalar and vector fields, gradient, divergence, rotation, line and surface integrations, and (2) to understand Gauss’ divergence theorem and Stokes’ theorem, and to be capable of performing practical computations by using these theorems. Corresponding criteria in the Diploma Policy: See the Curriculum maps.

Course schedule

1. Inner and cross products, and planes and space curves 2. Mappings and Derivatives of multivariable functions 3. Vector fields and derivatives of vector fields 4. Length of curves and Line integrals 5. Line integral and Green’s theorem 6. Geometry of surfaces 7. Midterm examination 8. Integral of multivariable functions and change of variables 9. Surface integral and flux integral 10. Rotation of vector fields and Stokes’ theorem I 11. Stokes’ theorem II 12. Gauss’ divergence theorem I 13. Gauss’ divergence theorem II 14. Green’s theorem 15. Term examination

Prerequisites

Knowledge of the courses of “Calculus Ⅰ/Ⅱ and Exercise” will be used in this course. In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below.

Required Text(s) and Materials

I will show in the first class.

References

I will show in the first class.

Assessment/Grading

We planned to have "50% for the mid-term exam and 50% for the final exam", but if the test cannot be performed due to the coronavirus, we will inform you of alternative methods such as reports at a later date. After all, considering the situation of Corona, I will evaluate the grades with the weekly assignment submission status and report. 2019：S13%,A37%,B26%,C21%,D3%

Message from instructor(s)

Try to solve questions that I give in the class and exercises in the textbook very much. You can ask me anything whenever you want. Enjoy mathematics and celebrate the joy of youth.

Course keywords

Scalar field, Vector field, Divergence, Gradient, Rotation, Gauss’ divergence theorem, Stokes’ theorem.

Office hours

Before or After the class. Ask me if it is inconvenient for you. I might change the date.

Remarks 1

Remarks 2

Related URL

http://web.tuat.ac.jp/~goda/lecture/lecture3.html

Lecture Language

Japanese

Language Subject

Last update

10/10/2020 9:17:17 AM